[ { "id": "cycle-easy-graph216", "image": "data/cycle/graph_visual/easy/graph216.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,2) (3,6) (1,0) (5,4) (3,1) (0,8) (6,7) (1,5) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph78", "image": "data/cycle/graph_visual/easy/graph78.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,0) (2,5) (2,1) (4,6) (0,6) (7,4) (1,4) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph74", "image": "data/cycle/graph_visual/easy/graph74.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,3) (7,1) (6,4) (4,8) (2,3) (1,0) (2,4) (1,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph70", "image": "data/cycle/graph_visual/easy/graph70.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,1) (0,7) (8,6) (6,2) (0,4) (8,0) (3,5) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph210", "image": "data/cycle/graph_visual/easy/graph210.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,5) (4,0) (3,1) (8,2) (2,0) (4,3) (0,3) (7,4) (7,2) (0,1) (6,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph116", "image": "data/cycle/graph_visual/easy/graph116.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,0) (8,9) (5,1) (8,4) (2,3) (9,6) (6,2) (5,3) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph31", "image": "data/cycle/graph_visual/easy/graph31.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,5) (4,1) (6,3) (0,4) (3,0) (7,5) (7,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph255", "image": "data/cycle/graph_visual/easy/graph255.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,9) (1,2) (1,0) (6,7) (4,7) (5,8) (0,3) (3,4) (0,5) (2,7) (4,0) (2,0) (5,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph29", "image": "data/cycle/graph_visual/easy/graph29.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,2) (6,0) (7,4) (5,3) (7,0) (1,6) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph163", "image": "data/cycle/graph_visual/easy/graph163.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,2) (0,5) (6,0) (0,2) (6,1) (4,0) (0,3) (0,1) (2,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph245", "image": "data/cycle/graph_visual/easy/graph245.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,1) (9,8) (0,3) (6,4) (0,4) (8,4) (0,5) (4,7) (0,2) (3,5) (0,1) (2,6) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph233", "image": "data/cycle/graph_visual/easy/graph233.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,5) (7,3) (4,5) (6,3) (4,2) (1,8) (1,0) (1,5) (7,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph209", "image": "data/cycle/graph_visual/easy/graph209.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,3) (2,0) (6,2) (0,1) (0,3) (3,5) (2,8) (5,0) (2,3) (4,0) (2,4) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph279", "image": "data/cycle/graph_visual/easy/graph279.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,4) (2,6) (5,3) (0,8) (0,1) (8,7) (0,9) (9,5) (6,0) (1,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph26", "image": "data/cycle/graph_visual/easy/graph26.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,6) (4,3) (2,4) (1,6) (5,3) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph17", "image": "data/cycle/graph_visual/easy/graph17.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,1) (1,4) (3,2) (4,0) (5,6) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph284", "image": "data/cycle/graph_visual/easy/graph284.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,4) (7,6) (7,8) (3,0) (0,4) (4,9) (2,6) (8,5) (1,6) (1,0) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph11", "image": "data/cycle/graph_visual/easy/graph11.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (3,5) (1,0) (2,5) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph57", "image": "data/cycle/graph_visual/easy/graph57.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,5) (3,5) (0,7) (6,8) (3,4) (1,6) (0,8) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph278", "image": "data/cycle/graph_visual/easy/graph278.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,3) (0,1) (9,5) (2,5) (0,7) (3,0) (1,8) (2,0) (6,0) (5,6) (9,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph247", "image": "data/cycle/graph_visual/easy/graph247.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,4) (2,0) (7,4) (1,2) (0,3) (5,0) (0,1) (2,7) (2,9) (5,8) (1,5) (7,6) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph219", "image": "data/cycle/graph_visual/easy/graph219.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,0) (4,8) (1,0) (3,2) (5,0) (5,3) (1,2) (6,4) (2,4) (0,3) (0,4) (7,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph201", "image": "data/cycle/graph_visual/easy/graph201.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,1) (2,6) (2,0) (5,3) (1,4) (4,7) (3,7) (6,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph203", "image": "data/cycle/graph_visual/easy/graph203.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,4) (0,6) (0,1) (8,5) (2,0) (2,8) (5,0) (2,3) (7,1) (0,4) (4,3) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph179", "image": "data/cycle/graph_visual/easy/graph179.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,6) (4,5) (0,3) (3,7) (0,1) (0,4) (5,2) (5,0) (0,2) (1,7) (2,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph199", "image": "data/cycle/graph_visual/easy/graph199.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (5,1) (1,6) (7,0) (3,5) (0,1) (0,5) (2,1) (0,2) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph101", "image": "data/cycle/graph_visual/easy/graph101.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,8) (5,3) (7,2) (7,6) (7,0) (8,6) (8,4) (9,0) (5,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph110", "image": "data/cycle/graph_visual/easy/graph110.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,1) (7,0) (2,7) (7,4) (3,4) (7,1) (8,6) (6,1) (5,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph10", "image": "data/cycle/graph_visual/easy/graph10.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,3) (0,2) (1,2) (4,5) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph166", "image": "data/cycle/graph_visual/easy/graph166.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,0) (5,4) (4,3) (6,3) (6,0) (1,0) (5,0) (2,1) (3,0) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph92", "image": "data/cycle/graph_visual/easy/graph92.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,7) (3,1) (8,5) (4,3) (2,7) (2,8) (6,8) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph269", "image": "data/cycle/graph_visual/easy/graph269.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,0) (1,6) (6,5) (4,9) (0,4) (0,8) (8,2) (4,3) (7,2) (3,0) (0,1) (5,4) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph125", "image": "data/cycle/graph_visual/easy/graph125.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,4) (3,6) (4,0) (7,9) (2,5) (7,4) (3,1) (5,3) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph190", "image": "data/cycle/graph_visual/easy/graph190.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,4) (0,3) (1,2) (7,4) (2,6) (0,6) (4,0) (6,3) (2,0) (0,1) (5,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph167", "image": "data/cycle/graph_visual/easy/graph167.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (4,0) (5,0) (6,1) (2,3) (0,6) (1,0) (6,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph276", "image": "data/cycle/graph_visual/easy/graph276.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,9) (0,2) (1,5) (9,1) (0,8) (1,0) (6,7) (8,6) (3,4) (2,7) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph270", "image": "data/cycle/graph_visual/easy/graph270.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,2) (1,2) (7,2) (1,0) (7,9) (0,3) (3,2) (8,4) (2,0) (5,9) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph257", "image": "data/cycle/graph_visual/easy/graph257.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,6) (9,2) (4,8) (4,0) (0,3) (7,5) (1,0) (4,1) (0,2) (0,5) (7,0) (8,7) (5,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph185", "image": "data/cycle/graph_visual/easy/graph185.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,0) (5,4) (5,0) (1,0) (2,7) (3,7) (0,3) (3,6) (1,7) (4,6) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph176", "image": "data/cycle/graph_visual/easy/graph176.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (3,6) (4,6) (1,0) (0,3) (2,0) (4,1) (6,5) (6,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph38", "image": "data/cycle/graph_visual/easy/graph38.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,4) (6,7) (7,3) (2,5) (4,3) (1,4) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph162", "image": "data/cycle/graph_visual/easy/graph162.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,4) (3,1) (1,0) (6,5) (0,2) (4,5) (5,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph281", "image": "data/cycle/graph_visual/easy/graph281.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,7) (1,9) (6,0) (0,1) (9,8) (7,5) (2,9) (1,3) (4,8) (2,0) (0,3) (5,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph265", "image": "data/cycle/graph_visual/easy/graph265.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (0,4) (1,8) (0,6) (3,4) (2,1) (9,8) (1,5) (7,3) (3,2) (0,3) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph129", "image": "data/cycle/graph_visual/easy/graph129.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,9) (9,6) (5,3) (3,7) (3,2) (8,0) (4,3) (0,3) (6,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph37", "image": "data/cycle/graph_visual/easy/graph37.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,4) (2,3) (4,1) (5,6) (7,3) (1,5) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph173", "image": "data/cycle/graph_visual/easy/graph173.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,5) (4,3) (0,1) (0,3) (2,4) (1,6) (1,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph241", "image": "data/cycle/graph_visual/easy/graph241.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,2) (3,6) (3,7) (4,3) (0,1) (6,1) (2,3) (6,0) (2,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph99", "image": "data/cycle/graph_visual/easy/graph99.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,7) (6,7) (1,5) (8,6) (1,9) (4,9) (8,0) (3,0) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph254", "image": "data/cycle/graph_visual/easy/graph254.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,8) (0,4) (3,4) (5,9) (1,0) (0,6) (7,9) (8,1) (2,4) (0,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph242", "image": "data/cycle/graph_visual/easy/graph242.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,4) (2,0) (5,0) (3,0) (8,6) (0,1) (7,3) (6,4) (3,1) (3,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph54", "image": "data/cycle/graph_visual/easy/graph54.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,8) (2,7) (6,1) (0,7) (5,1) (3,5) (4,1) (2,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph253", "image": "data/cycle/graph_visual/easy/graph253.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,6) (0,5) (0,4) (1,4) (2,0) (4,8) (7,8) (3,0) (0,1) (0,6) (7,5) (9,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph285", "image": "data/cycle/graph_visual/easy/graph285.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,1) (7,3) (2,9) (1,3) (6,2) (8,1) (2,0) (0,3) (4,5) (2,5) (0,4) (4,7) (9,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph184", "image": "data/cycle/graph_visual/easy/graph184.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,1) (1,0) (5,0) (1,5) (0,2) (5,7) (5,2) (3,6) (6,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph197", "image": "data/cycle/graph_visual/easy/graph197.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,4) (7,3) (7,6) (1,0) (0,2) (3,0) (1,2) (3,5) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph165", "image": "data/cycle/graph_visual/easy/graph165.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (4,6) (5,3) (2,1) (0,1) (3,4) (0,2) (0,4) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph189", "image": "data/cycle/graph_visual/easy/graph189.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (0,6) (1,3) (5,4) (1,0) (0,4) (2,0) (7,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph264", "image": "data/cycle/graph_visual/easy/graph264.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,4) (3,0) (1,0) (1,7) (4,7) (9,3) (0,2) (5,0) (5,6) (4,0) (9,5) (2,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph115", "image": "data/cycle/graph_visual/easy/graph115.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,3) (0,8) (9,7) (2,0) (7,2) (3,6) (6,8) (9,5) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph218", "image": "data/cycle/graph_visual/easy/graph218.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,0) (3,8) (7,4) (5,7) (5,6) (0,1) (1,4) (0,8) (0,3) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph46", "image": "data/cycle/graph_visual/easy/graph46.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (6,4) (3,4) (7,6) (5,3) (1,2) (0,3) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph14", "image": "data/cycle/graph_visual/easy/graph14.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (4,2) (1,0) (2,6) (5,3) (2,0) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph144", "image": "data/cycle/graph_visual/easy/graph144.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,1) (9,7) (7,5) (3,7) (9,6) (2,0) (8,0) (0,3) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph194", "image": "data/cycle/graph_visual/easy/graph194.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,7) (2,4) (4,3) (6,2) (5,0) (4,0) (2,0) (1,0) (1,7) (3,0) (5,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph205", "image": "data/cycle/graph_visual/easy/graph205.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,7) (5,7) (8,2) (7,6) (7,1) (0,1) (6,8) (2,0) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph294", "image": "data/cycle/graph_visual/easy/graph294.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,0) (3,6) (3,1) (1,0) (3,7) (2,0) (9,8) (6,9) (4,2) (3,0) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph230", "image": "data/cycle/graph_visual/easy/graph230.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,4) (1,0) (7,1) (7,5) (0,2) (2,5) (0,8) (6,2) (4,3) (6,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph169", "image": "data/cycle/graph_visual/easy/graph169.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,0) (0,1) (0,6) (2,6) (4,0) (1,2) (0,3) (1,6) (2,3) (5,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph64", "image": "data/cycle/graph_visual/easy/graph64.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,7) (4,8) (4,3) (2,1) (3,0) (7,5) (5,6) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph262", "image": "data/cycle/graph_visual/easy/graph262.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,4) (2,0) (9,0) (2,4) (6,7) (8,6) (1,0) (3,1) (0,3) (5,4) (9,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph109", "image": "data/cycle/graph_visual/easy/graph109.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,0) (1,3) (3,6) (9,7) (2,7) (4,3) (0,8) (8,6) (9,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph187", "image": "data/cycle/graph_visual/easy/graph187.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,6) (6,3) (0,1) (2,7) (1,7) (2,0) (5,0) (4,5) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph18", "image": "data/cycle/graph_visual/easy/graph18.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,3) (0,2) (6,0) (1,0) (4,3) (3,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph42", "image": "data/cycle/graph_visual/easy/graph42.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,1) (2,4) (4,6) (4,0) (0,1) (7,6) (5,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph69", "image": "data/cycle/graph_visual/easy/graph69.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,4) (4,2) (5,7) (5,2) (8,6) (3,2) (0,8) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph20", "image": "data/cycle/graph_visual/easy/graph20.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (3,0) (3,6) (6,4) (5,6) (6,1) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph27", "image": "data/cycle/graph_visual/easy/graph27.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,6) (5,6) (3,5) (0,4) (1,2) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph15", "image": "data/cycle/graph_visual/easy/graph15.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,6) (5,0) (4,0) (3,2) (1,6) (6,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph160", "image": "data/cycle/graph_visual/easy/graph160.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (5,0) (4,5) (2,5) (1,3) (2,0) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph127", "image": "data/cycle/graph_visual/easy/graph127.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,9) (1,0) (3,7) (1,4) (4,8) (6,4) (2,6) (7,4) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph122", "image": "data/cycle/graph_visual/easy/graph122.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,4) (7,6) (8,3) (5,9) (2,8) (7,9) (6,3) (7,0) (9,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph232", "image": "data/cycle/graph_visual/easy/graph232.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,5) (1,0) (0,8) (3,4) (0,2) (0,3) (8,6) (0,7) (6,1) (2,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph182", "image": "data/cycle/graph_visual/easy/graph182.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,5) (6,2) (5,0) (7,1) (7,0) (4,0) (0,3) (7,3) (6,5) (0,2) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph87", "image": "data/cycle/graph_visual/easy/graph87.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,5) (2,3) (2,6) (0,4) (8,2) (3,7) (1,4) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph177", "image": "data/cycle/graph_visual/easy/graph177.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,3) (0,4) (2,0) (1,0) (2,1) (1,4) (5,0) (3,5) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph111", "image": "data/cycle/graph_visual/easy/graph111.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,8) (5,7) (5,8) (5,4) (8,2) (6,1) (4,0) (3,6) (9,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph240", "image": "data/cycle/graph_visual/easy/graph240.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,2) (3,7) (3,0) (1,0) (8,1) (2,0) (6,2) (2,3) (6,0) (2,4) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph102", "image": "data/cycle/graph_visual/easy/graph102.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,9) (7,9) (4,1) (0,6) (2,8) (5,8) (9,1) (4,8) (8,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph244", "image": "data/cycle/graph_visual/easy/graph244.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,6) (1,0) (6,3) (5,7) (0,2) (0,4) (7,8) (0,8) (7,4) (9,5) (0,3) (7,1) (2,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph208", "image": "data/cycle/graph_visual/easy/graph208.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,7) (4,0) (5,7) (2,8) (7,3) (0,3) (8,6) (0,1) (7,4) (0,2) (8,1) (2,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph53", "image": "data/cycle/graph_visual/easy/graph53.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,8) (4,7) (0,1) (1,4) (3,5) (3,4) (2,8) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph2", "image": "data/cycle/graph_visual/easy/graph2.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (1,0) (1,4) (3,1) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph32", "image": "data/cycle/graph_visual/easy/graph32.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,1) (0,7) (6,4) (3,1) (6,0) (3,2) (5,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph72", "image": "data/cycle/graph_visual/easy/graph72.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,3) (4,3) (5,7) (2,5) (0,8) (7,1) (1,0) (2,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph80", "image": "data/cycle/graph_visual/easy/graph80.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,8) (2,5) (0,8) (2,4) (3,2) (6,4) (7,5) (5,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph55", "image": "data/cycle/graph_visual/easy/graph55.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,0) (3,7) (1,4) (4,2) (5,2) (8,7) (6,7) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph267", "image": "data/cycle/graph_visual/easy/graph267.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (8,5) (9,8) (5,6) (2,4) (2,1) (0,1) (3,0) (5,7) (1,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph9", "image": "data/cycle/graph_visual/easy/graph9.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (1,2) (4,2) (0,4) (3,5) (2,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph287", "image": "data/cycle/graph_visual/easy/graph287.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,7) (5,4) (0,4) (9,0) (6,4) (6,8) (0,1) (1,3) (5,0) (9,8) (4,2) (0,3) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph89", "image": "data/cycle/graph_visual/easy/graph89.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,6) (6,8) (3,4) (7,0) (0,3) (8,4) (7,2) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph22", "image": "data/cycle/graph_visual/easy/graph22.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,5) (2,0) (1,5) (0,3) (4,6) (1,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph45", "image": "data/cycle/graph_visual/easy/graph45.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,4) (0,1) (2,6) (0,5) (7,6) (7,3) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph295", "image": "data/cycle/graph_visual/easy/graph295.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,7) (5,1) (0,9) (4,0) (1,3) (0,1) (4,5) (5,0) (6,3) (5,2) (8,0) (0,3) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph195", "image": "data/cycle/graph_visual/easy/graph195.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (6,2) (6,0) (7,0) (5,3) (0,5) (0,3) (1,2) (0,2) (3,1) (4,0) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph75", "image": "data/cycle/graph_visual/easy/graph75.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,4) (0,1) (2,4) (8,7) (3,1) (6,5) (4,6) (8,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph73", "image": "data/cycle/graph_visual/easy/graph73.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,5) (5,2) (7,1) (0,8) (6,0) (6,2) (8,4) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph6", "image": "data/cycle/graph_visual/easy/graph6.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (1,3) (5,3) (5,0) (5,2) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph225", "image": "data/cycle/graph_visual/easy/graph225.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,7) (0,2) (3,5) (3,7) (1,0) (6,3) (5,4) (3,0) (7,1) (1,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph130", "image": "data/cycle/graph_visual/easy/graph130.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,4) (0,1) (8,9) (9,0) (4,6) (3,1) (6,8) (7,6) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph161", "image": "data/cycle/graph_visual/easy/graph161.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (1,0) (3,0) (3,4) (4,1) (2,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph273", "image": "data/cycle/graph_visual/easy/graph273.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,0) (5,9) (2,0) (0,1) (3,0) (8,2) (4,7) (3,9) (6,5) (1,7) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph142", "image": "data/cycle/graph_visual/easy/graph142.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,0) (4,1) (3,6) (9,7) (5,2) (1,3) (4,7) (8,3) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph97", "image": "data/cycle/graph_visual/easy/graph97.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,3) (0,1) (1,8) (4,8) (4,6) (5,0) (5,7) (2,0) (9,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph271", "image": "data/cycle/graph_visual/easy/graph271.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (7,3) (3,5) (0,1) (0,3) (0,9) (4,8) (8,2) (7,1) (6,2) (5,0) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph164", "image": "data/cycle/graph_visual/easy/graph164.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,2) (0,1) (4,0) (6,1) (4,3) (4,2) (1,2) (3,0) (2,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph272", "image": "data/cycle/graph_visual/easy/graph272.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,8) (0,4) (2,0) (0,3) (4,6) (6,7) (8,5) (4,9) (1,0) (6,2) (1,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph251", "image": "data/cycle/graph_visual/easy/graph251.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,2) (7,5) (2,1) (0,3) (3,8) (1,0) (2,9) (2,0) (6,5) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph171", "image": "data/cycle/graph_visual/easy/graph171.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,0) (1,2) (6,2) (1,5) (2,0) (0,3) (0,1) (5,0) (4,0) (5,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph153", "image": "data/cycle/graph_visual/easy/graph153.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (3,2) (3,1) (1,0) (3,0) (0,2) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph157", "image": "data/cycle/graph_visual/easy/graph157.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (1,5) (4,0) (5,0) (2,0) (1,4) (0,1) (2,4) (4,3) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph48", "image": "data/cycle/graph_visual/easy/graph48.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,1) (1,4) (5,6) (2,0) (7,5) (2,3) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph3", "image": "data/cycle/graph_visual/easy/graph3.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (4,3) (2,1) (1,0) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph180", "image": "data/cycle/graph_visual/easy/graph180.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,7) (0,1) (0,3) (3,6) (4,0) (6,7) (4,3) (6,0) (3,1) (5,0) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph68", "image": "data/cycle/graph_visual/easy/graph68.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,2) (3,8) (6,5) (7,5) (3,0) (7,8) (0,1) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph193", "image": "data/cycle/graph_visual/easy/graph193.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,4) (2,6) (0,3) (2,0) (1,3) (2,5) (0,1) (5,7) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph288", "image": "data/cycle/graph_visual/easy/graph288.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,6) (4,7) (5,8) (9,7) (5,3) (1,0) (2,0) (0,4) (1,4) (0,5) (8,0) (7,3) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph214", "image": "data/cycle/graph_visual/easy/graph214.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,5) (1,5) (3,2) (2,8) (7,8) (8,0) (0,2) (0,1) (6,4) (8,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph33", "image": "data/cycle/graph_visual/easy/graph33.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,4) (3,0) (1,2) (7,5) (1,5) (5,6) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph124", "image": "data/cycle/graph_visual/easy/graph124.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,3) (1,2) (6,8) (8,7) (2,9) (3,4) (4,7) (0,9) (8,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph105", "image": "data/cycle/graph_visual/easy/graph105.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,4) (7,3) (7,8) (1,2) (1,7) (7,9) (3,6) (5,3) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph47", "image": "data/cycle/graph_visual/easy/graph47.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (6,3) (0,6) (3,7) (6,1) (2,3) (2,5) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph24", "image": "data/cycle/graph_visual/easy/graph24.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,5) (4,2) (4,0) (2,1) (6,2) (3,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph152", "image": "data/cycle/graph_visual/easy/graph152.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (1,0) (4,0) (3,0) (2,4) (0,2) (2,1) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph7", "image": "data/cycle/graph_visual/easy/graph7.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,3) (0,5) (0,2) (1,5) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph61", "image": "data/cycle/graph_visual/easy/graph61.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,1) (8,0) (7,4) (5,7) (5,6) (8,3) (0,6) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph200", "image": "data/cycle/graph_visual/easy/graph200.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (6,0) (2,7) (7,5) (0,2) (0,1) (7,1) (3,5) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph23", "image": "data/cycle/graph_visual/easy/graph23.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (3,1) (5,2) (3,5) (6,4) (5,6) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph19", "image": "data/cycle/graph_visual/easy/graph19.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,1) (5,1) (2,5) (0,3) (2,6) (1,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph192", "image": "data/cycle/graph_visual/easy/graph192.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,7) (5,4) (0,2) (3,2) (4,3) (1,4) (6,4) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph172", "image": "data/cycle/graph_visual/easy/graph172.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,6) (4,2) (2,0) (1,5) (1,0) (1,3) (4,0) (1,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph84", "image": "data/cycle/graph_visual/easy/graph84.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,1) (4,8) (3,8) (4,5) (7,6) (1,6) (0,5) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph94", "image": "data/cycle/graph_visual/easy/graph94.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,2) (5,4) (3,7) (0,5) (8,4) (5,3) (2,8) (1,7) (9,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph131", "image": "data/cycle/graph_visual/easy/graph131.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,8) (7,5) (7,3) (5,6) (7,1) (8,9) (6,2) (0,2) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph229", "image": "data/cycle/graph_visual/easy/graph229.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,7) (1,0) (7,1) (5,2) (7,8) (2,3) (5,4) (6,3) (0,3) (0,2) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph41", "image": "data/cycle/graph_visual/easy/graph41.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,2) (6,5) (2,4) (7,3) (0,1) (1,5) (1,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph50", "image": "data/cycle/graph_visual/easy/graph50.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,5) (6,1) (7,0) (4,3) (7,5) (3,2) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph280", "image": "data/cycle/graph_visual/easy/graph280.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,4) (5,4) (0,4) (1,0) (3,0) (1,9) (7,2) (1,6) (3,4) (7,0) (1,7) (6,8) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph226", "image": "data/cycle/graph_visual/easy/graph226.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (1,2) (4,3) (8,7) (2,0) (1,7) (6,7) (5,7) (3,0) (1,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph96", "image": "data/cycle/graph_visual/easy/graph96.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,3) (8,4) (0,1) (6,3) (4,7) (1,9) (1,4) (2,9) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph183", "image": "data/cycle/graph_visual/easy/graph183.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,1) (0,1) (6,3) (0,3) (2,0) (7,1) (5,4) (5,3) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph215", "image": "data/cycle/graph_visual/easy/graph215.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,4) (2,8) (7,6) (2,0) (7,0) (3,0) (8,4) (1,8) (2,5) (0,1) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph268", "image": "data/cycle/graph_visual/easy/graph268.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,5) (7,8) (1,0) (6,1) (9,4) (2,0) (0,4) (6,2) (5,8) (3,0) (7,6) (6,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph85", "image": "data/cycle/graph_visual/easy/graph85.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,5) (2,6) (3,6) (7,3) (4,7) (0,2) (8,7) (1,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph121", "image": "data/cycle/graph_visual/easy/graph121.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,6) (3,4) (0,1) (8,4) (1,4) (2,9) (8,5) (4,7) (9,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph88", "image": "data/cycle/graph_visual/easy/graph88.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,3) (8,2) (7,3) (6,3) (2,3) (1,6) (0,6) (2,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph228", "image": "data/cycle/graph_visual/easy/graph228.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,7) (2,3) (1,3) (1,0) (6,8) (3,0) (3,4) (0,2) (0,5) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph82", "image": "data/cycle/graph_visual/easy/graph82.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,5) (6,3) (3,1) (2,4) (8,4) (7,1) (1,4) (7,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph107", "image": "data/cycle/graph_visual/easy/graph107.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,5) (8,0) (6,5) (7,3) (1,8) (2,0) (9,8) (1,4) (6,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph40", "image": "data/cycle/graph_visual/easy/graph40.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,1) (6,2) (2,0) (5,2) (3,4) (5,7) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph35", "image": "data/cycle/graph_visual/easy/graph35.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (5,7) (4,3) (0,2) (7,1) (4,1) (7,6) (2,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph224", "image": "data/cycle/graph_visual/easy/graph224.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (6,2) (7,8) (2,1) (4,7) (0,3) (6,7) (7,5) (0,4) (2,3) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph222", "image": "data/cycle/graph_visual/easy/graph222.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,0) (3,8) (2,0) (7,4) (0,1) (1,4) (5,7) (8,0) (5,6) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph13", "image": "data/cycle/graph_visual/easy/graph13.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,6) (3,2) (6,1) (3,5) (0,3) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph59", "image": "data/cycle/graph_visual/easy/graph59.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,3) (3,7) (5,2) (8,2) (3,2) (6,3) (1,6) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph283", "image": "data/cycle/graph_visual/easy/graph283.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,5) (7,8) (4,0) (0,9) (0,6) (1,0) (3,5) (1,3) (0,3) (2,6) (2,0) (8,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph148", "image": "data/cycle/graph_visual/easy/graph148.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,7) (3,7) (1,4) (8,9) (0,1) (6,2) (4,6) (4,8) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph104", "image": "data/cycle/graph_visual/easy/graph104.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,5) (3,4) (6,7) (7,3) (0,3) (0,8) (9,6) (2,3) (1,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph39", "image": "data/cycle/graph_visual/easy/graph39.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,2) (7,3) (4,2) (0,4) (1,4) (5,3) (6,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph62", "image": "data/cycle/graph_visual/easy/graph62.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,4) (3,8) (4,1) (5,2) (8,0) (6,0) (4,6) (2,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph86", "image": "data/cycle/graph_visual/easy/graph86.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,7) (1,3) (2,8) (2,0) (2,7) (6,8) (3,4) (5,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph223", "image": "data/cycle/graph_visual/easy/graph223.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,5) (4,8) (2,0) (1,0) (2,8) (6,3) (1,3) (7,4) (7,6) (0,3) (7,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph275", "image": "data/cycle/graph_visual/easy/graph275.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,0) (3,1) (9,2) (5,0) (0,6) (8,9) (8,4) (5,7) (9,1) (0,1) (8,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph95", "image": "data/cycle/graph_visual/easy/graph95.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,5) (1,3) (4,7) (6,9) (0,4) (8,2) (9,4) (8,1) (7,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph168", "image": "data/cycle/graph_visual/easy/graph168.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,3) (4,5) (3,6) (1,5) (5,0) (0,2) (3,1) (1,2) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph119", "image": "data/cycle/graph_visual/easy/graph119.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,6) (4,8) (9,2) (8,7) (3,0) (5,7) (0,2) (5,6) (1,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph21", "image": "data/cycle/graph_visual/easy/graph21.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,1) (3,5) (2,6) (3,4) (2,0) (1,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph120", "image": "data/cycle/graph_visual/easy/graph120.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,2) (5,2) (3,9) (2,8) (5,4) (6,1) (5,1) (1,7) (7,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph100", "image": "data/cycle/graph_visual/easy/graph100.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,1) (7,4) (7,2) (6,1) (9,1) (6,8) (5,4) (7,0) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph274", "image": "data/cycle/graph_visual/easy/graph274.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,3) (6,1) (4,5) (1,0) (7,3) (8,9) (3,0) (0,2) (8,7) (4,7) (2,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph159", "image": "data/cycle/graph_visual/easy/graph159.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,2) (4,5) (1,4) (0,1) (2,5) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph213", "image": "data/cycle/graph_visual/easy/graph213.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,4) (1,0) (0,3) (5,4) (3,5) (2,1) (7,0) (8,2) (6,3) (0,2) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph143", "image": "data/cycle/graph_visual/easy/graph143.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,5) (6,8) (2,8) (4,5) (4,0) (6,3) (6,1) (5,8) (6,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph114", "image": "data/cycle/graph_visual/easy/graph114.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,4) (1,8) (7,4) (3,6) (5,8) (2,0) (0,7) (9,3) (8,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph298", "image": "data/cycle/graph_visual/easy/graph298.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,7) (3,0) (6,8) (4,9) (9,1) (1,0) (5,8) (0,4) (3,2) (2,0) (4,5) (5,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph206", "image": "data/cycle/graph_visual/easy/graph206.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,3) (3,0) (3,7) (1,0) (3,6) (2,0) (4,2) (4,6) (6,8) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph263", "image": "data/cycle/graph_visual/easy/graph263.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,9) (3,0) (2,8) (8,6) (5,1) (0,1) (5,2) (0,8) (4,7) (8,4) (8,3) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph155", "image": "data/cycle/graph_visual/easy/graph155.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (2,0) (0,3) (4,1) (5,2) (0,5) (0,1) (2,1) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph52", "image": "data/cycle/graph_visual/easy/graph52.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,4) (0,8) (2,8) (6,5) (4,2) (7,8) (6,1) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph137", "image": "data/cycle/graph_visual/easy/graph137.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,4) (7,9) (4,9) (6,7) (8,5) (1,6) (2,1) (5,0) (8,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph81", "image": "data/cycle/graph_visual/easy/graph81.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,2) (0,3) (7,3) (0,6) (8,1) (0,4) (5,8) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph231", "image": "data/cycle/graph_visual/easy/graph231.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,0) (0,2) (2,1) (2,8) (3,0) (3,6) (5,4) (8,5) (5,3) (4,0) (4,7) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph249", "image": "data/cycle/graph_visual/easy/graph249.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,1) (0,2) (6,2) (1,5) (3,7) (0,9) (4,3) (0,1) (4,2) (8,0) (7,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph66", "image": "data/cycle/graph_visual/easy/graph66.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,5) (1,8) (7,5) (1,4) (8,0) (6,4) (8,5) (1,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph238", "image": "data/cycle/graph_visual/easy/graph238.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,1) (0,8) (0,2) (8,7) (3,0) (6,4) (1,0) (5,2) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph289", "image": "data/cycle/graph_visual/easy/graph289.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,6) (7,5) (2,7) (4,7) (8,2) (0,3) (0,1) (4,9) (0,4) (8,1) (2,0) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph138", "image": "data/cycle/graph_visual/easy/graph138.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,1) (3,7) (8,0) (8,9) (8,5) (2,0) (6,3) (8,1) (5,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph90", "image": "data/cycle/graph_visual/easy/graph90.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,7) (0,2) (2,8) (1,6) (7,4) (4,5) (3,1) (2,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph156", "image": "data/cycle/graph_visual/easy/graph156.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,0) (5,2) (5,4) (0,4) (3,1) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph235", "image": "data/cycle/graph_visual/easy/graph235.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,0) (1,2) (7,0) (1,5) (4,7) (6,2) (1,0) (0,8) (7,3) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph277", "image": "data/cycle/graph_visual/easy/graph277.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,5) (5,0) (0,2) (4,7) (2,4) (0,1) (6,7) (6,3) (9,0) (1,8) (1,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph28", "image": "data/cycle/graph_visual/easy/graph28.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,5) (0,3) (1,3) (4,6) (2,4) (7,3) (3,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph211", "image": "data/cycle/graph_visual/easy/graph211.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,2) (1,7) (4,5) (0,3) (0,2) (0,4) (6,0) (0,1) (8,7) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph239", "image": "data/cycle/graph_visual/easy/graph239.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,7) (0,3) (1,8) (6,5) (4,3) (2,0) (6,2) (0,1) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph151", "image": "data/cycle/graph_visual/easy/graph151.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (0,3) (1,4) (2,3) (0,2) (2,1) (1,0) (4,3) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph79", "image": "data/cycle/graph_visual/easy/graph79.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,8) (0,4) (3,4) (7,2) (5,6) (7,3) (1,5) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph126", "image": "data/cycle/graph_visual/easy/graph126.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,6) (4,5) (7,5) (2,8) (6,1) (6,8) (4,0) (6,9) (5,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph117", "image": "data/cycle/graph_visual/easy/graph117.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (4,2) (7,2) (2,9) (8,4) (2,6) (8,3) (7,1) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph258", "image": "data/cycle/graph_visual/easy/graph258.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,8) (0,3) (0,7) (3,4) (0,1) (2,4) (1,5) (0,2) (9,0) (4,0) (7,3) (2,6) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph296", "image": "data/cycle/graph_visual/easy/graph296.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,0) (2,9) (2,6) (2,3) (1,4) (0,4) (5,3) (0,2) (7,3) (2,8) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph771", "image": "data/cycle/graph_visual/medium/graph771.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (18,3) (13,1) (10,2) (12,15) (11,1) (4,1) (19,8) (2,7) (13,9) (15,14) (15,10) (22,13) (14,6) (0,18) (8,20) (16,15) (20,5) (21,16) (17,18) (11,7) (1,5) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1146", "image": "data/cycle/graph_visual/medium/graph1146.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,4) (5,8) (2,5) (12,9) (0,1) (7,5) (8,3) (13,14) (6,10) (0,9) (3,0) (13,10) (4,6) (4,0) (2,0) (11,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph849", "image": "data/cycle/graph_visual/medium/graph849.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (15,16) (8,23) (2,6) (3,16) (19,9) (19,5) (11,18) (14,4) (24,4) (20,16) (17,1) (23,13) (14,13) (10,20) (14,21) (19,22) (0,21) (11,14) (19,2) (21,3) (12,9) (23,12) (1,20) (7,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph839", "image": "data/cycle/graph_visual/medium/graph839.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (22,17) (9,8) (15,16) (3,21) (6,5) (8,0) (10,20) (4,23) (22,19) (3,7) (22,10) (3,11) (8,12) (12,2) (15,2) (11,0) (17,18) (6,17) (14,20) (13,10) (16,19) (23,22) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph252", "image": "data/cycle/graph_visual/medium/graph252.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,14) (1,8) (11,9) (3,5) (2,1) (8,0) (5,12) (6,14) (5,6) (9,4) (13,10) (7,9) (1,4) (13,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph403", "image": "data/cycle/graph_visual/medium/graph403.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,8) (4,13) (5,16) (9,12) (11,6) (10,11) (13,7) (1,12) (16,15) (8,2) (14,1) (12,7) (5,7) (12,0) (3,12) (0,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph47", "image": "data/cycle/graph_visual/medium/graph47.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,6) (0,9) (3,7) (9,6) (6,3) (2,4) (8,3) (0,10) (0,5) (1,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1569", "image": "data/cycle/graph_visual/medium/graph1569.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (14,15) (10,7) (21,15) (19,14) (6,0) (3,10) (18,8) (0,3) (21,7) (0,11) (9,1) (0,4) (13,0) (6,11) (16,17) (18,12) (20,3) (1,0) (17,1) (5,13) (5,0) (4,6) (0,2) (2,20) (8,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph478", "image": "data/cycle/graph_visual/medium/graph478.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,4) (17,2) (7,4) (5,12) (11,6) (15,12) (6,13) (9,14) (7,8) (4,5) (6,16) (17,6) (3,5) (13,10) (14,4) (4,6) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1595", "image": "data/cycle/graph_visual/medium/graph1595.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (20,11) (7,1) (8,2) (18,3) (1,16) (16,21) (15,21) (15,13) (14,6) (10,2) (21,9) (11,17) (11,21) (19,8) (1,0) (3,10) (8,15) (5,13) (18,4) (12,21) (14,21) (0,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1204", "image": "data/cycle/graph_visual/medium/graph1204.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,14) (6,9) (4,2) (8,1) (8,6) (5,0) (7,14) (1,12) (13,0) (2,15) (11,4) (0,1) (3,0) (0,7) (10,12) (0,2) (3,9) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1327", "image": "data/cycle/graph_visual/medium/graph1327.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (14,3) (5,16) (6,11) (14,13) (2,0) (0,16) (3,0) (5,10) (7,5) (5,17) (12,2) (0,9) (5,6) (0,1) (12,1) (4,9) (2,4) (15,14) (6,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph555", "image": "data/cycle/graph_visual/medium/graph555.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,9) (10,14) (0,17) (5,16) (12,11) (1,11) (13,12) (18,11) (5,0) (13,9) (7,16) (1,2) (12,19) (19,4) (10,15) (3,18) (19,16) (7,8) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1432", "image": "data/cycle/graph_visual/medium/graph1432.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (13,7) (3,7) (18,8) (11,2) (18,17) (9,14) (0,4) (6,16) (0,18) (10,8) (12,16) (15,13) (10,2) (1,0) (5,15) (6,0) (3,11) (1,17) (9,17) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1545", "image": "data/cycle/graph_visual/medium/graph1545.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (8,11) (6,18) (17,4) (11,2) (9,10) (1,4) (18,7) (12,20) (6,0) (2,3) (8,15) (14,16) (18,14) (20,1) (2,17) (11,13) (1,0) (15,5) (8,9) (9,18) (19,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1275", "image": "data/cycle/graph_visual/medium/graph1275.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,0) (12,8) (15,7) (13,3) (3,0) (0,5) (1,8) (11,1) (5,9) (0,2) (6,0) (0,4) (9,1) (3,6) (15,10) (3,14) (6,16) (9,13) (16,10) (2,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1753", "image": "data/cycle/graph_visual/medium/graph1753.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,0) (3,0) (17,13) (6,23) (0,1) (2,15) (0,8) (23,20) (10,11) (4,21) (1,12) (11,21) (7,24) (23,13) (24,17) (8,9) (2,0) (18,15) (18,3) (4,14) (2,5) (6,15) (18,16) (24,10) (8,15) (19,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph155", "image": "data/cycle/graph_visual/medium/graph155.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (4,11) (12,9) (6,1) (7,12) (0,3) (0,1) (5,1) (8,10) (11,2) (2,5) (4,10) (4,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1217", "image": "data/cycle/graph_visual/medium/graph1217.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,0) (2,3) (12,9) (11,7) (1,4) (9,6) (15,1) (8,11) (2,4) (0,1) (10,14) (2,11) (5,15) (6,0) (15,13) (14,8) (8,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph517", "image": "data/cycle/graph_visual/medium/graph517.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,0) (0,16) (6,9) (13,18) (7,0) (13,3) (16,14) (16,5) (4,9) (5,1) (7,15) (6,15) (18,11) (13,17) (15,8) (12,5) (16,10) (2,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph128", "image": "data/cycle/graph_visual/medium/graph128.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,8) (10,7) (10,11) (4,1) (7,2) (2,12) (10,1) (7,3) (9,3) (6,7) (3,5) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph663", "image": "data/cycle/graph_visual/medium/graph663.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (6,0) (20,6) (19,6) (19,4) (16,6) (13,6) (7,4) (11,20) (14,13) (12,5) (5,9) (17,4) (1,3) (10,7) (5,4) (3,17) (14,15) (8,19) (21,0) (18,12) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph271", "image": "data/cycle/graph_visual/medium/graph271.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,14) (3,6) (7,3) (10,8) (9,5) (12,7) (4,8) (6,13) (5,7) (7,4) (2,7) (14,9) (14,0) (2,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph646", "image": "data/cycle/graph_visual/medium/graph646.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (15,11) (8,2) (12,9) (6,4) (1,15) (14,4) (15,14) (19,4) (11,5) (8,13) (16,3) (18,7) (8,20) (19,16) (19,0) (0,10) (7,17) (11,12) (20,14) (17,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1733", "image": "data/cycle/graph_visual/medium/graph1733.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,19) (21,3) (10,14) (15,17) (9,13) (3,0) (9,3) (8,5) (10,0) (15,7) (0,1) (18,9) (13,6) (23,8) (2,12) (20,22) (4,8) (0,15) (8,11) (2,16) (2,19) (20,1) (0,4) (2,0) (9,23) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph217", "image": "data/cycle/graph_visual/medium/graph217.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,0) (3,9) (7,2) (8,9) (9,5) (4,5) (10,11) (1,12) (11,13) (11,4) (2,5) (8,12) (11,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph919", "image": "data/cycle/graph_visual/medium/graph919.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,4) (6,2) (1,8) (0,4) (7,8) (1,0) (8,9) (1,2) (5,6) (3,6) (0,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1364", "image": "data/cycle/graph_visual/medium/graph1364.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,0) (1,13) (4,17) (11,7) (0,13) (5,8) (9,17) (14,7) (15,0) (12,9) (16,2) (5,16) (3,7) (3,6) (10,12) (3,5) (0,1) (16,9) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph958", "image": "data/cycle/graph_visual/medium/graph958.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,0) (8,4) (7,8) (2,10) (7,5) (1,4) (0,3) (2,9) (2,0) (1,0) (4,0) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1702", "image": "data/cycle/graph_visual/medium/graph1702.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (6,19) (5,16) (16,7) (3,23) (14,7) (20,13) (18,12) (19,11) (10,15) (1,0) (3,0) (0,2) (0,23) (8,0) (12,3) (13,9) (11,12) (20,0) (4,18) (22,12) (5,21) (1,11) (1,2) (10,17) (9,15) (16,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1735", "image": "data/cycle/graph_visual/medium/graph1735.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,0) (21,23) (23,6) (15,16) (2,5) (10,11) (20,13) (17,22) (0,2) (3,18) (18,14) (0,4) (0,3) (15,6) (4,12) (10,0) (9,1) (18,23) (15,2) (13,17) (8,7) (17,21) (4,21) (8,0) (8,15) (11,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1745", "image": "data/cycle/graph_visual/medium/graph1745.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (9,21) (11,8) (2,0) (23,13) (22,10) (1,0) (0,3) (24,13) (22,5) (18,22) (11,19) (24,6) (14,19) (11,18) (24,17) (15,20) (16,0) (3,12) (1,2) (4,14) (0,21) (13,16) (4,7) (1,9) (17,19) (19,15) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1718", "image": "data/cycle/graph_visual/medium/graph1718.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,5) (4,0) (16,17) (10,1) (3,18) (2,18) (17,11) (22,1) (5,15) (23,20) (21,8) (3,0) (3,14) (10,21) (2,0) (15,16) (13,8) (4,13) (20,19) (12,18) (0,1) (0,20) (16,6) (17,9) (7,18) (18,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1536", "image": "data/cycle/graph_visual/medium/graph1536.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,19) (14,6) (0,14) (2,3) (4,9) (5,9) (5,20) (12,16) (17,15) (18,19) (20,2) (0,15) (0,1) (1,7) (10,18) (17,9) (15,12) (0,7) (11,0) (10,5) (8,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1760", "image": "data/cycle/graph_visual/medium/graph1760.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (3,4) (17,1) (2,5) (17,8) (18,19) (0,21) (0,2) (13,20) (0,7) (11,15) (1,0) (0,23) (13,22) (8,3) (0,17) (11,14) (9,5) (23,14) (24,11) (0,3) (8,19) (9,16) (9,13) (13,6) (15,12) (10,21) (13,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph875", "image": "data/cycle/graph_visual/medium/graph875.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (17,5) (7,16) (1,18) (10,17) (4,11) (12,15) (13,0) (2,20) (6,20) (20,24) (2,15) (23,20) (19,6) (19,16) (23,18) (4,0) (3,24) (23,9) (19,0) (1,21) (8,17) (4,14) (8,6) (22,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1679", "image": "data/cycle/graph_visual/medium/graph1679.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (11,7) (8,17) (1,16) (6,17) (10,3) (1,0) (5,4) (14,21) (4,22) (0,19) (2,14) (5,16) (0,15) (9,21) (9,7) (0,3) (17,14) (13,12) (0,2) (21,4) (11,20) (18,19) (15,12) (9,10) (0,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph530", "image": "data/cycle/graph_visual/medium/graph530.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,10) (6,0) (8,11) (18,13) (14,9) (11,2) (2,17) (9,7) (17,4) (5,18) (6,18) (18,4) (16,15) (8,9) (15,3) (1,2) (15,8) (12,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1234", "image": "data/cycle/graph_visual/medium/graph1234.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,0) (9,13) (11,14) (14,4) (2,0) (3,5) (1,0) (12,10) (1,3) (13,7) (4,13) (8,14) (6,10) (4,0) (13,15) (5,2) (14,10) (2,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1357", "image": "data/cycle/graph_visual/medium/graph1357.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,1) (17,10) (12,10) (5,9) (11,2) (14,12) (3,4) (7,5) (0,2) (0,4) (3,0) (11,17) (15,16) (2,6) (13,12) (16,12) (2,8) (9,15) (9,4) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph783", "image": "data/cycle/graph_visual/medium/graph783.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (4,17) (21,0) (17,9) (0,1) (17,18) (15,18) (4,14) (9,16) (13,16) (2,10) (3,2) (4,0) (20,1) (1,6) (8,18) (19,1) (7,12) (16,23) (5,12) (11,18) (20,10) (20,7) (22,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph978", "image": "data/cycle/graph_visual/medium/graph978.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,10) (1,0) (10,9) (2,6) (2,0) (7,4) (1,5) (7,6) (8,11) (1,8) (3,0) (2,1) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph79", "image": "data/cycle/graph_visual/medium/graph79.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,4) (10,5) (5,1) (7,9) (8,0) (2,8) (6,1) (6,11) (3,0) (6,0) (3,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph840", "image": "data/cycle/graph_visual/medium/graph840.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (6,14) (24,17) (20,15) (10,22) (19,24) (8,17) (9,16) (17,16) (21,4) (9,12) (6,7) (3,15) (7,20) (6,24) (22,18) (4,2) (5,13) (21,3) (17,11) (17,0) (23,16) (1,10) (22,13) (5,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1690", "image": "data/cycle/graph_visual/medium/graph1690.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (22,16) (21,13) (6,13) (9,10) (17,8) (7,0) (2,15) (23,4) (20,18) (3,15) (9,5) (10,21) (7,11) (14,0) (9,20) (11,1) (1,0) (14,12) (7,8) (4,21) (9,0) (23,22) (2,0) (15,13) (7,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph729", "image": "data/cycle/graph_visual/medium/graph729.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (10,7) (19,8) (15,21) (0,1) (6,4) (11,8) (3,21) (16,0) (0,2) (11,6) (11,0) (18,17) (10,3) (15,14) (18,13) (5,13) (20,14) (2,20) (7,9) (9,22) (12,1) (17,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph615", "image": "data/cycle/graph_visual/medium/graph615.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (18,1) (14,9) (18,11) (14,10) (3,5) (12,2) (5,12) (6,15) (7,6) (17,19) (4,5) (8,7) (6,19) (14,16) (2,0) (8,14) (12,6) (2,20) (11,15) (14,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph387", "image": "data/cycle/graph_visual/medium/graph387.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,6) (11,9) (2,13) (8,13) (9,5) (5,8) (12,7) (16,10) (4,9) (8,16) (7,0) (10,15) (3,0) (13,12) (1,16) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1700", "image": "data/cycle/graph_visual/medium/graph1700.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (12,7) (21,23) (9,14) (21,16) (6,7) (3,1) (2,0) (6,20) (17,20) (5,19) (15,18) (13,15) (2,21) (3,10) (22,8) (10,16) (0,1) (10,11) (15,9) (8,6) (3,0) (14,8) (15,5) (0,5) (22,3) (14,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1437", "image": "data/cycle/graph_visual/medium/graph1437.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,18) (10,1) (15,6) (8,13) (2,15) (11,0) (18,0) (17,0) (11,3) (6,12) (1,11) (1,5) (1,0) (3,0) (2,16) (1,12) (0,2) (13,15) (17,9) (7,11) (14,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph857", "image": "data/cycle/graph_visual/medium/graph857.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (8,15) (13,7) (14,17) (1,14) (16,7) (10,19) (24,22) (5,11) (14,10) (17,5) (11,21) (16,6) (4,23) (12,18) (21,18) (8,23) (9,3) (2,22) (19,3) (17,20) (24,23) (20,24) (13,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph668", "image": "data/cycle/graph_visual/medium/graph668.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,12) (17,15) (20,10) (8,9) (5,10) (14,12) (9,10) (13,0) (2,11) (0,16) (7,6) (20,0) (18,11) (3,5) (6,10) (16,21) (19,5) (1,15) (14,10) (17,4) (11,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph458", "image": "data/cycle/graph_visual/medium/graph458.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (10,11) (8,1) (6,17) (13,11) (6,1) (14,8) (15,17) (12,5) (2,14) (16,12) (9,5) (4,14) (2,3) (13,3) (0,4) (3,16) (14,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph285", "image": "data/cycle/graph_visual/medium/graph285.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,4) (4,14) (8,4) (3,6) (1,9) (7,13) (6,7) (1,0) (5,0) (0,7) (1,4) (11,5) (12,1) (10,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1062", "image": "data/cycle/graph_visual/medium/graph1062.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (4,1) (8,4) (2,11) (3,6) (1,0) (3,2) (5,1) (11,10) (2,0) (5,12) (7,11) (9,1) (0,3) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1150", "image": "data/cycle/graph_visual/medium/graph1150.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (4,7) (7,8) (1,13) (2,4) (3,9) (5,6) (0,2) (12,13) (0,12) (14,3) (10,3) (3,11) (9,8) (4,1) (3,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1503", "image": "data/cycle/graph_visual/medium/graph1503.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,0) (6,11) (19,8) (20,12) (15,13) (4,0) (4,5) (16,18) (19,17) (11,19) (9,1) (0,3) (17,13) (0,2) (7,3) (0,14) (4,14) (19,10) (1,2) (1,0) (11,18) (9,15) (3,14) (13,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph909", "image": "data/cycle/graph_visual/medium/graph909.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,10) (2,6) (9,7) (7,10) (2,0) (2,1) (9,5) (3,2) (0,1) (8,3) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph815", "image": "data/cycle/graph_visual/medium/graph815.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (12,7) (17,18) (9,16) (23,16) (20,1) (1,19) (12,5) (4,14) (2,22) (0,1) (1,6) (18,15) (17,4) (18,8) (20,10) (0,4) (13,16) (2,3) (2,10) (21,0) (11,18) (7,20) (9,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph806", "image": "data/cycle/graph_visual/medium/graph806.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,21) (7,14) (18,22) (18,13) (23,11) (0,2) (3,19) (23,20) (23,16) (17,21) (5,20) (12,8) (15,4) (16,7) (4,23) (6,7) (1,13) (2,6) (9,3) (1,0) (7,8) (2,17) (10,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph215", "image": "data/cycle/graph_visual/medium/graph215.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (10,8) (4,7) (5,0) (4,3) (12,2) (6,2) (9,10) (10,5) (7,1) (6,0) (4,13) (11,8) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1430", "image": "data/cycle/graph_visual/medium/graph1430.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (7,12) (5,18) (17,10) (3,12) (15,12) (17,1) (17,0) (12,1) (2,8) (5,7) (1,0) (13,6) (2,0) (7,16) (4,17) (11,8) (11,0) (11,14) (9,11) (12,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph357", "image": "data/cycle/graph_visual/medium/graph357.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,0) (5,4) (4,9) (4,7) (13,9) (15,0) (0,11) (11,8) (12,1) (10,2) (3,11) (3,13) (8,10) (10,6) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph597", "image": "data/cycle/graph_visual/medium/graph597.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,9) (11,1) (15,19) (14,18) (16,7) (0,14) (4,2) (12,14) (7,3) (15,17) (12,6) (1,2) (16,0) (15,12) (7,4) (6,10) (13,6) (11,5) (8,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph772", "image": "data/cycle/graph_visual/medium/graph772.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (6,16) (11,17) (4,2) (9,12) (19,13) (4,21) (16,17) (10,1) (15,20) (22,10) (14,6) (22,18) (8,17) (6,7) (22,17) (13,5) (17,0) (16,9) (7,20) (15,3) (5,4) (21,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph468", "image": "data/cycle/graph_visual/medium/graph468.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,7) (9,4) (0,6) (0,15) (12,15) (14,17) (10,5) (11,0) (2,14) (8,0) (13,12) (10,16) (5,17) (3,2) (4,7) (9,15) (9,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1174", "image": "data/cycle/graph_visual/medium/graph1174.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,5) (12,4) (1,4) (8,14) (13,1) (3,0) (0,4) (10,8) (0,1) (6,3) (3,14) (13,7) (2,0) (5,12) (9,13) (11,8) (2,11) (5,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1576", "image": "data/cycle/graph_visual/medium/graph1576.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (6,9) (1,19) (14,0) (5,8) (9,4) (2,20) (10,21) (6,16) (14,2) (1,7) (2,12) (3,14) (9,18) (0,1) (21,7) (13,12) (11,2) (21,20) (15,21) (19,9) (8,15) (17,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1695", "image": "data/cycle/graph_visual/medium/graph1695.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,22) (0,19) (16,2) (1,0) (12,7) (13,6) (3,20) (15,21) (5,12) (14,0) (0,2) (1,22) (8,18) (23,9) (22,4) (9,18) (21,14) (4,17) (22,20) (23,3) (5,10) (3,0) (6,11) (5,6) (21,5) (14,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph188", "image": "data/cycle/graph_visual/medium/graph188.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,12) (8,5) (2,9) (0,6) (10,12) (4,12) (3,8) (7,9) (1,8) (12,13) (10,11) (12,9) (8,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph467", "image": "data/cycle/graph_visual/medium/graph467.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (11,0) (5,13) (14,2) (0,9) (6,11) (15,14) (0,1) (2,0) (16,8) (7,1) (1,13) (17,12) (10,3) (15,3) (17,10) (8,11) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph284", "image": "data/cycle/graph_visual/medium/graph284.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (5,4) (0,8) (3,12) (12,8) (2,6) (0,11) (9,13) (14,5) (6,13) (13,7) (9,0) (1,3) (12,14) (12,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1350", "image": "data/cycle/graph_visual/medium/graph1350.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,4) (12,4) (12,17) (1,0) (6,14) (7,5) (0,16) (9,8) (3,10) (2,6) (3,9) (11,17) (11,5) (1,13) (7,0) (15,12) (13,8) (15,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1656", "image": "data/cycle/graph_visual/medium/graph1656.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (17,3) (1,0) (1,19) (14,3) (5,18) (19,11) (6,18) (3,8) (15,5) (10,4) (18,17) (1,16) (13,12) (2,11) (20,21) (4,5) (0,15) (21,19) (12,11) (22,3) (9,2) (3,12) (7,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1465", "image": "data/cycle/graph_visual/medium/graph1465.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,8) (6,3) (4,8) (10,18) (11,8) (10,11) (0,6) (3,0) (9,10) (5,0) (10,13) (4,0) (2,17) (16,19) (3,10) (12,14) (1,0) (13,5) (6,12) (11,7) (16,4) (2,0) (1,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph369", "image": "data/cycle/graph_visual/medium/graph369.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,4) (9,5) (6,5) (2,1) (0,15) (9,2) (1,12) (13,1) (4,13) (3,14) (10,12) (6,15) (14,6) (4,8) (7,2) (11,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1454", "image": "data/cycle/graph_visual/medium/graph1454.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,14) (3,5) (6,5) (17,1) (2,17) (0,14) (13,16) (10,16) (14,8) (12,6) (3,14) (1,0) (11,18) (14,7) (19,17) (18,5) (19,15) (9,4) (4,2) (15,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph165", "image": "data/cycle/graph_visual/medium/graph165.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,5) (7,8) (4,12) (1,8) (8,11) (9,3) (12,2) (2,3) (8,12) (10,9) (0,7) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph375", "image": "data/cycle/graph_visual/medium/graph375.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,12) (0,2) (4,2) (0,6) (13,15) (8,6) (12,3) (6,14) (15,1) (7,0) (14,13) (12,2) (4,11) (10,8) (3,5) (6,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1011", "image": "data/cycle/graph_visual/medium/graph1011.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,2) (1,0) (8,0) (3,11) (2,0) (4,1) (9,7) (5,0) (0,3) (3,2) (3,1) (4,10) (5,8) (5,6) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1026", "image": "data/cycle/graph_visual/medium/graph1026.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (10,7) (2,0) (5,3) (12,2) (7,6) (4,1) (5,8) (1,10) (0,1) (10,11) (7,3) (2,7) (9,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1344", "image": "data/cycle/graph_visual/medium/graph1344.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,0) (7,0) (16,1) (16,10) (12,17) (8,12) (16,15) (8,7) (9,17) (4,7) (3,5) (7,5) (13,14) (2,0) (11,12) (17,6) (10,11) (2,17) (14,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph159", "image": "data/cycle/graph_visual/medium/graph159.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,9) (7,6) (10,9) (8,7) (7,5) (3,2) (4,12) (8,1) (11,8) (0,7) (12,2) (8,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph658", "image": "data/cycle/graph_visual/medium/graph658.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,3) (4,17) (1,5) (15,20) (14,8) (9,17) (10,9) (13,1) (19,6) (15,13) (12,5) (16,18) (3,15) (8,5) (5,11) (7,16) (9,6) (0,4) (15,2) (18,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph506", "image": "data/cycle/graph_visual/medium/graph506.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,9) (16,8) (11,9) (13,17) (13,2) (3,0) (8,13) (17,5) (12,10) (7,0) (18,12) (3,15) (1,16) (14,8) (11,6) (16,10) (9,5) (7,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph852", "image": "data/cycle/graph_visual/medium/graph852.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (17,12) (15,3) (24,5) (1,4) (12,13) (8,3) (15,9) (0,22) (18,6) (3,6) (24,19) (20,16) (0,15) (12,20) (24,21) (10,24) (14,15) (0,23) (19,13) (7,2) (18,4) (14,11) (22,24) (2,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1601", "image": "data/cycle/graph_visual/medium/graph1601.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,11) (19,2) (4,19) (5,17) (14,6) (15,14) (1,0) (18,11) (8,4) (2,0) (1,8) (7,11) (14,21) (0,3) (11,13) (16,12) (16,0) (5,1) (20,5) (7,14) (10,15) (16,9) (0,4) (6,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1526", "image": "data/cycle/graph_visual/medium/graph1526.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (7,10) (3,0) (5,2) (14,4) (0,1) (19,2) (2,0) (13,18) (11,14) (1,3) (17,19) (16,10) (12,13) (5,3) (14,15) (17,14) (17,8) (18,16) (6,11) (10,17) (9,13) (20,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph495", "image": "data/cycle/graph_visual/medium/graph495.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (15,10) (4,0) (12,17) (5,0) (7,16) (3,18) (15,0) (13,9) (18,12) (9,14) (2,1) (8,10) (11,1) (7,6) (11,12) (13,12) (11,16) (5,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph979", "image": "data/cycle/graph_visual/medium/graph979.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,8) (0,9) (2,0) (0,3) (4,1) (6,1) (0,1) (11,9) (5,0) (2,9) (8,10) (7,3) (10,3) (9,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph869", "image": "data/cycle/graph_visual/medium/graph869.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (2,10) (14,15) (1,13) (12,13) (18,3) (10,15) (8,21) (5,1) (7,23) (8,20) (19,18) (16,22) (7,2) (11,23) (15,17) (6,0) (4,13) (1,11) (5,20) (16,15) (24,4) (1,9) (18,0) (14,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph289", "image": "data/cycle/graph_visual/medium/graph289.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,12) (12,10) (6,0) (12,6) (12,14) (1,8) (12,4) (5,8) (8,3) (4,8) (11,14) (2,9) (9,7) (13,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1494", "image": "data/cycle/graph_visual/medium/graph1494.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,16) (7,17) (10,0) (13,14) (3,0) (4,16) (3,7) (2,6) (5,14) (5,18) (12,1) (0,12) (10,19) (14,15) (10,13) (9,0) (5,8) (0,2) (4,19) (3,4) (0,1) (6,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph819", "image": "data/cycle/graph_visual/medium/graph819.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (5,2) (17,6) (18,12) (9,19) (14,0) (8,1) (11,0) (4,2) (17,3) (9,10) (12,20) (7,0) (6,8) (1,12) (23,19) (13,19) (15,20) (4,20) (0,2) (7,16) (16,22) (21,14) (19,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph105", "image": "data/cycle/graph_visual/medium/graph105.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,9) (8,1) (9,10) (9,7) (1,4) (8,5) (1,2) (6,5) (8,0) (6,11) (3,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1225", "image": "data/cycle/graph_visual/medium/graph1225.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,0) (7,12) (4,11) (5,4) (2,14) (8,1) (5,8) (7,5) (6,2) (9,0) (3,9) (13,4) (10,7) (13,0) (15,4) (6,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1449", "image": "data/cycle/graph_visual/medium/graph1449.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (6,3) (6,4) (10,3) (5,17) (18,2) (19,16) (8,12) (3,11) (13,17) (17,15) (12,2) (11,0) (1,0) (10,14) (9,10) (4,1) (7,8) (8,0) (16,15) (0,2) (19,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph531", "image": "data/cycle/graph_visual/medium/graph531.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (3,4) (11,17) (5,9) (6,2) (15,12) (17,16) (7,5) (8,2) (16,12) (12,10) (14,12) (9,15) (9,4) (10,13) (2,11) (0,2) (18,13) (1,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1143", "image": "data/cycle/graph_visual/medium/graph1143.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,11) (9,13) (8,12) (7,6) (11,0) (3,6) (9,3) (2,7) (11,5) (13,10) (7,14) (1,9) (0,1) (4,11) (1,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph277", "image": "data/cycle/graph_visual/medium/graph277.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,10) (7,14) (1,7) (4,10) (10,6) (0,3) (8,9) (11,2) (5,13) (7,12) (9,11) (9,4) (3,1) (5,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1617", "image": "data/cycle/graph_visual/medium/graph1617.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (15,9) (0,2) (2,10) (16,13) (8,19) (0,18) (3,11) (5,15) (18,8) (21,18) (16,14) (7,13) (1,17) (19,11) (17,9) (2,17) (20,6) (0,6) (0,1) (3,7) (12,20) (20,10) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph182", "image": "data/cycle/graph_visual/medium/graph182.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,13) (9,2) (6,4) (5,13) (3,8) (2,10) (2,7) (12,10) (11,0) (10,1) (9,6) (3,2) (11,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph814", "image": "data/cycle/graph_visual/medium/graph814.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (20,5) (21,15) (5,4) (18,1) (23,0) (3,0) (17,5) (6,2) (2,7) (14,7) (3,5) (15,16) (9,21) (16,13) (18,0) (20,8) (11,5) (16,0) (19,8) (5,14) (10,9) (12,11) (15,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph26", "image": "data/cycle/graph_visual/medium/graph26.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,10) (4,2) (4,7) (1,0) (6,3) (7,6) (4,5) (8,1) (0,5) (9,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph71", "image": "data/cycle/graph_visual/medium/graph71.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,6) (1,10) (8,10) (0,11) (7,4) (5,9) (10,4) (10,3) (9,2) (5,1) (2,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph472", "image": "data/cycle/graph_visual/medium/graph472.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,9) (11,10) (16,8) (14,7) (14,1) (0,13) (11,2) (9,10) (12,15) (10,8) (13,4) (11,5) (6,3) (2,3) (5,1) (11,13) (17,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph171", "image": "data/cycle/graph_visual/medium/graph171.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,6) (6,12) (2,12) (0,4) (8,7) (6,1) (7,12) (8,9) (5,0) (6,10) (11,4) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1440", "image": "data/cycle/graph_visual/medium/graph1440.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,12) (14,13) (4,19) (16,11) (19,10) (0,3) (10,6) (2,6) (0,1) (7,3) (8,5) (10,0) (13,10) (0,12) (15,14) (2,0) (4,3) (18,5) (16,4) (14,5) (7,17) (9,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1621", "image": "data/cycle/graph_visual/medium/graph1621.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (6,2) (16,18) (3,16) (0,2) (4,14) (11,14) (15,1) (13,14) (1,0) (21,0) (12,9) (21,7) (3,21) (14,20) (13,12) (17,11) (10,16) (19,5) (2,19) (21,19) (4,22) (9,19) (20,8) (1,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph146", "image": "data/cycle/graph_visual/medium/graph146.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,4) (6,8) (2,9) (4,11) (3,2) (8,3) (8,1) (7,12) (7,8) (5,8) (3,10) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1199", "image": "data/cycle/graph_visual/medium/graph1199.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (8,5) (13,6) (4,6) (12,1) (4,0) (13,11) (14,10) (6,8) (2,0) (14,2) (5,14) (9,0) (4,9) (1,0) (3,12) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1456", "image": "data/cycle/graph_visual/medium/graph1456.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,1) (3,0) (12,9) (0,2) (6,18) (8,2) (7,0) (17,4) (13,14) (16,3) (6,11) (15,16) (10,9) (4,0) (17,6) (10,5) (14,0) (18,0) (2,16) (11,19) (3,13) (3,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1666", "image": "data/cycle/graph_visual/medium/graph1666.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,0) (4,3) (12,17) (7,17) (3,10) (9,11) (18,10) (3,0) (11,7) (18,20) (15,12) (19,2) (2,0) (19,21) (6,0) (14,18) (6,7) (17,16) (21,13) (1,22) (22,14) (8,14) (6,5) (21,7) (18,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph536", "image": "data/cycle/graph_visual/medium/graph536.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,1) (11,13) (5,14) (1,6) (1,9) (9,16) (2,0) (2,3) (8,6) (5,15) (18,5) (13,8) (13,7) (8,10) (14,4) (15,12) (14,17) (3,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph957", "image": "data/cycle/graph_visual/medium/graph957.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,8) (1,0) (8,2) (9,0) (8,1) (7,6) (7,0) (2,0) (8,4) (2,5) (10,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph627", "image": "data/cycle/graph_visual/medium/graph627.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (19,4) (11,4) (4,3) (10,14) (8,20) (16,10) (14,5) (7,12) (13,12) (17,6) (14,9) (6,13) (18,7) (1,9) (3,15) (2,16) (0,3) (20,12) (10,8) (19,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1586", "image": "data/cycle/graph_visual/medium/graph1586.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,21) (2,4) (12,0) (8,20) (1,0) (6,0) (3,0) (14,13) (20,18) (2,0) (13,20) (20,3) (16,8) (15,6) (12,9) (11,21) (4,19) (15,1) (6,14) (6,17) (3,5) (7,19) (10,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1770", "image": "data/cycle/graph_visual/medium/graph1770.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (2,12) (20,22) (20,1) (0,10) (19,1) (1,0) (2,4) (14,10) (18,9) (17,15) (0,3) (9,13) (3,9) (8,23) (21,3) (5,8) (11,8) (2,19) (13,6) (24,23) (16,2) (7,15) (8,4) (23,9) (15,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph296", "image": "data/cycle/graph_visual/medium/graph296.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,12) (9,3) (5,9) (7,13) (8,1) (13,14) (0,13) (5,1) (13,11) (6,8) (12,14) (10,4) (2,4) (14,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1484", "image": "data/cycle/graph_visual/medium/graph1484.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,16) (11,18) (16,12) (13,4) (9,15) (2,13) (5,1) (0,17) (7,0) (0,1) (5,14) (15,16) (9,8) (6,10) (0,11) (18,13) (13,3) (15,6) (2,19) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1422", "image": "data/cycle/graph_visual/medium/graph1422.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (18,16) (14,13) (7,4) (17,12) (11,6) (17,14) (13,18) (5,14) (1,3) (2,10) (1,0) (11,17) (9,7) (18,8) (10,12) (6,3) (7,15) (7,18) (6,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1527", "image": "data/cycle/graph_visual/medium/graph1527.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (3,7) (16,5) (0,18) (1,0) (12,20) (12,10) (5,3) (9,13) (9,16) (7,11) (1,13) (3,6) (9,20) (16,2) (12,19) (8,5) (17,18) (4,17) (7,15) (0,2) (0,3) (14,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph184", "image": "data/cycle/graph_visual/medium/graph184.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,2) (5,10) (2,8) (1,13) (8,12) (0,9) (3,11) (2,5) (9,1) (4,7) (4,10) (13,2) (3,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1734", "image": "data/cycle/graph_visual/medium/graph1734.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,4) (23,1) (18,16) (0,14) (9,4) (17,2) (3,5) (1,0) (8,14) (16,15) (13,6) (3,14) (19,21) (17,7) (6,5) (1,20) (20,15) (22,20) (10,14) (22,17) (19,5) (9,14) (16,11) (12,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph70", "image": "data/cycle/graph_visual/medium/graph70.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,6) (11,6) (4,1) (10,7) (0,2) (4,5) (7,9) (7,8) (1,7) (9,2) (1,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph604", "image": "data/cycle/graph_visual/medium/graph604.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,7) (17,12) (5,3) (0,10) (16,9) (18,20) (7,12) (2,19) (1,16) (17,3) (3,18) (15,7) (20,14) (15,11) (20,8) (8,4) (11,19) (1,5) (6,11) (0,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph343", "image": "data/cycle/graph_visual/medium/graph343.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,13) (11,13) (9,14) (8,12) (9,4) (9,10) (4,3) (1,8) (6,11) (4,6) (12,0) (7,15) (15,12) (5,1) (3,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph441", "image": "data/cycle/graph_visual/medium/graph441.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (13,12) (9,4) (12,14) (11,17) (2,11) (7,5) (10,17) (4,3) (16,12) (1,6) (5,9) (9,15) (2,0) (12,10) (6,2) (8,2) (15,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1692", "image": "data/cycle/graph_visual/medium/graph1692.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (4,14) (3,0) (1,2) (6,4) (7,11) (3,10) (0,1) (15,19) (17,19) (8,21) (11,18) (14,3) (0,2) (1,9) (22,18) (22,5) (11,19) (16,0) (23,12) (14,19) (13,16) (13,17) (9,22) (0,21) (13,12) (20,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1177", "image": "data/cycle/graph_visual/medium/graph1177.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (4,2) (6,10) (13,14) (11,13) (3,5) (8,12) (1,8) (6,2) (5,1) (1,10) (9,5) (0,14) (0,9) (7,0) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1121", "image": "data/cycle/graph_visual/medium/graph1121.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,4) (1,0) (13,0) (2,6) (5,2) (1,13) (11,7) (5,11) (3,7) (2,12) (9,1) (1,10) (5,8) (6,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph548", "image": "data/cycle/graph_visual/medium/graph548.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (13,18) (7,2) (4,12) (7,19) (16,6) (14,1) (11,3) (13,17) (15,16) (1,2) (17,10) (6,1) (12,3) (1,8) (10,0) (9,2) (2,13) (11,18) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph8", "image": "data/cycle/graph_visual/medium/graph8.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,2) (6,3) (0,8) (8,2) (8,7) (4,9) (5,1) (4,8) (3,8) (10,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1543", "image": "data/cycle/graph_visual/medium/graph1543.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,19) (7,20) (17,8) (0,3) (1,6) (11,9) (19,13) (3,18) (4,6) (11,12) (2,18) (15,1) (8,14) (6,5) (0,1) (13,9) (12,16) (6,14) (10,6) (0,20) (18,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph660", "image": "data/cycle/graph_visual/medium/graph660.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,5) (10,21) (16,14) (11,19) (21,7) (6,14) (17,8) (6,13) (11,20) (2,9) (9,10) (15,1) (10,12) (3,1) (15,18) (8,16) (17,15) (4,19) (4,17) (16,0) (12,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph207", "image": "data/cycle/graph_visual/medium/graph207.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,13) (7,12) (5,1) (4,5) (13,2) (11,7) (7,0) (8,1) (10,9) (11,3) (5,12) (3,10) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph880", "image": "data/cycle/graph_visual/medium/graph880.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,0) (2,11) (11,7) (23,12) (13,12) (4,17) (19,8) (11,6) (14,3) (10,19) (7,20) (18,19) (20,14) (2,15) (17,19) (2,5) (2,9) (3,1) (17,24) (9,21) (13,0) (22,16) (15,10) (16,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph371", "image": "data/cycle/graph_visual/medium/graph371.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,10) (5,2) (2,15) (0,9) (7,8) (7,16) (11,15) (3,9) (12,1) (8,9) (10,14) (4,12) (1,7) (4,6) (13,14) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph608", "image": "data/cycle/graph_visual/medium/graph608.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (2,17) (12,14) (19,12) (7,8) (10,7) (3,12) (7,6) (4,20) (20,11) (9,16) (13,8) (10,11) (2,14) (8,15) (5,16) (9,18) (1,19) (0,3) (3,8) (14,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1468", "image": "data/cycle/graph_visual/medium/graph1468.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (3,0) (1,5) (1,13) (13,15) (18,6) (5,12) (5,8) (3,16) (4,3) (0,2) (11,5) (0,5) (1,0) (9,10) (9,6) (3,19) (4,0) (7,16) (8,14) (15,2) (17,9) (15,18) (17,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph966", "image": "data/cycle/graph_visual/medium/graph966.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,3) (1,0) (11,1) (10,2) (2,4) (5,8) (11,10) (0,4) (11,7) (9,6) (0,2) (2,3) (2,8) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1476", "image": "data/cycle/graph_visual/medium/graph1476.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,11) (3,0) (13,8) (13,6) (13,18) (17,7) (4,0) (17,10) (2,0) (6,0) (9,19) (7,19) (6,2) (0,1) (16,5) (14,1) (13,5) (12,4) (1,19) (15,16) (4,15) (6,3) (7,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1431", "image": "data/cycle/graph_visual/medium/graph1431.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (3,8) (15,10) (17,12) (16,7) (14,2) (18,11) (7,1) (15,9) (13,4) (12,3) (0,2) (11,17) (4,2) (7,5) (12,0) (1,0) (6,9) (1,9) (17,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1559", "image": "data/cycle/graph_visual/medium/graph1559.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (8,6) (1,12) (3,0) (19,9) (20,13) (11,19) (6,15) (2,14) (16,19) (20,12) (1,8) (0,20) (2,0) (7,0) (9,5) (10,0) (18,4) (2,4) (0,14) (12,17) (17,3) (7,16) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph574", "image": "data/cycle/graph_visual/medium/graph574.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,9) (19,10) (5,14) (14,12) (7,4) (6,4) (5,18) (8,7) (2,11) (2,7) (0,19) (19,1) (17,5) (15,3) (8,1) (3,11) (16,10) (1,13) (13,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1538", "image": "data/cycle/graph_visual/medium/graph1538.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,0) (15,10) (13,9) (4,3) (8,17) (12,11) (11,20) (8,16) (3,8) (7,0) (17,0) (13,6) (9,5) (1,0) (0,3) (11,13) (0,19) (2,5) (18,13) (0,2) (19,15) (1,17) (9,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph699", "image": "data/cycle/graph_visual/medium/graph699.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,11) (13,12) (5,2) (15,21) (10,19) (11,7) (9,17) (2,9) (0,1) (8,19) (2,15) (18,16) (17,4) (11,16) (12,19) (14,20) (14,3) (11,6) (3,1) (7,20) (13,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph168", "image": "data/cycle/graph_visual/medium/graph168.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,3) (7,3) (1,4) (10,7) (11,10) (3,5) (5,8) (2,12) (7,2) (1,10) (7,6) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph972", "image": "data/cycle/graph_visual/medium/graph972.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (0,9) (9,10) (5,7) (5,2) (8,3) (4,7) (0,6) (8,5) (6,9) (11,4) (0,1) (0,4) (0,5) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1154", "image": "data/cycle/graph_visual/medium/graph1154.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,9) (4,12) (0,4) (3,0) (1,13) (10,4) (12,8) (1,0) (3,11) (3,14) (6,11) (13,6) (2,0) (0,5) (14,8) (2,8) (7,10) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1625", "image": "data/cycle/graph_visual/medium/graph1625.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (2,17) (19,13) (0,2) (11,18) (7,21) (10,2) (6,16) (1,6) (16,18) (4,0) (17,22) (8,20) (1,15) (1,0) (0,3) (7,2) (5,4) (14,3) (13,20) (2,1) (17,12) (1,9) (2,13) (0,10) (3,11) (4,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1140", "image": "data/cycle/graph_visual/medium/graph1140.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (1,0) (1,3) (0,13) (7,14) (2,0) (6,11) (12,4) (4,11) (11,9) (4,1) (6,14) (3,5) (14,0) (13,2) (13,10) (10,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph662", "image": "data/cycle/graph_visual/medium/graph662.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (19,5) (21,18) (11,16) (5,13) (1,18) (19,6) (9,8) (17,1) (21,10) (0,1) (13,20) (6,15) (4,2) (11,2) (16,12) (2,3) (8,19) (7,5) (11,21) (9,14) (20,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph393", "image": "data/cycle/graph_visual/medium/graph393.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,7) (2,9) (15,10) (13,11) (0,16) (1,3) (11,4) (14,6) (15,14) (8,4) (1,15) (9,6) (16,8) (16,12) (12,14) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1776", "image": "data/cycle/graph_visual/medium/graph1776.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (10,6) (18,24) (22,2) (0,14) (9,23) (4,0) (11,2) (24,23) (17,23) (22,16) (3,13) (18,0) (13,14) (3,16) (8,0) (21,12) (0,1) (19,20) (20,9) (16,15) (24,10) (5,17) (23,7) (12,3) (1,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph87", "image": "data/cycle/graph_visual/medium/graph87.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,0) (4,9) (9,6) (11,4) (10,8) (3,5) (2,6) (4,8) (3,2) (7,11) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph414", "image": "data/cycle/graph_visual/medium/graph414.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (15,10) (2,7) (16,1) (14,15) (5,1) (10,2) (3,1) (0,6) (8,5) (13,4) (8,13) (16,7) (0,11) (15,9) (14,6) (12,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph411", "image": "data/cycle/graph_visual/medium/graph411.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,7) (0,3) (6,8) (11,10) (2,0) (14,7) (7,11) (14,9) (15,12) (2,16) (10,5) (13,3) (1,6) (13,14) (4,3) (6,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1115", "image": "data/cycle/graph_visual/medium/graph1115.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,4) (11,12) (7,5) (10,2) (6,3) (0,1) (3,0) (0,5) (1,5) (0,2) (10,1) (11,7) (9,1) (11,8) (6,12) (13,0) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph974", "image": "data/cycle/graph_visual/medium/graph974.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,1) (1,0) (4,11) (2,7) (1,7) (7,11) (11,9) (0,4) (2,6) (5,8) (3,0) (5,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1152", "image": "data/cycle/graph_visual/medium/graph1152.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,6) (2,0) (11,10) (12,11) (8,2) (4,0) (5,10) (7,9) (3,0) (2,7) (1,7) (5,13) (1,12) (11,4) (9,14) (1,0) (5,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph422", "image": "data/cycle/graph_visual/medium/graph422.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,9) (9,14) (10,8) (8,6) (3,11) (4,0) (15,5) (15,13) (2,10) (6,17) (6,0) (0,16) (11,2) (1,17) (7,3) (12,16) (7,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph307", "image": "data/cycle/graph_visual/medium/graph307.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,2) (1,10) (12,5) (7,3) (5,14) (15,13) (1,11) (8,6) (4,13) (5,8) (13,5) (1,0) (5,0) (10,2) (3,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph706", "image": "data/cycle/graph_visual/medium/graph706.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (18,8) (10,7) (6,11) (15,21) (17,1) (0,11) (16,17) (14,15) (20,3) (13,5) (20,2) (3,10) (2,0) (18,12) (6,4) (7,21) (11,8) (0,13) (9,1) (19,14) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1247", "image": "data/cycle/graph_visual/medium/graph1247.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (0,5) (9,5) (4,3) (8,6) (3,2) (0,2) (13,11) (10,15) (13,0) (2,12) (15,14) (7,3) (13,14) (8,10) (1,4) (4,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1585", "image": "data/cycle/graph_visual/medium/graph1585.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (12,4) (0,21) (12,0) (14,16) (2,0) (6,21) (10,4) (0,3) (17,7) (1,0) (19,20) (2,8) (11,13) (15,8) (21,19) (0,17) (11,9) (8,20) (19,14) (1,15) (15,11) (3,21) (7,18) (16,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1209", "image": "data/cycle/graph_visual/medium/graph1209.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (8,9) (13,8) (11,1) (4,12) (12,14) (15,5) (7,0) (3,10) (1,0) (3,0) (13,6) (4,1) (7,5) (2,0) (2,6) (9,3) (6,15) (12,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1541", "image": "data/cycle/graph_visual/medium/graph1541.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (8,10) (1,3) (15,13) (1,0) (19,3) (6,19) (14,17) (1,17) (13,7) (20,18) (8,15) (20,17) (9,18) (7,12) (16,2) (5,17) (5,11) (16,11) (4,3) (10,14) (14,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph469", "image": "data/cycle/graph_visual/medium/graph469.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,7) (8,10) (14,9) (13,16) (16,11) (10,13) (12,11) (9,4) (3,8) (8,17) (16,5) (8,4) (6,12) (3,2) (3,15) (1,16) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1726", "image": "data/cycle/graph_visual/medium/graph1726.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (20,22) (16,8) (1,0) (6,9) (1,15) (9,13) (19,17) (5,12) (0,2) (8,11) (8,10) (14,2) (7,21) (2,6) (0,20) (3,22) (5,7) (4,8) (15,2) (12,11) (23,2) (18,23) (18,20) (17,10) (7,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1784", "image": "data/cycle/graph_visual/medium/graph1784.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (13,0) (24,6) (20,18) (4,10) (21,7) (22,13) (18,14) (3,0) (9,24) (0,5) (20,16) (3,4) (10,15) (1,23) (21,8) (0,1) (10,19) (2,3) (8,12) (6,13) (2,23) (13,14) (4,11) (2,0) (21,5) (18,15) (3,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1098", "image": "data/cycle/graph_visual/medium/graph1098.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (5,13) (12,3) (8,11) (12,6) (1,11) (9,4) (2,0) (13,6) (2,4) (3,0) (5,10) (2,13) (9,7) (1,2) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1593", "image": "data/cycle/graph_visual/medium/graph1593.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (5,8) (6,2) (7,3) (14,17) (20,9) (3,0) (6,10) (10,13) (20,7) (5,19) (1,0) (18,4) (10,0) (14,13) (0,15) (14,5) (4,19) (10,21) (16,12) (12,1) (3,4) (11,0) (16,21) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1557", "image": "data/cycle/graph_visual/medium/graph1557.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,3) (0,2) (9,16) (12,14) (12,3) (3,8) (6,7) (1,0) (11,20) (2,14) (10,7) (13,8) (10,11) (9,18) (2,17) (20,4) (8,7) (8,15) (4,0) (19,12) (5,16) (9,14) (19,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph917", "image": "data/cycle/graph_visual/medium/graph917.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,8) (10,0) (3,7) (1,0) (1,3) (3,6) (0,9) (0,5) (6,9) (2,4) (6,4) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1616", "image": "data/cycle/graph_visual/medium/graph1616.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (9,3) (9,15) (8,0) (20,8) (2,10) (7,14) (15,0) (6,11) (7,10) (19,13) (1,8) (0,16) (4,7) (4,17) (15,21) (1,0) (16,19) (21,18) (12,17) (6,5) (17,20) (6,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph415", "image": "data/cycle/graph_visual/medium/graph415.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,11) (14,13) (3,14) (15,11) (9,15) (8,3) (4,14) (0,10) (1,9) (12,5) (13,12) (16,0) (5,16) (6,4) (13,11) (1,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph67", "image": "data/cycle/graph_visual/medium/graph67.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,2) (6,7) (4,11) (11,10) (1,2) (4,3) (0,1) (1,5) (7,8) (2,10) (9,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1499", "image": "data/cycle/graph_visual/medium/graph1499.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,8) (4,19) (10,16) (14,9) (3,4) (10,14) (0,4) (7,12) (14,5) (16,2) (11,4) (1,0) (17,6) (3,0) (13,6) (18,7) (15,3) (8,19) (2,12) (0,2) (12,13) (1,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph181", "image": "data/cycle/graph_visual/medium/graph181.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,5) (9,1) (6,11) (10,8) (0,13) (11,10) (0,8) (13,7) (11,3) (5,4) (9,11) (4,2) (13,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph749", "image": "data/cycle/graph_visual/medium/graph749.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (13,6) (7,8) (8,17) (3,15) (11,7) (21,4) (1,11) (2,15) (5,9) (9,20) (18,20) (4,22) (10,21) (12,14) (7,0) (10,9) (14,0) (21,13) (7,19) (13,15) (22,16) (9,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph232", "image": "data/cycle/graph_visual/medium/graph232.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,12) (2,9) (4,2) (7,10) (0,1) (6,9) (8,11) (11,1) (2,10) (7,12) (2,3) (3,11) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1414", "image": "data/cycle/graph_visual/medium/graph1414.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,16) (10,12) (13,8) (14,8) (9,4) (0,2) (13,2) (6,11) (0,3) (16,10) (18,12) (9,11) (5,9) (0,1) (5,17) (16,8) (7,0) (15,3) (17,13) (7,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph589", "image": "data/cycle/graph_visual/medium/graph589.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,9) (13,8) (14,9) (3,8) (7,8) (5,7) (9,17) (2,16) (3,12) (6,8) (0,3) (10,7) (2,14) (1,19) (19,11) (12,14) (11,10) (12,18) (16,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1747", "image": "data/cycle/graph_visual/medium/graph1747.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (3,0) (0,1) (16,4) (12,11) (5,11) (2,20) (4,24) (8,11) (4,0) (9,13) (17,12) (10,9) (16,18) (18,6) (8,3) (3,22) (19,0) (3,10) (2,0) (15,7) (0,14) (19,11) (18,21) (13,2) (23,4) (0,7) (24,0) (1,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph762", "image": "data/cycle/graph_visual/medium/graph762.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,15) (1,4) (18,10) (9,18) (6,0) (2,17) (18,12) (8,9) (13,9) (21,7) (11,2) (14,18) (19,11) (14,20) (1,22) (16,20) (8,11) (4,17) (6,15) (5,2) (15,21) (22,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph229", "image": "data/cycle/graph_visual/medium/graph229.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,8) (8,6) (2,10) (11,7) (9,13) (11,5) (8,12) (0,2) (13,12) (1,12) (12,2) (8,3) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1285", "image": "data/cycle/graph_visual/medium/graph1285.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (9,1) (16,12) (15,0) (2,0) (3,0) (13,11) (14,7) (4,0) (14,16) (8,6) (9,13) (1,0) (0,7) (4,6) (12,10) (5,9) (3,2) (11,4) (8,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1797", "image": "data/cycle/graph_visual/medium/graph1797.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (10,13) (24,15) (22,3) (14,5) (4,19) (6,2) (21,4) (0,1) (0,10) (3,7) (17,0) (6,10) (0,11) (16,12) (14,13) (14,20) (23,7) (12,1) (20,9) (24,10) (22,16) (5,19) (8,5) (21,18) (2,0) (22,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph454", "image": "data/cycle/graph_visual/medium/graph454.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,10) (12,4) (9,13) (15,13) (17,1) (1,3) (14,0) (6,16) (11,5) (8,2) (14,11) (4,5) (8,11) (17,16) (1,0) (7,15) (13,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph121", "image": "data/cycle/graph_visual/medium/graph121.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,5) (3,6) (11,2) (5,12) (11,10) (4,2) (3,2) (11,7) (1,9) (4,8) (1,0) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph747", "image": "data/cycle/graph_visual/medium/graph747.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (6,0) (4,20) (19,22) (0,12) (18,6) (17,10) (3,5) (14,6) (7,19) (9,12) (11,21) (21,20) (2,4) (20,17) (16,8) (20,3) (15,6) (22,8) (14,13) (15,1) (0,22) (2,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph466", "image": "data/cycle/graph_visual/medium/graph466.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (7,0) (11,5) (12,17) (8,9) (6,14) (16,0) (13,1) (15,12) (8,13) (7,5) (3,10) (11,17) (6,2) (4,1) (12,4) (3,9) (6,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1799", "image": "data/cycle/graph_visual/medium/graph1799.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,0) (18,13) (4,1) (0,4) (11,22) (8,17) (18,2) (8,23) (2,0) (7,8) (13,20) (5,7) (9,6) (0,16) (0,3) (2,9) (15,13) (0,5) (12,24) (16,5) (20,21) (20,14) (3,10) (10,0) (2,17) (11,17) (19,23) (15,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1584", "image": "data/cycle/graph_visual/medium/graph1584.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,14) (21,17) (7,19) (3,18) (17,5) (20,12) (6,7) (6,15) (0,16) (20,17) (7,1) (19,10) (17,8) (19,2) (4,11) (0,15) (13,18) (4,9) (1,0) (11,15) (8,18) (15,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph368", "image": "data/cycle/graph_visual/medium/graph368.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,8) (7,10) (0,8) (2,5) (6,14) (8,9) (1,13) (16,10) (13,2) (15,3) (4,11) (12,14) (3,0) (0,13) (1,12) (11,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph730", "image": "data/cycle/graph_visual/medium/graph730.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (3,13) (20,7) (9,5) (12,1) (22,10) (1,8) (20,3) (18,3) (21,18) (21,6) (18,9) (9,1) (19,16) (19,10) (18,17) (6,16) (15,13) (6,0) (11,15) (12,2) (14,8) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph103", "image": "data/cycle/graph_visual/medium/graph103.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,9) (6,2) (2,4) (8,4) (5,11) (2,1) (1,10) (5,6) (9,3) (1,0) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph532", "image": "data/cycle/graph_visual/medium/graph532.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (2,13) (16,9) (18,2) (6,15) (13,5) (14,15) (11,9) (7,8) (2,1) (17,3) (15,0) (1,9) (2,8) (8,4) (12,10) (0,10) (3,9) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph623", "image": "data/cycle/graph_visual/medium/graph623.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (18,9) (17,13) (7,5) (15,7) (0,6) (7,10) (2,3) (17,12) (7,18) (18,14) (19,1) (11,8) (20,19) (14,19) (18,17) (14,6) (10,3) (16,19) (12,11) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph24", "image": "data/cycle/graph_visual/medium/graph24.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (9,3) (6,4) (3,7) (10,6) (1,5) (0,7) (5,7) (2,7) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1368", "image": "data/cycle/graph_visual/medium/graph1368.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (17,8) (3,4) (1,0) (9,10) (11,2) (14,7) (9,13) (3,8) (16,4) (16,15) (1,16) (0,6) (2,13) (11,5) (0,7) (10,3) (11,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1359", "image": "data/cycle/graph_visual/medium/graph1359.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,4) (10,2) (13,4) (12,15) (2,0) (7,17) (5,13) (14,2) (16,3) (1,0) (11,8) (3,0) (1,15) (5,17) (6,16) (5,0) (3,8) (5,16) (9,17) (1,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1215", "image": "data/cycle/graph_visual/medium/graph1215.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (15,7) (14,2) (1,15) (2,12) (6,9) (14,0) (4,9) (9,1) (2,9) (0,1) (2,11) (8,2) (6,13) (8,5) (12,10) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1012", "image": "data/cycle/graph_visual/medium/graph1012.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,6) (8,3) (2,10) (0,3) (0,2) (4,0) (0,1) (8,7) (7,0) (8,1) (0,5) (9,0) (8,5) (9,11) (11,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph970", "image": "data/cycle/graph_visual/medium/graph970.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (3,1) (7,0) (1,10) (10,0) (4,2) (2,0) (11,4) (0,1) (10,11) (6,7) (5,3) (9,0) (0,4) (8,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph86", "image": "data/cycle/graph_visual/medium/graph86.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,8) (4,7) (10,9) (8,5) (10,3) (3,0) (11,3) (1,7) (2,9) (6,0) (10,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph619", "image": "data/cycle/graph_visual/medium/graph619.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (10,20) (14,11) (15,6) (0,3) (17,12) (17,2) (20,6) (6,19) (8,5) (13,14) (19,4) (18,6) (5,12) (1,4) (19,3) (4,5) (4,7) (9,7) (4,16) (13,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph157", "image": "data/cycle/graph_visual/medium/graph157.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,8) (5,11) (2,12) (3,12) (4,0) (11,1) (9,0) (7,5) (1,10) (0,12) (8,12) (8,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph533", "image": "data/cycle/graph_visual/medium/graph533.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,7) (4,5) (10,4) (1,16) (15,5) (11,3) (9,2) (0,15) (1,17) (18,6) (18,12) (14,3) (5,18) (2,11) (8,3) (13,12) (17,3) (11,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1165", "image": "data/cycle/graph_visual/medium/graph1165.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,11) (5,14) (12,8) (0,8) (13,7) (5,4) (0,2) (6,13) (14,12) (6,2) (12,3) (0,9) (10,12) (13,9) (1,0) (1,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1551", "image": "data/cycle/graph_visual/medium/graph1551.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,5) (2,0) (3,0) (2,3) (19,2) (13,14) (10,4) (3,4) (20,8) (10,11) (13,17) (10,15) (18,14) (13,0) (4,1) (18,15) (18,12) (7,8) (6,20) (13,6) (3,9) (1,0) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1082", "image": "data/cycle/graph_visual/medium/graph1082.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (11,4) (4,6) (8,2) (12,0) (8,3) (13,5) (7,5) (2,1) (9,4) (13,1) (0,10) (7,10) (1,0) (13,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1792", "image": "data/cycle/graph_visual/medium/graph1792.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (3,10) (11,5) (0,14) (9,13) (2,0) (12,17) (2,13) (1,16) (11,8) (3,22) (0,3) (1,0) (0,24) (2,20) (18,6) (19,0) (19,11) (23,4) (9,10) (7,0) (4,24) (21,18) (3,8) (7,15) (11,12) (16,18) (16,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1689", "image": "data/cycle/graph_visual/medium/graph1689.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,11) (22,6) (17,13) (8,13) (18,16) (19,1) (4,17) (11,10) (12,14) (20,17) (12,17) (1,0) (15,11) (0,23) (11,9) (22,19) (12,7) (12,1) (8,2) (12,3) (16,5) (18,0) (7,21) (7,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph843", "image": "data/cycle/graph_visual/medium/graph843.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (14,8) (6,7) (21,15) (12,17) (7,17) (3,4) (18,11) (24,9) (5,6) (20,17) (19,18) (7,24) (19,2) (24,18) (1,22) (6,0) (24,10) (23,19) (21,18) (3,10) (13,11) (7,14) (12,16) (21,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph761", "image": "data/cycle/graph_visual/medium/graph761.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (20,13) (6,12) (7,11) (11,10) (19,10) (18,0) (6,3) (1,17) (15,12) (8,4) (20,2) (3,10) (8,11) (8,2) (1,22) (21,10) (22,16) (9,10) (14,21) (4,16) (0,5) (13,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1415", "image": "data/cycle/graph_visual/medium/graph1415.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (10,3) (1,15) (11,7) (5,13) (12,6) (10,11) (1,0) (6,3) (2,8) (14,12) (17,10) (2,0) (4,8) (18,4) (10,13) (16,2) (0,6) (4,0) (0,5) (10,9) (11,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph408", "image": "data/cycle/graph_visual/medium/graph408.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,2) (2,15) (11,10) (4,15) (1,0) (1,9) (15,8) (3,16) (3,13) (14,11) (6,15) (7,8) (12,4) (0,8) (0,10) (6,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1452", "image": "data/cycle/graph_visual/medium/graph1452.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,13) (0,5) (17,16) (1,0) (1,18) (9,17) (0,12) (1,15) (5,17) (8,2) (19,0) (3,6) (10,4) (2,0) (0,4) (11,15) (0,3) (14,2) (8,6) (19,3) (6,18) (16,7) (19,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph91", "image": "data/cycle/graph_visual/medium/graph91.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,11) (9,5) (2,5) (4,5) (1,9) (7,11) (4,11) (6,2) (8,10) (9,8) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1727", "image": "data/cycle/graph_visual/medium/graph1727.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,9) (0,15) (8,23) (18,6) (14,10) (0,2) (0,1) (23,22) (13,19) (11,15) (0,22) (15,3) (2,5) (2,8) (20,12) (4,1) (16,20) (12,13) (21,14) (12,17) (19,0) (18,4) (8,14) (7,3) (3,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1208", "image": "data/cycle/graph_visual/medium/graph1208.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,13) (4,8) (3,14) (15,0) (2,0) (5,6) (10,1) (9,5) (0,3) (2,1) (13,15) (12,6) (9,2) (2,7) (0,1) (12,4) (6,14) (11,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1618", "image": "data/cycle/graph_visual/medium/graph1618.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (3,14) (2,5) (8,9) (4,6) (13,1) (4,21) (11,15) (18,16) (10,1) (17,4) (16,15) (6,2) (7,15) (16,1) (0,19) (19,11) (0,12) (9,7) (20,10) (0,17) (1,0) (10,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1381", "image": "data/cycle/graph_visual/medium/graph1381.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (15,11) (6,7) (2,5) (2,0) (18,12) (16,11) (5,14) (1,18) (4,12) (5,3) (13,14) (6,15) (14,9) (14,10) (8,7) (17,6) (14,8) (3,0) (6,12) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph335", "image": "data/cycle/graph_visual/medium/graph335.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (5,7) (11,0) (12,0) (12,7) (8,2) (1,12) (11,8) (7,13) (11,10) (11,6) (14,1) (3,12) (13,4) (15,5) (9,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1620", "image": "data/cycle/graph_visual/medium/graph1620.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (14,8) (20,7) (19,16) (13,15) (1,9) (20,3) (0,6) (1,0) (15,11) (9,18) (12,2) (21,6) (4,0) (16,6) (18,21) (18,3) (13,3) (19,10) (1,8) (22,10) (12,1) (18,17) (9,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph695", "image": "data/cycle/graph_visual/medium/graph695.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (10,8) (1,3) (19,2) (4,14) (1,6) (16,19) (4,21) (17,9) (12,14) (7,11) (11,13) (20,17) (14,18) (5,3) (13,15) (10,16) (18,13) (17,14) (10,17) (5,2) (21,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph790", "image": "data/cycle/graph_visual/medium/graph790.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (8,10) (9,13) (16,18) (6,11) (22,0) (15,6) (14,17) (4,3) (1,19) (19,0) (3,14) (21,14) (3,12) (5,10) (23,22) (16,8) (9,5) (16,19) (14,5) (7,10) (3,11) (16,2) (8,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1007", "image": "data/cycle/graph_visual/medium/graph1007.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,6) (2,3) (9,10) (0,2) (8,3) (3,0) (1,0) (4,0) (0,11) (7,2) (11,10) (3,6) (2,10) (9,4) (5,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph617", "image": "data/cycle/graph_visual/medium/graph617.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (12,8) (7,18) (2,10) (1,12) (9,17) (5,20) (0,17) (4,14) (19,4) (12,18) (6,5) (11,12) (0,7) (15,9) (18,13) (8,16) (10,5) (0,14) (10,4) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph433", "image": "data/cycle/graph_visual/medium/graph433.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (3,7) (3,13) (15,0) (11,12) (4,9) (11,6) (3,12) (1,17) (10,12) (5,1) (11,16) (14,5) (11,2) (2,8) (5,4) (3,17) (3,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph723", "image": "data/cycle/graph_visual/medium/graph723.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (4,0) (0,19) (8,15) (1,17) (19,6) (5,17) (16,19) (4,10) (20,21) (16,7) (13,4) (18,16) (20,6) (0,12) (3,20) (2,14) (17,9) (8,6) (3,22) (20,2) (18,1) (15,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph558", "image": "data/cycle/graph_visual/medium/graph558.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (19,15) (14,0) (11,5) (0,16) (7,3) (17,15) (13,6) (4,2) (4,9) (16,7) (4,7) (6,12) (15,12) (12,8) (2,1) (6,10) (14,12) (14,18) (1,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1194", "image": "data/cycle/graph_visual/medium/graph1194.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,2) (10,5) (6,3) (1,0) (14,8) (4,12) (7,13) (11,2) (11,8) (4,0) (5,12) (4,1) (9,13) (1,13) (10,8) (3,0) (3,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph848", "image": "data/cycle/graph_visual/medium/graph848.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,9) (21,16) (7,13) (18,0) (16,22) (7,17) (3,7) (17,4) (8,3) (2,16) (1,13) (14,9) (24,12) (0,15) (3,5) (5,10) (18,19) (23,9) (24,5) (6,22) (12,11) (20,12) (22,20) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph97", "image": "data/cycle/graph_visual/medium/graph97.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,7) (3,6) (4,5) (10,4) (7,1) (4,8) (0,5) (9,1) (0,1) (11,7) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph666", "image": "data/cycle/graph_visual/medium/graph666.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (20,11) (4,7) (10,7) (4,5) (17,3) (0,6) (3,1) (6,19) (2,4) (13,14) (5,9) (6,16) (21,0) (19,8) (5,12) (4,17) (20,6) (6,13) (4,19) (14,15) (12,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph731", "image": "data/cycle/graph_visual/medium/graph731.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (16,11) (13,19) (6,15) (8,4) (15,14) (16,19) (20,22) (18,0) (16,17) (7,3) (9,21) (10,18) (7,20) (8,17) (2,20) (5,1) (14,9) (21,20) (5,12) (21,10) (15,16) (5,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph997", "image": "data/cycle/graph_visual/medium/graph997.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,2) (9,11) (8,5) (2,0) (3,0) (1,0) (4,11) (0,4) (7,8) (7,0) (2,6) (8,1) (3,8) (9,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1263", "image": "data/cycle/graph_visual/medium/graph1263.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,14) (1,0) (7,3) (3,4) (7,15) (5,8) (9,0) (0,10) (5,14) (12,0) (4,13) (16,14) (2,6) (4,5) (0,2) (16,11) (12,1) (6,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1560", "image": "data/cycle/graph_visual/medium/graph1560.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (17,12) (20,7) (20,8) (0,2) (6,5) (16,1) (14,8) (0,4) (1,6) (3,18) (11,12) (18,2) (1,0) (6,4) (6,10) (21,15) (9,11) (15,0) (19,13) (19,14) (9,13) (9,18) (0,3) (14,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1781", "image": "data/cycle/graph_visual/medium/graph1781.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (19,21) (21,3) (12,0) (15,1) (21,6) (2,8) (0,2) (20,22) (19,22) (13,12) (1,0) (4,19) (16,5) (24,14) (11,16) (21,0) (11,15) (10,4) (14,4) (17,7) (0,3) (11,9) (20,8) (18,14) (23,7) (15,8) (0,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1190", "image": "data/cycle/graph_visual/medium/graph1190.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,2) (2,0) (13,1) (1,0) (10,3) (11,8) (5,0) (13,12) (6,8) (5,8) (3,13) (4,8) (4,0) (0,3) (13,9) (7,2) (14,4) (13,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph566", "image": "data/cycle/graph_visual/medium/graph566.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,9) (14,0) (3,8) (4,16) (6,18) (15,7) (12,0) (18,17) (16,1) (7,0) (3,10) (8,19) (2,13) (2,11) (11,5) (13,9) (16,18) (12,11) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph629", "image": "data/cycle/graph_visual/medium/graph629.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,8) (2,6) (10,8) (14,20) (16,0) (1,19) (8,2) (16,11) (12,4) (15,16) (19,0) (3,10) (16,6) (1,17) (0,9) (14,11) (6,18) (16,5) (19,7) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph12", "image": "data/cycle/graph_visual/medium/graph12.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,2) (0,10) (4,3) (6,3) (8,7) (2,6) (8,9) (0,4) (6,5) (1,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1418", "image": "data/cycle/graph_visual/medium/graph1418.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,2) (12,15) (9,4) (7,5) (12,10) (4,3) (17,11) (17,16) (11,2) (1,6) (9,15) (12,16) (6,2) (5,9) (10,13) (2,8) (1,0) (18,13) (12,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph823", "image": "data/cycle/graph_visual/medium/graph823.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (16,21) (1,4) (15,12) (13,1) (6,0) (11,1) (18,17) (13,23) (13,9) (14,15) (1,5) (6,14) (15,16) (10,15) (23,7) (8,20) (8,19) (5,20) (10,2) (0,18) (2,7) (18,3) (22,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph796", "image": "data/cycle/graph_visual/medium/graph796.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (18,23) (4,21) (21,23) (1,9) (13,17) (8,7) (0,8) (21,17) (11,10) (16,15) (5,2) (2,15) (8,15) (0,1) (22,17) (13,20) (18,14) (4,12) (0,10) (6,15) (23,6) (19,11) (3,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1252", "image": "data/cycle/graph_visual/medium/graph1252.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,11) (11,5) (13,7) (2,0) (2,9) (14,6) (11,0) (6,12) (1,12) (9,13) (0,1) (4,1) (15,2) (11,3) (15,0) (3,0) (10,15) (1,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph113", "image": "data/cycle/graph_visual/medium/graph113.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,2) (2,4) (3,7) (1,2) (9,10) (8,5) (11,0) (4,6) (8,2) (0,2) (4,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1173", "image": "data/cycle/graph_visual/medium/graph1173.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (5,7) (4,9) (0,1) (13,14) (10,4) (7,9) (0,4) (3,0) (4,14) (12,6) (1,12) (6,7) (9,11) (0,2) (3,6) (5,0) (6,8) (2,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1117", "image": "data/cycle/graph_visual/medium/graph1117.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,7) (10,7) (3,2) (1,13) (7,0) (6,12) (5,13) (13,8) (7,11) (0,1) (8,4) (3,9) (9,12) (2,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1315", "image": "data/cycle/graph_visual/medium/graph1315.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,11) (15,2) (12,6) (0,15) (11,0) (4,1) (12,1) (5,11) (10,15) (7,13) (11,3) (9,2) (8,1) (9,13) (0,16) (0,1) (14,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1256", "image": "data/cycle/graph_visual/medium/graph1256.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,0) (13,0) (7,0) (12,10) (5,0) (1,8) (7,14) (6,8) (1,12) (4,11) (12,14) (4,2) (15,2) (9,3) (0,2) (9,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph685", "image": "data/cycle/graph_visual/medium/graph685.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (21,12) (5,4) (3,14) (8,3) (14,4) (0,15) (18,20) (11,18) (6,11) (19,17) (19,9) (13,17) (16,0) (13,12) (21,7) (2,1) (13,16) (11,19) (1,9) (15,10) (14,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1423", "image": "data/cycle/graph_visual/medium/graph1423.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,11) (15,18) (13,14) (15,10) (13,0) (4,10) (9,18) (1,0) (13,12) (8,6) (5,0) (7,3) (1,4) (10,8) (14,17) (4,3) (18,13) (2,16) (2,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph736", "image": "data/cycle/graph_visual/medium/graph736.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (14,2) (8,7) (20,6) (7,22) (22,9) (15,17) (13,10) (0,15) (11,3) (20,17) (1,8) (11,10) (19,21) (7,18) (2,17) (4,11) (12,15) (5,11) (10,16) (4,2) (21,3) (7,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph656", "image": "data/cycle/graph_visual/medium/graph656.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,19) (16,12) (3,18) (13,9) (15,1) (18,9) (6,10) (0,20) (14,6) (17,8) (14,19) (7,20) (6,5) (6,1) (3,0) (14,8) (6,4) (11,9) (18,2) (12,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1579", "image": "data/cycle/graph_visual/medium/graph1579.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (10,19) (16,20) (1,16) (17,14) (0,2) (10,18) (11,12) (9,12) (13,17) (12,8) (4,7) (0,7) (21,18) (6,17) (17,16) (8,21) (5,3) (7,5) (15,14) (11,20) (7,8) (17,2) (0,1) (3,0) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1316", "image": "data/cycle/graph_visual/medium/graph1316.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,7) (5,11) (1,10) (12,2) (16,6) (1,0) (9,15) (5,15) (5,14) (1,13) (2,10) (16,3) (16,5) (5,0) (2,0) (13,4) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph167", "image": "data/cycle/graph_visual/medium/graph167.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,11) (12,3) (4,3) (9,2) (0,12) (4,2) (8,9) (7,10) (4,1) (0,5) (6,4) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph721", "image": "data/cycle/graph_visual/medium/graph721.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (14,18) (1,22) (3,22) (9,8) (4,17) (11,19) (14,20) (21,7) (2,11) (9,18) (8,15) (21,15) (2,17) (1,4) (10,18) (20,16) (13,9) (0,6) (12,18) (2,5) (11,8) (15,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph96", "image": "data/cycle/graph_visual/medium/graph96.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,3) (7,5) (8,11) (7,0) (5,1) (7,10) (6,10) (4,5) (1,8) (11,3) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph572", "image": "data/cycle/graph_visual/medium/graph572.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (8,11) (9,13) (1,10) (4,15) (11,14) (17,12) (5,4) (16,6) (13,5) (14,19) (0,1) (15,7) (11,5) (0,18) (17,1) (2,8) (14,12) (16,13) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph521", "image": "data/cycle/graph_visual/medium/graph521.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,4) (17,2) (5,10) (7,11) (8,18) (4,12) (17,13) (9,3) (8,1) (14,7) (6,9) (0,8) (4,5) (13,4) (2,15) (7,5) (0,9) (16,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph710", "image": "data/cycle/graph_visual/medium/graph710.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (10,15) (1,11) (21,19) (1,9) (17,3) (6,0) (12,8) (18,15) (4,0) (9,18) (16,6) (6,20) (20,7) (21,18) (12,2) (13,14) (5,9) (16,19) (18,3) (1,8) (13,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1609", "image": "data/cycle/graph_visual/medium/graph1609.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (15,21) (7,12) (16,4) (6,17) (21,6) (1,4) (11,8) (20,1) (9,21) (3,18) (3,0) (20,13) (14,0) (18,4) (9,7) (11,19) (0,1) (0,16) (2,0) (2,14) (1,10) (6,20) (14,8) (16,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1534", "image": "data/cycle/graph_visual/medium/graph1534.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,1) (17,14) (2,0) (12,6) (0,15) (1,9) (15,4) (4,10) (7,4) (1,19) (13,4) (14,16) (17,7) (3,5) (4,0) (7,12) (0,1) (3,0) (18,1) (11,3) (17,3) (8,4) (16,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph312", "image": "data/cycle/graph_visual/medium/graph312.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,12) (3,8) (5,1) (13,15) (13,2) (14,4) (14,3) (12,14) (11,6) (1,4) (7,14) (2,0) (1,2) (10,9) (11,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph162", "image": "data/cycle/graph_visual/medium/graph162.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,2) (11,6) (10,7) (2,8) (4,12) (5,7) (0,10) (4,1) (4,9) (6,0) (5,4) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph577", "image": "data/cycle/graph_visual/medium/graph577.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,11) (13,17) (18,15) (7,6) (1,13) (4,3) (3,5) (0,2) (19,16) (0,9) (7,16) (2,14) (4,12) (17,3) (7,8) (10,8) (18,19) (6,2) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph163", "image": "data/cycle/graph_visual/medium/graph163.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,6) (8,1) (3,7) (4,5) (0,10) (7,6) (8,5) (7,12) (2,0) (9,8) (2,7) (11,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1058", "image": "data/cycle/graph_visual/medium/graph1058.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,0) (3,0) (5,4) (8,12) (0,8) (2,4) (8,11) (1,6) (6,4) (2,0) (12,2) (11,10) (11,9) (5,7) (12,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1581", "image": "data/cycle/graph_visual/medium/graph1581.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (11,21) (15,17) (19,20) (0,2) (1,0) (18,14) (3,2) (10,3) (7,10) (4,6) (8,11) (7,21) (14,6) (16,7) (18,17) (6,0) (21,14) (7,5) (12,17) (19,18) (9,18) (12,13) (3,0) (19,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph407", "image": "data/cycle/graph_visual/medium/graph407.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,1) (15,7) (13,5) (2,11) (2,0) (16,9) (14,1) (3,10) (6,3) (10,16) (1,12) (1,16) (14,4) (4,8) (7,9) (8,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph42", "image": "data/cycle/graph_visual/medium/graph42.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,4) (1,4) (0,1) (6,8) (1,9) (0,10) (2,7) (6,7) (2,1) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph328", "image": "data/cycle/graph_visual/medium/graph328.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,10) (9,0) (13,7) (11,0) (5,14) (3,7) (2,6) (14,10) (6,10) (12,4) (4,3) (15,14) (12,1) (5,8) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1433", "image": "data/cycle/graph_visual/medium/graph1433.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,12) (9,12) (4,9) (17,18) (14,2) (14,7) (10,18) (0,1) (6,1) (7,11) (17,3) (16,6) (12,6) (10,13) (5,15) (15,17) (15,8) (15,1) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph633", "image": "data/cycle/graph_visual/medium/graph633.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (11,16) (11,2) (5,7) (17,11) (17,20) (13,5) (2,4) (14,6) (1,18) (19,6) (13,20) (0,1) (1,15) (8,19) (2,3) (12,19) (10,9) (16,12) (9,8) (18,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph554", "image": "data/cycle/graph_visual/medium/graph554.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,5) (6,2) (7,17) (15,14) (5,18) (10,13) (19,10) (1,12) (3,7) (16,11) (9,0) (16,4) (12,0) (3,4) (10,0) (6,10) (4,19) (13,14) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph479", "image": "data/cycle/graph_visual/medium/graph479.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (13,10) (9,12) (11,8) (6,12) (11,4) (1,0) (10,7) (2,15) (2,8) (3,6) (10,3) (16,10) (13,5) (10,11) (5,0) (8,17) (1,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph149", "image": "data/cycle/graph_visual/medium/graph149.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,4) (8,9) (4,0) (6,1) (0,5) (4,11) (8,7) (12,2) (12,7) (6,10) (3,6) (12,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph40", "image": "data/cycle/graph_visual/medium/graph40.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,0) (7,2) (0,3) (5,9) (8,10) (6,8) (6,7) (10,1) (4,1) (3,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1667", "image": "data/cycle/graph_visual/medium/graph1667.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,17) (21,10) (4,3) (17,8) (8,3) (22,14) (11,13) (21,0) (14,11) (5,9) (0,1) (13,6) (5,2) (20,13) (11,15) (18,19) (9,13) (16,9) (13,0) (8,19) (7,0) (15,12) (0,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1155", "image": "data/cycle/graph_visual/medium/graph1155.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (6,13) (4,2) (11,5) (2,8) (9,0) (14,0) (0,1) (7,12) (4,9) (5,3) (2,12) (4,6) (11,10) (3,0) (8,1) (2,0) (5,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1425", "image": "data/cycle/graph_visual/medium/graph1425.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,18) (14,18) (5,3) (10,15) (13,9) (2,4) (16,17) (1,3) (0,2) (17,14) (17,10) (16,13) (5,10) (12,14) (1,0) (11,2) (8,14) (17,6) (7,13) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1254", "image": "data/cycle/graph_visual/medium/graph1254.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,10) (11,4) (15,8) (5,2) (1,12) (0,1) (8,0) (13,0) (14,6) (12,11) (13,2) (1,13) (9,8) (3,0) (7,10) (3,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph365", "image": "data/cycle/graph_visual/medium/graph365.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (9,0) (7,11) (4,12) (4,3) (10,8) (13,14) (0,2) (7,16) (1,13) (16,15) (3,5) (1,0) (8,7) (3,2) (6,2) (6,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph556", "image": "data/cycle/graph_visual/medium/graph556.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (6,14) (19,3) (12,5) (6,17) (7,4) (5,8) (4,15) (18,6) (14,10) (11,13) (4,19) (3,0) (6,13) (6,19) (2,17) (4,5) (4,1) (16,12) (7,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph584", "image": "data/cycle/graph_visual/medium/graph584.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,6) (9,1) (14,0) (13,9) (2,0) (4,11) (19,0) (2,3) (7,19) (13,12) (10,9) (12,16) (18,14) (0,16) (14,8) (17,7) (6,8) (15,11) (18,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph90", "image": "data/cycle/graph_visual/medium/graph90.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,4) (6,3) (11,9) (3,1) (9,8) (5,3) (2,5) (4,7) (7,8) (1,4) (10,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1005", "image": "data/cycle/graph_visual/medium/graph1005.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (8,1) (11,4) (8,5) (2,0) (3,6) (5,6) (3,0) (0,8) (2,10) (1,0) (0,7) (3,10) (1,9) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph732", "image": "data/cycle/graph_visual/medium/graph732.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (22,19) (1,10) (21,9) (18,4) (6,19) (14,0) (7,9) (21,11) (2,14) (6,17) (11,8) (6,20) (20,1) (4,16) (8,14) (5,16) (18,3) (12,7) (20,13) (1,4) (16,0) (15,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph16", "image": "data/cycle/graph_visual/medium/graph16.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,3) (0,9) (10,5) (10,2) (4,7) (6,5) (2,8) (1,7) (5,0) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph526", "image": "data/cycle/graph_visual/medium/graph526.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (9,12) (14,7) (6,16) (6,12) (1,15) (15,5) (10,13) (18,10) (11,7) (0,4) (14,12) (4,9) (2,14) (6,1) (17,18) (17,15) (15,8) (3,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1420", "image": "data/cycle/graph_visual/medium/graph1420.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (18,17) (4,0) (3,0) (15,5) (0,6) (18,0) (8,18) (0,2) (0,1) (2,11) (8,10) (9,17) (16,6) (12,16) (2,10) (17,1) (3,7) (15,13) (11,3) (13,7) (9,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph832", "image": "data/cycle/graph_visual/medium/graph832.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,21) (22,17) (10,20) (0,8) (3,11) (9,8) (12,2) (13,10) (12,8) (17,6) (20,14) (15,2) (22,23) (1,4) (4,23) (11,0) (16,19) (6,5) (22,19) (17,18) (22,10) (15,16) (3,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph622", "image": "data/cycle/graph_visual/medium/graph622.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (2,4) (5,11) (7,14) (14,18) (15,5) (14,13) (6,13) (4,16) (14,20) (10,7) (12,9) (17,3) (2,0) (8,9) (11,2) (9,1) (16,19) (13,5) (8,17) (15,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1066", "image": "data/cycle/graph_visual/medium/graph1066.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,6) (0,1) (10,4) (6,0) (0,2) (9,8) (7,12) (11,2) (4,3) (5,0) (7,1) (5,7) (8,10) (5,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1645", "image": "data/cycle/graph_visual/medium/graph1645.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (9,20) (2,16) (9,18) (8,5) (20,1) (2,0) (14,10) (8,11) (2,19) (2,4) (4,8) (12,2) (6,13) (9,13) (15,7) (15,0) (19,1) (10,0) (1,0) (3,9) (3,0) (4,0) (3,21) (8,22) (17,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph924", "image": "data/cycle/graph_visual/medium/graph924.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,4) (7,5) (3,10) (2,0) (9,0) (1,2) (3,0) (1,0) (6,5) (3,8) (3,2) (2,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph680", "image": "data/cycle/graph_visual/medium/graph680.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (15,10) (6,16) (15,14) (11,15) (21,17) (19,3) (12,9) (0,12) (6,18) (17,8) (19,8) (12,13) (16,7) (1,5) (20,9) (8,1) (18,11) (13,2) (4,3) (9,4) (4,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph872", "image": "data/cycle/graph_visual/medium/graph872.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (17,16) (9,13) (1,15) (19,8) (11,3) (3,23) (23,1) (14,18) (10,4) (0,17) (8,13) (21,22) (7,23) (11,24) (18,24) (9,4) (12,10) (16,24) (20,11) (4,6) (8,20) (18,22) (5,24) (10,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1211", "image": "data/cycle/graph_visual/medium/graph1211.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,10) (9,4) (15,7) (5,2) (12,3) (6,2) (0,3) (1,15) (10,13) (2,0) (11,15) (14,11) (4,6) (10,1) (0,1) (0,9) (7,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph358", "image": "data/cycle/graph_visual/medium/graph358.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,9) (6,9) (13,1) (15,2) (4,15) (1,5) (12,8) (0,4) (11,5) (9,4) (6,3) (13,15) (14,3) (10,5) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1321", "image": "data/cycle/graph_visual/medium/graph1321.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (11,9) (9,13) (8,14) (0,13) (11,12) (8,17) (9,5) (16,13) (2,5) (0,15) (4,3) (13,6) (10,15) (0,7) (3,8) (17,1) (0,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph647", "image": "data/cycle/graph_visual/medium/graph647.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (19,11) (5,0) (10,12) (10,7) (8,16) (1,3) (6,14) (1,15) (9,2) (11,18) (6,9) (0,16) (16,14) (17,15) (14,12) (17,8) (20,10) (4,19) (13,15) (4,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1736", "image": "data/cycle/graph_visual/medium/graph1736.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,2) (10,1) (12,6) (21,1) (4,15) (17,7) (23,18) (8,4) (3,5) (16,4) (1,0) (22,14) (3,12) (1,19) (21,20) (17,3) (7,4) (4,1) (21,9) (22,23) (0,15) (3,0) (4,0) (4,11) (7,13) (23,17) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1467", "image": "data/cycle/graph_visual/medium/graph1467.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (16,10) (17,13) (0,1) (8,19) (0,7) (15,14) (7,8) (12,11) (16,1) (0,2) (9,12) (3,5) (14,17) (6,17) (18,11) (18,10) (4,7) (2,17) (5,7) (4,0) (12,8) (0,3) (17,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph74", "image": "data/cycle/graph_visual/medium/graph74.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,4) (5,1) (8,6) (8,10) (3,4) (7,9) (2,7) (9,6) (3,0) (0,10) (10,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph306", "image": "data/cycle/graph_visual/medium/graph306.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,11) (8,13) (12,10) (4,11) (10,8) (3,0) (9,2) (15,12) (9,6) (7,12) (5,9) (5,8) (13,14) (0,7) (1,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1398", "image": "data/cycle/graph_visual/medium/graph1398.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,5) (11,2) (17,8) (7,10) (14,17) (9,8) (4,16) (15,3) (13,3) (0,2) (5,18) (0,3) (15,5) (1,9) (12,9) (13,6) (0,1) (7,14) (14,16) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph606", "image": "data/cycle/graph_visual/medium/graph606.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,15) (18,4) (4,14) (8,0) (17,19) (8,9) (15,2) (17,13) (1,12) (5,18) (10,11) (0,1) (6,15) (7,2) (20,3) (3,17) (11,18) (0,10) (13,6) (8,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph516", "image": "data/cycle/graph_visual/medium/graph516.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (7,6) (0,10) (0,18) (4,12) (0,5) (5,16) (3,8) (15,8) (2,11) (18,12) (7,12) (6,1) (2,9) (13,6) (0,11) (9,17) (8,11) (0,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1544", "image": "data/cycle/graph_visual/medium/graph1544.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,0) (3,17) (3,5) (16,1) (20,14) (9,16) (19,11) (7,13) (4,8) (11,15) (3,18) (2,19) (14,0) (7,15) (7,12) (6,11) (20,8) (20,18) (17,12) (0,10) (5,1) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1151", "image": "data/cycle/graph_visual/medium/graph1151.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,13) (3,0) (2,4) (4,0) (0,5) (6,3) (14,4) (1,4) (5,11) (7,6) (4,8) (1,9) (10,4) (7,0) (12,1) (1,0) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1706", "image": "data/cycle/graph_visual/medium/graph1706.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,14) (5,6) (23,4) (23,10) (8,12) (0,2) (0,1) (16,8) (5,12) (4,21) (12,1) (22,10) (0,20) (7,21) (18,11) (3,0) (9,17) (19,7) (3,7) (18,17) (12,23) (18,0) (14,4) (10,2) (9,15) (22,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1249", "image": "data/cycle/graph_visual/medium/graph1249.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,0) (10,11) (14,8) (7,14) (1,0) (6,13) (6,4) (3,10) (0,3) (4,3) (2,0) (2,15) (9,1) (12,2) (12,13) (9,4) (7,12) (5,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph612", "image": "data/cycle/graph_visual/medium/graph612.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,13) (16,14) (19,12) (19,3) (2,13) (10,11) (18,1) (8,0) (10,8) (14,7) (8,15) (9,18) (5,2) (15,20) (17,6) (17,12) (11,4) (13,0) (0,3) (16,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph250", "image": "data/cycle/graph_visual/medium/graph250.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,3) (14,6) (2,3) (13,3) (4,1) (11,6) (9,8) (2,12) (5,6) (3,7) (6,0) (11,4) (2,9) (12,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph92", "image": "data/cycle/graph_visual/medium/graph92.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,7) (8,7) (8,1) (8,6) (7,11) (2,8) (9,10) (0,7) (3,9) (7,4) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph44", "image": "data/cycle/graph_visual/medium/graph44.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,7) (8,0) (2,6) (9,3) (6,0) (3,10) (10,0) (4,7) (2,1) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph742", "image": "data/cycle/graph_visual/medium/graph742.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (13,22) (8,10) (11,7) (3,5) (19,18) (17,14) (17,10) (13,11) (1,3) (0,21) (15,13) (14,4) (17,9) (1,6) (17,21) (14,18) (12,14) (20,16) (16,10) (4,13) (19,2) (2,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph704", "image": "data/cycle/graph_visual/medium/graph704.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (10,3) (4,6) (21,2) (16,19) (9,10) (4,1) (0,8) (21,20) (17,14) (17,5) (10,17) (12,8) (7,8) (11,0) (15,18) (2,12) (2,19) (15,16) (13,20) (3,6) (11,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph69", "image": "data/cycle/graph_visual/medium/graph69.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,2) (3,0) (11,10) (0,7) (10,0) (1,3) (0,4) (6,11) (8,5) (9,0) (2,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph929", "image": "data/cycle/graph_visual/medium/graph929.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,3) (10,1) (1,6) (7,4) (0,7) (2,0) (7,10) (4,5) (9,6) (8,1) (3,0) (7,2) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph684", "image": "data/cycle/graph_visual/medium/graph684.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (4,9) (11,12) (13,2) (0,20) (2,20) (18,20) (8,10) (15,1) (19,7) (5,7) (7,15) (6,9) (10,17) (2,6) (8,11) (17,16) (18,21) (2,15) (8,14) (12,5) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph626", "image": "data/cycle/graph_visual/medium/graph626.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,4) (13,11) (17,2) (9,6) (8,17) (19,8) (18,20) (5,7) (10,0) (3,10) (20,15) (0,16) (2,9) (11,17) (16,13) (5,14) (20,12) (7,8) (1,0) (2,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1222", "image": "data/cycle/graph_visual/medium/graph1222.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,15) (5,8) (13,8) (3,1) (6,0) (1,5) (3,0) (0,11) (13,4) (14,6) (1,15) (12,15) (10,14) (2,10) (2,0) (2,7) (15,7) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph486", "image": "data/cycle/graph_visual/medium/graph486.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,9) (10,8) (2,16) (14,5) (12,7) (11,4) (10,16) (6,13) (10,14) (15,3) (3,0) (7,17) (4,3) (2,12) (12,13) (14,9) (4,6) (8,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph741", "image": "data/cycle/graph_visual/medium/graph741.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (7,17) (22,13) (0,4) (6,21) (10,2) (16,13) (6,0) (11,3) (2,19) (8,20) (9,17) (18,0) (20,10) (16,14) (7,3) (20,12) (15,5) (11,19) (17,1) (18,8) (15,9) (22,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph973", "image": "data/cycle/graph_visual/medium/graph973.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,11) (11,9) (11,4) (0,3) (0,1) (2,6) (2,4) (1,5) (8,3) (10,0) (3,7) (7,0) (1,3) (2,0) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph226", "image": "data/cycle/graph_visual/medium/graph226.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,1) (12,6) (12,5) (0,2) (4,1) (12,7) (11,7) (9,4) (7,13) (1,7) (10,12) (9,2) (3,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1778", "image": "data/cycle/graph_visual/medium/graph1778.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (20,12) (18,11) (5,19) (6,17) (4,2) (9,15) (8,22) (3,13) (16,15) (5,16) (2,13) (0,1) (7,24) (0,21) (6,15) (1,5) (10,13) (0,22) (7,16) (4,24) (11,0) (7,23) (18,13) (20,16) (14,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph319", "image": "data/cycle/graph_visual/medium/graph319.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,11) (9,6) (0,13) (9,7) (14,15) (8,11) (5,7) (4,0) (10,4) (8,14) (1,4) (1,6) (2,14) (1,3) (6,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph446", "image": "data/cycle/graph_visual/medium/graph446.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (8,13) (1,5) (7,8) (9,14) (6,15) (6,16) (14,11) (17,12) (0,2) (14,5) (12,6) (2,5) (3,12) (11,15) (4,14) (14,10) (6,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph947", "image": "data/cycle/graph_visual/medium/graph947.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,8) (5,2) (1,0) (9,7) (10,9) (4,10) (2,0) (5,4) (8,6) (1,9) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph811", "image": "data/cycle/graph_visual/medium/graph811.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (19,23) (10,21) (13,14) (13,4) (20,8) (14,11) (10,19) (10,11) (23,7) (3,2) (1,19) (23,22) (11,2) (5,17) (21,16) (0,20) (18,11) (22,8) (15,1) (5,18) (9,3) (13,6) (12,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1175", "image": "data/cycle/graph_visual/medium/graph1175.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,0) (1,5) (6,12) (8,2) (9,7) (9,13) (6,14) (14,3) (8,0) (14,0) (5,13) (4,5) (0,2) (6,1) (3,10) (11,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph686", "image": "data/cycle/graph_visual/medium/graph686.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (15,12) (14,6) (1,4) (21,1) (8,18) (0,17) (11,1) (7,2) (14,15) (20,16) (5,1) (13,18) (0,6) (18,3) (8,20) (7,11) (15,10) (19,5) (13,9) (16,15) (10,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph835", "image": "data/cycle/graph_visual/medium/graph835.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,20) (3,2) (20,12) (15,0) (1,7) (4,8) (0,19) (14,21) (14,6) (23,21) (13,0) (7,0) (17,15) (15,12) (5,9) (23,5) (18,10) (9,4) (22,11) (18,22) (17,9) (19,16) (10,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph539", "image": "data/cycle/graph_visual/medium/graph539.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (16,10) (5,3) (7,14) (17,1) (17,18) (4,2) (15,5) (14,3) (9,14) (14,8) (4,9) (12,6) (16,13) (14,0) (2,17) (18,11) (15,16) (5,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph98", "image": "data/cycle/graph_visual/medium/graph98.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,2) (10,11) (11,4) (8,7) (0,1) (5,1) (2,1) (3,4) (9,5) (7,6) (2,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1291", "image": "data/cycle/graph_visual/medium/graph1291.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,11) (7,15) (2,0) (8,6) (0,1) (14,16) (3,9) (12,10) (1,12) (0,3) (9,6) (0,4) (0,5) (4,2) (8,1) (16,2) (12,14) (0,13) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph429", "image": "data/cycle/graph_visual/medium/graph429.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (10,12) (8,4) (9,2) (4,11) (0,15) (6,16) (14,1) (1,12) (11,17) (1,13) (2,7) (1,2) (13,4) (9,5) (14,3) (15,6) (5,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1299", "image": "data/cycle/graph_visual/medium/graph1299.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,2) (3,0) (15,16) (15,14) (16,1) (5,2) (3,10) (4,6) (10,13) (2,6) (1,10) (0,9) (8,7) (11,3) (12,16) (15,7) (0,1) (9,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1110", "image": "data/cycle/graph_visual/medium/graph1110.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (2,8) (3,10) (13,1) (3,11) (0,2) (5,9) (3,9) (11,7) (2,7) (6,5) (4,0) (11,12) (3,0) (1,0) (1,2) (0,5) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph487", "image": "data/cycle/graph_visual/medium/graph487.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (7,0) (10,3) (18,13) (6,15) (7,5) (12,15) (3,9) (5,11) (14,1) (0,17) (8,9) (8,13) (13,11) (4,12) (6,2) (1,4) (12,17) (6,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph711", "image": "data/cycle/graph_visual/medium/graph711.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,8) (15,11) (16,14) (20,19) (4,12) (8,15) (15,1) (18,7) (9,11) (17,0) (16,5) (0,12) (0,21) (3,21) (21,19) (7,17) (14,19) (10,4) (11,13) (8,20) (21,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph82", "image": "data/cycle/graph_visual/medium/graph82.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,3) (10,2) (8,0) (2,3) (5,6) (5,0) (4,9) (10,8) (7,0) (0,1) (1,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph338", "image": "data/cycle/graph_visual/medium/graph338.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,7) (4,14) (2,10) (8,9) (5,6) (0,14) (12,5) (4,13) (7,0) (1,12) (4,15) (12,8) (10,9) (3,7) (11,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1399", "image": "data/cycle/graph_visual/medium/graph1399.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (3,0) (17,7) (9,2) (16,15) (13,9) (18,0) (8,4) (10,12) (5,11) (15,6) (1,5) (10,16) (14,15) (7,3) (18,13) (16,5) (8,16) (2,17) (0,2) (1,0) (9,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1084", "image": "data/cycle/graph_visual/medium/graph1084.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,10) (12,5) (10,3) (11,1) (5,13) (12,6) (10,13) (12,7) (2,4) (8,2) (0,11) (1,13) (0,1) (4,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph399", "image": "data/cycle/graph_visual/medium/graph399.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (2,11) (4,3) (11,12) (0,2) (2,6) (13,12) (8,2) (16,14) (10,16) (10,12) (9,5) (5,7) (12,15) (1,6) (9,4) (9,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1650", "image": "data/cycle/graph_visual/medium/graph1650.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,18) (5,1) (12,22) (22,19) (17,16) (20,11) (0,12) (0,11) (7,11) (0,2) (2,17) (9,21) (0,21) (4,18) (0,1) (1,20) (6,12) (13,8) (15,6) (1,10) (2,15) (14,9) (13,15) (3,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1442", "image": "data/cycle/graph_visual/medium/graph1442.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,5) (8,7) (9,6) (0,10) (17,11) (8,17) (18,2) (17,2) (2,0) (16,8) (18,13) (14,13) (12,5) (3,10) (1,0) (1,4) (19,13) (15,11) (0,16) (9,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph943", "image": "data/cycle/graph_visual/medium/graph943.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,8) (6,2) (3,5) (2,0) (0,1) (1,5) (4,0) (2,4) (3,0) (0,7) (10,5) (8,9) (10,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph543", "image": "data/cycle/graph_visual/medium/graph543.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,9) (14,19) (14,4) (19,9) (11,7) (6,17) (5,16) (0,10) (10,3) (15,12) (14,2) (17,8) (9,10) (0,15) (4,5) (17,0) (18,11) (16,1) (13,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1214", "image": "data/cycle/graph_visual/medium/graph1214.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (5,8) (7,3) (8,6) (4,13) (14,5) (0,1) (10,2) (15,3) (1,10) (2,9) (13,5) (0,3) (11,1) (5,0) (15,13) (2,0) (5,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph923", "image": "data/cycle/graph_visual/medium/graph923.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,6) (0,6) (8,4) (7,4) (0,1) (2,6) (3,5) (4,10) (2,3) (9,8) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1323", "image": "data/cycle/graph_visual/medium/graph1323.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,8) (16,14) (6,11) (6,5) (15,0) (6,3) (9,15) (16,8) (17,12) (17,0) (13,7) (4,17) (10,7) (3,9) (0,2) (4,7) (0,1) (2,10) (8,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph529", "image": "data/cycle/graph_visual/medium/graph529.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,9) (7,15) (2,4) (16,6) (10,1) (4,3) (13,5) (15,3) (4,5) (17,18) (7,6) (13,14) (9,16) (17,16) (0,17) (12,6) (17,10) (8,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1504", "image": "data/cycle/graph_visual/medium/graph1504.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (20,14) (5,14) (4,14) (19,11) (12,13) (0,3) (2,0) (19,9) (19,15) (8,16) (6,8) (5,1) (3,2) (7,13) (10,8) (1,17) (0,4) (1,0) (18,5) (1,9) (3,13) (15,13) (20,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph76", "image": "data/cycle/graph_visual/medium/graph76.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,1) (4,7) (8,9) (10,3) (6,3) (3,5) (2,5) (8,7) (4,0) (11,9) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph464", "image": "data/cycle/graph_visual/medium/graph464.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (12,11) (7,0) (16,10) (16,15) (8,12) (1,16) (5,3) (7,8) (7,5) (13,14) (12,17) (17,6) (10,11) (17,14) (17,2) (17,9) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1083", "image": "data/cycle/graph_visual/medium/graph1083.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,12) (11,12) (10,8) (9,7) (3,0) (8,6) (11,4) (1,0) (9,6) (0,10) (7,2) (0,2) (0,5) (4,0) (3,4) (1,5) (10,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph295", "image": "data/cycle/graph_visual/medium/graph295.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,8) (1,6) (3,5) (10,2) (2,7) (14,6) (0,11) (11,12) (12,8) (5,14) (13,0) (0,9) (4,3) (13,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph813", "image": "data/cycle/graph_visual/medium/graph813.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,11) (17,5) (14,13) (6,13) (9,3) (11,14) (0,20) (19,23) (22,8) (19,1) (5,18) (22,23) (11,18) (20,8) (13,4) (10,11) (21,10) (10,19) (12,22) (2,3) (1,15) (7,23) (21,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph694", "image": "data/cycle/graph_visual/medium/graph694.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,6) (13,10) (4,3) (2,0) (12,18) (17,14) (20,21) (2,8) (16,19) (21,9) (9,4) (20,17) (15,11) (12,10) (5,7) (15,12) (12,16) (9,5) (17,13) (6,2) (2,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph362", "image": "data/cycle/graph_visual/medium/graph362.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,8) (3,13) (13,11) (3,2) (14,2) (6,1) (14,4) (16,6) (14,7) (12,16) (0,4) (5,12) (11,10) (5,9) (8,14) (15,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1574", "image": "data/cycle/graph_visual/medium/graph1574.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (16,20) (9,18) (1,0) (13,8) (0,4) (2,18) (15,2) (0,8) (15,12) (9,19) (0,5) (2,0) (0,3) (17,5) (16,6) (14,3) (16,7) (1,8) (3,4) (16,12) (11,18) (6,14) (15,10) (14,5) (21,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1169", "image": "data/cycle/graph_visual/medium/graph1169.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,7) (0,6) (8,14) (3,7) (7,8) (13,6) (4,2) (4,1) (12,7) (5,13) (11,8) (4,8) (14,5) (0,1) (3,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph805", "image": "data/cycle/graph_visual/medium/graph805.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (6,22) (13,21) (15,21) (14,10) (23,16) (16,2) (10,3) (22,7) (19,21) (12,13) (12,20) (17,19) (0,3) (22,5) (9,14) (7,12) (8,14) (4,3) (1,9) (4,21) (6,18) (2,20) (11,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1053", "image": "data/cycle/graph_visual/medium/graph1053.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,3) (8,6) (0,9) (1,0) (0,10) (3,10) (2,0) (7,1) (0,3) (0,6) (5,7) (1,2) (12,2) (3,2) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph625", "image": "data/cycle/graph_visual/medium/graph625.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,4) (5,11) (4,6) (0,19) (13,8) (19,16) (18,7) (0,10) (19,4) (3,16) (15,14) (9,12) (15,1) (8,2) (14,20) (8,20) (12,11) (17,7) (17,0) (15,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph510", "image": "data/cycle/graph_visual/medium/graph510.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (2,13) (7,8) (0,3) (6,15) (3,17) (8,2) (2,18) (11,9) (4,8) (2,1) (1,9) (5,13) (16,9) (9,3) (0,15) (10,12) (14,15) (10,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph904", "image": "data/cycle/graph_visual/medium/graph904.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,0) (6,9) (0,4) (5,0) (7,3) (1,9) (10,7) (0,6) (0,1) (9,7) (0,2) (3,0) (5,7) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph992", "image": "data/cycle/graph_visual/medium/graph992.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,4) (0,1) (4,1) (11,10) (8,3) (8,9) (8,11) (11,2) (7,1) (3,6) (5,10) (2,0) (5,4) (0,3) (5,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1664", "image": "data/cycle/graph_visual/medium/graph1664.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (13,19) (1,0) (22,18) (21,10) (22,9) (15,21) (5,3) (11,9) (12,4) (0,3) (8,17) (7,12) (0,2) (14,11) (5,11) (19,2) (19,22) (1,2) (0,20) (7,10) (4,17) (16,19) (6,22) (0,22) (4,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph80", "image": "data/cycle/graph_visual/medium/graph80.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,8) (6,4) (1,7) (4,9) (9,0) (6,10) (4,3) (5,8) (11,2) (1,0) (2,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1020", "image": "data/cycle/graph_visual/medium/graph1020.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (4,0) (11,4) (2,1) (9,8) (7,8) (1,0) (3,0) (11,8) (5,6) (3,6) (2,0) (6,2) (10,1) (12,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph256", "image": "data/cycle/graph_visual/medium/graph256.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,9) (13,4) (13,12) (4,11) (0,1) (1,14) (1,8) (10,7) (7,4) (3,12) (14,6) (8,12) (5,6) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph89", "image": "data/cycle/graph_visual/medium/graph89.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,1) (5,7) (3,11) (10,3) (4,7) (0,10) (9,3) (6,0) (0,8) (6,2) (1,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph143", "image": "data/cycle/graph_visual/medium/graph143.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,1) (10,5) (9,3) (3,2) (1,10) (1,11) (10,12) (4,8) (7,0) (4,3) (0,11) (11,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1603", "image": "data/cycle/graph_visual/medium/graph1603.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (15,10) (3,11) (1,0) (13,0) (21,8) (2,20) (7,8) (13,14) (4,10) (20,9) (14,18) (15,18) (5,17) (18,16) (5,0) (13,21) (6,4) (10,12) (2,3) (3,4) (1,21) (13,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1096", "image": "data/cycle/graph_visual/medium/graph1096.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (4,6) (0,3) (8,3) (4,7) (6,10) (9,0) (9,11) (9,12) (10,13) (5,8) (7,5) (0,1) (5,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph862", "image": "data/cycle/graph_visual/medium/graph862.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (23,8) (7,4) (0,7) (11,12) (14,23) (16,17) (1,16) (10,20) (7,5) (8,7) (24,12) (17,13) (9,12) (18,10) (17,22) (22,19) (6,17) (15,14) (2,17) (3,5) (18,21) (20,16) (21,11) (12,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1015", "image": "data/cycle/graph_visual/medium/graph1015.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,6) (4,3) (0,2) (10,1) (9,6) (2,7) (1,11) (0,3) (7,4) (7,0) (5,4) (0,1) (10,7) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1479", "image": "data/cycle/graph_visual/medium/graph1479.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,18) (0,2) (10,1) (18,13) (0,16) (11,7) (1,6) (2,3) (17,14) (18,8) (18,9) (3,0) (1,0) (1,15) (0,4) (5,12) (17,4) (10,2) (7,16) (19,17) (12,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph988", "image": "data/cycle/graph_visual/medium/graph988.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,7) (2,0) (0,11) (6,8) (0,1) (9,2) (9,10) (3,6) (7,4) (10,7) (10,8) (7,1) (5,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph333", "image": "data/cycle/graph_visual/medium/graph333.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,8) (13,1) (11,4) (7,10) (2,5) (14,3) (2,13) (10,12) (3,0) (12,1) (14,6) (0,8) (12,11) (15,8) (13,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1161", "image": "data/cycle/graph_visual/medium/graph1161.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (3,12) (6,4) (1,12) (0,3) (0,2) (0,1) (8,6) (14,5) (2,14) (9,4) (13,11) (6,13) (14,10) (8,5) (0,4) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph55", "image": "data/cycle/graph_visual/medium/graph55.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,9) (2,6) (7,5) (1,2) (0,8) (3,10) (7,1) (6,0) (10,0) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph48", "image": "data/cycle/graph_visual/medium/graph48.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,2) (5,6) (8,4) (6,1) (7,3) (7,10) (6,7) (9,6) (1,0) (9,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph28", "image": "data/cycle/graph_visual/medium/graph28.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,5) (3,8) (7,10) (9,10) (2,4) (5,2) (0,3) (8,9) (7,6) (9,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1264", "image": "data/cycle/graph_visual/medium/graph1264.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,1) (10,15) (2,7) (5,10) (1,8) (7,4) (6,4) (0,3) (3,14) (14,0) (2,0) (5,12) (2,11) (8,7) (5,13) (13,1) (1,0) (0,9) (11,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1600", "image": "data/cycle/graph_visual/medium/graph1600.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (3,10) (5,15) (20,12) (11,21) (8,11) (4,17) (8,12) (6,2) (7,5) (2,0) (11,14) (6,0) (8,19) (16,0) (9,16) (0,1) (10,14) (11,4) (3,7) (13,1) (1,21) (7,18) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph38", "image": "data/cycle/graph_visual/medium/graph38.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,2) (1,3) (0,10) (6,0) (1,4) (7,10) (9,2) (6,4) (4,8) (3,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph384", "image": "data/cycle/graph_visual/medium/graph384.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,8) (13,8) (5,4) (11,8) (14,3) (12,1) (4,9) (16,1) (10,6) (9,13) (11,3) (7,4) (11,0) (15,16) (2,10) (0,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph203", "image": "data/cycle/graph_visual/medium/graph203.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (5,13) (5,7) (8,2) (13,1) (3,8) (7,10) (13,6) (1,2) (12,0) (4,9) (4,6) (10,0) (4,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph551", "image": "data/cycle/graph_visual/medium/graph551.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,7) (1,12) (1,16) (0,18) (16,15) (14,16) (10,17) (2,6) (4,9) (8,7) (10,1) (2,5) (13,3) (0,19) (0,9) (11,19) (3,10) (15,11) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph938", "image": "data/cycle/graph_visual/medium/graph938.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,3) (7,2) (9,5) (6,2) (2,0) (5,6) (10,1) (8,1) (7,4) (6,8) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph582", "image": "data/cycle/graph_visual/medium/graph582.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,10) (11,12) (0,12) (18,6) (2,13) (11,5) (13,9) (16,4) (11,2) (18,16) (17,18) (10,3) (7,0) (4,3) (8,3) (0,14) (19,8) (7,15) (1,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph829", "image": "data/cycle/graph_visual/medium/graph829.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (18,23) (5,3) (10,23) (14,0) (7,12) (20,13) (3,17) (20,1) (0,16) (16,19) (2,19) (18,3) (11,8) (15,11) (17,12) (23,6) (15,7) (8,4) (5,1) (7,14) (9,22) (20,21) (11,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph624", "image": "data/cycle/graph_visual/medium/graph624.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (17,20) (13,15) (16,2) (17,1) (12,7) (14,17) (9,18) (10,8) (20,18) (5,17) (19,3) (11,16) (15,8) (3,1) (6,19) (4,3) (14,0) (11,5) (7,13) (14,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1712", "image": "data/cycle/graph_visual/medium/graph1712.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,12) (16,20) (6,2) (3,10) (23,13) (2,5) (11,19) (10,21) (17,23) (11,15) (16,1) (0,17) (22,15) (1,0) (19,0) (6,4) (18,3) (4,9) (0,2) (3,0) (7,9) (16,22) (7,15) (1,10) (8,22) (14,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph292", "image": "data/cycle/graph_visual/medium/graph292.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,3) (0,1) (5,10) (13,11) (5,14) (9,4) (9,7) (13,2) (2,1) (8,11) (2,4) (6,5) (1,12) (13,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1562", "image": "data/cycle/graph_visual/medium/graph1562.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (17,16) (12,6) (20,15) (2,4) (5,13) (1,0) (9,16) (21,4) (10,1) (17,20) (21,16) (18,3) (11,9) (7,6) (17,10) (7,19) (6,16) (14,13) (4,5) (17,8) (17,0) (15,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1766", "image": "data/cycle/graph_visual/medium/graph1766.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (21,15) (9,5) (7,23) (6,0) (4,0) (13,5) (6,3) (22,23) (3,0) (24,15) (2,0) (22,9) (7,17) (15,13) (20,4) (22,18) (7,16) (2,4) (1,4) (14,5) (10,11) (2,11) (0,11) (1,0) (19,12) (23,3) (15,19) (14,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph298", "image": "data/cycle/graph_visual/medium/graph298.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,12) (2,9) (8,6) (1,14) (2,11) (11,13) (6,10) (1,12) (6,5) (2,0) (7,12) (3,7) (7,4) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph308", "image": "data/cycle/graph_visual/medium/graph308.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,15) (15,1) (6,8) (13,14) (12,3) (6,14) (3,5) (6,0) (8,10) (4,2) (6,9) (13,12) (7,0) (2,0) (4,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph474", "image": "data/cycle/graph_visual/medium/graph474.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (11,2) (2,1) (6,9) (3,8) (2,10) (9,10) (5,2) (5,14) (4,13) (7,17) (7,0) (11,12) (10,13) (4,8) (0,14) (16,6) (15,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1490", "image": "data/cycle/graph_visual/medium/graph1490.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (19,11) (15,19) (4,0) (18,9) (12,13) (1,0) (4,14) (1,9) (13,7) (13,3) (8,10) (14,5) (3,2) (13,15) (19,14) (6,1) (1,5) (0,5) (5,17) (8,16) (0,3) (2,0) (6,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph3", "image": "data/cycle/graph_visual/medium/graph3.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,10) (0,2) (6,7) (9,0) (8,1) (2,5) (3,8) (8,2) (8,4) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph59", "image": "data/cycle/graph_visual/medium/graph59.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,10) (5,6) (7,5) (2,8) (3,6) (6,8) (9,8) (1,6) (5,4) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1546", "image": "data/cycle/graph_visual/medium/graph1546.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,8) (13,20) (3,9) (6,15) (7,0) (13,11) (17,0) (0,1) (2,6) (5,7) (9,8) (20,4) (1,20) (12,15) (19,6) (14,1) (16,4) (18,12) (10,3) (11,5) (0,2) (17,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph332", "image": "data/cycle/graph_visual/medium/graph332.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,3) (6,3) (10,15) (5,9) (10,6) (8,12) (2,12) (15,7) (9,1) (1,8) (0,4) (11,1) (13,9) (6,0) (3,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1790", "image": "data/cycle/graph_visual/medium/graph1790.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (13,4) (18,5) (8,4) (15,22) (12,19) (14,5) (1,0) (14,19) (23,6) (24,7) (1,2) (9,22) (18,2) (4,20) (2,10) (21,22) (2,11) (19,0) (13,10) (2,0) (3,24) (10,21) (7,0) (17,11) (9,6) (16,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1324", "image": "data/cycle/graph_visual/medium/graph1324.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,2) (7,8) (0,10) (8,4) (0,3) (6,11) (13,14) (5,12) (2,0) (11,16) (1,0) (2,10) (12,1) (14,3) (17,14) (9,0) (10,17) (14,5) (16,1) (5,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1090", "image": "data/cycle/graph_visual/medium/graph1090.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,3) (0,9) (6,13) (0,6) (6,5) (10,3) (5,1) (4,11) (0,2) (3,7) (8,4) (7,2) (1,0) (12,4) (4,0) (3,0) (13,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph603", "image": "data/cycle/graph_visual/medium/graph603.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (7,20) (11,6) (0,11) (1,0) (18,12) (0,13) (2,20) (17,16) (18,8) (17,1) (14,19) (15,14) (0,2) (1,9) (15,3) (7,10) (3,10) (4,6) (8,11) (5,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph977", "image": "data/cycle/graph_visual/medium/graph977.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (3,6) (9,10) (5,11) (7,8) (1,0) (0,11) (2,0) (11,6) (11,4) (1,8) (1,9) (2,7) (3,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph400", "image": "data/cycle/graph_visual/medium/graph400.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (2,0) (11,10) (2,16) (10,5) (3,0) (14,9) (3,4) (12,15) (11,7) (13,14) (7,6) (8,6) (13,3) (7,14) (6,1) (12,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1120", "image": "data/cycle/graph_visual/medium/graph1120.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (4,0) (5,0) (1,0) (10,12) (1,9) (3,10) (0,3) (5,8) (12,11) (13,12) (5,9) (6,12) (1,2) (7,2) (13,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph826", "image": "data/cycle/graph_visual/medium/graph826.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,11) (14,6) (2,19) (5,19) (15,10) (16,23) (3,6) (23,5) (7,16) (4,8) (23,14) (21,4) (8,23) (18,0) (0,1) (14,17) (23,11) (1,5) (22,1) (12,22) (16,13) (11,20) (22,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1421", "image": "data/cycle/graph_visual/medium/graph1421.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,15) (6,0) (9,0) (2,0) (0,1) (0,3) (2,4) (3,5) (18,0) (16,13) (7,17) (8,11) (17,2) (12,0) (4,15) (13,14) (6,14) (12,2) (10,6) (3,12) (6,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1582", "image": "data/cycle/graph_visual/medium/graph1582.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (6,5) (9,3) (10,7) (9,15) (14,7) (4,7) (4,17) (12,17) (1,8) (0,1) (15,0) (19,16) (21,15) (6,11) (2,10) (0,16) (8,20) (0,2) (13,19) (6,3) (0,8) (20,17) (21,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1564", "image": "data/cycle/graph_visual/medium/graph1564.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,4) (19,8) (0,6) (20,10) (1,0) (15,5) (21,18) (0,3) (6,20) (2,17) (1,17) (12,20) (8,18) (14,16) (13,16) (0,2) (7,13) (10,2) (9,15) (3,7) (18,0) (19,11) (9,17) (11,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph259", "image": "data/cycle/graph_visual/medium/graph259.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,1) (10,5) (3,9) (11,0) (1,12) (14,11) (8,4) (13,14) (2,11) (7,0) (2,3) (6,1) (4,3) (11,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1453", "image": "data/cycle/graph_visual/medium/graph1453.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,11) (8,15) (2,12) (0,3) (10,9) (4,2) (7,10) (6,7) (0,15) (4,11) (10,14) (2,0) (17,13) (8,1) (19,7) (2,17) (5,11) (3,11) (15,7) (3,18) (0,1) (4,0) (16,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph690", "image": "data/cycle/graph_visual/medium/graph690.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (20,3) (13,0) (15,14) (1,9) (11,8) (13,5) (18,12) (17,1) (18,8) (11,6) (14,19) (0,1) (0,2) (4,6) (2,20) (21,15) (7,21) (10,7) (10,3) (11,0) (16,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1238", "image": "data/cycle/graph_visual/medium/graph1238.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,13) (3,0) (0,5) (1,11) (12,5) (15,3) (3,7) (0,2) (5,13) (10,1) (15,13) (8,5) (1,0) (8,6) (2,9) (10,2) (5,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1768", "image": "data/cycle/graph_visual/medium/graph1768.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,21) (21,15) (6,17) (7,14) (4,16) (1,0) (2,22) (4,5) (9,3) (19,23) (8,21) (23,9) (13,4) (20,5) (0,13) (21,10) (1,8) (18,7) (11,5) (9,0) (12,20) (2,17) (7,20) (21,24) (6,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1236", "image": "data/cycle/graph_visual/medium/graph1236.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,0) (10,9) (14,0) (7,14) (4,8) (12,4) (11,3) (7,13) (7,10) (6,9) (5,11) (15,0) (11,12) (0,3) (1,0) (2,5) (0,4) (2,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1257", "image": "data/cycle/graph_visual/medium/graph1257.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,10) (0,8) (13,1) (0,3) (2,0) (6,14) (0,1) (14,3) (12,11) (13,2) (13,0) (0,4) (11,4) (2,5) (10,12) (8,15) (12,1) (9,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph649", "image": "data/cycle/graph_visual/medium/graph649.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (7,14) (11,18) (10,16) (14,9) (2,4) (9,4) (15,20) (8,14) (5,19) (17,20) (1,17) (13,16) (14,0) (3,14) (6,5) (3,5) (12,6) (15,16) (18,19) (17,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph590", "image": "data/cycle/graph_visual/medium/graph590.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (6,17) (4,12) (19,8) (1,2) (5,3) (16,10) (7,10) (17,12) (5,11) (11,9) (0,19) (14,0) (11,13) (19,2) (9,19) (7,18) (4,15) (7,14) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1305", "image": "data/cycle/graph_visual/medium/graph1305.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (3,0) (1,0) (16,5) (11,7) (9,15) (8,3) (13,11) (12,13) (0,4) (9,1) (0,10) (0,16) (4,14) (14,13) (2,1) (6,4) (5,12) (3,14) (2,0) (11,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1212", "image": "data/cycle/graph_visual/medium/graph1212.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,2) (13,9) (6,8) (15,1) (10,8) (15,5) (0,14) (12,9) (0,4) (13,7) (11,3) (1,6) (2,11) (3,7) (2,0) (1,0) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph601", "image": "data/cycle/graph_visual/medium/graph601.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (15,17) (1,12) (4,12) (5,4) (14,10) (20,13) (6,9) (1,7) (13,0) (18,2) (0,19) (8,7) (8,16) (18,9) (4,11) (20,7) (1,10) (14,15) (2,5) (3,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1521", "image": "data/cycle/graph_visual/medium/graph1521.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (11,5) (9,13) (2,0) (11,14) (8,11) (13,16) (1,10) (4,15) (20,14) (13,5) (14,12) (19,0) (1,17) (15,7) (1,3) (18,20) (16,6) (1,0) (12,17) (5,4) (2,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph844", "image": "data/cycle/graph_visual/medium/graph844.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,16) (15,2) (20,7) (7,0) (12,14) (10,9) (8,7) (9,22) (15,13) (18,20) (4,21) (3,15) (0,9) (19,24) (0,14) (5,9) (13,21) (17,8) (6,13) (10,21) (1,11) (4,23) (23,19) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1099", "image": "data/cycle/graph_visual/medium/graph1099.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (2,0) (13,10) (9,11) (13,6) (2,12) (1,0) (0,4) (8,1) (10,9) (7,9) (12,3) (4,5) (0,6) (4,3) (8,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1050", "image": "data/cycle/graph_visual/medium/graph1050.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,6) (10,12) (8,5) (4,0) (4,8) (3,8) (10,11) (0,6) (2,0) (2,9) (12,4) (0,3) (1,0) (9,7) (8,1) (9,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph576", "image": "data/cycle/graph_visual/medium/graph576.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (18,0) (8,18) (15,13) (1,17) (11,3) (15,5) (19,11) (16,2) (0,4) (10,2) (14,9) (6,0) (12,16) (10,8) (7,3) (17,9) (17,6) (19,18) (7,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1587", "image": "data/cycle/graph_visual/medium/graph1587.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (7,13) (0,15) (1,20) (1,4) (0,3) (0,1) (4,8) (1,18) (21,19) (1,10) (4,15) (7,17) (14,17) (0,2) (4,11) (3,12) (12,6) (3,17) (7,4) (21,9) (4,16) (14,21) (3,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1193", "image": "data/cycle/graph_visual/medium/graph1193.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,14) (1,0) (13,8) (5,14) (4,13) (3,0) (0,9) (11,3) (13,6) (12,13) (2,12) (0,2) (1,6) (0,14) (7,10) (0,7) (10,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph858", "image": "data/cycle/graph_visual/medium/graph858.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,15) (18,4) (24,6) (3,5) (21,1) (23,20) (3,13) (21,23) (4,9) (2,0) (8,12) (4,12) (4,19) (11,1) (1,4) (22,1) (0,15) (7,17) (7,4) (21,10) (7,14) (16,24) (17,24) (3,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph903", "image": "data/cycle/graph_visual/medium/graph903.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,10) (6,9) (1,4) (2,4) (3,4) (8,2) (0,2) (0,4) (1,0) (3,0) (9,7) (7,3) (7,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1352", "image": "data/cycle/graph_visual/medium/graph1352.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,3) (1,8) (0,2) (12,1) (0,5) (7,16) (12,11) (3,17) (4,0) (14,13) (1,0) (7,0) (12,4) (2,4) (9,0) (8,6) (16,15) (10,6) (9,5) (2,17) (14,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1028", "image": "data/cycle/graph_visual/medium/graph1028.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,6) (7,5) (3,0) (5,10) (1,0) (0,2) (8,10) (7,1) (6,0) (3,4) (0,5) (2,11) (10,4) (9,8) (0,4) (12,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1474", "image": "data/cycle/graph_visual/medium/graph1474.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,17) (6,12) (6,1) (13,10) (16,12) (9,12) (4,0) (17,15) (18,10) (19,14) (15,1) (0,1) (17,3) (18,6) (14,2) (15,5) (14,7) (8,15) (9,4) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1029", "image": "data/cycle/graph_visual/medium/graph1029.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,9) (11,10) (4,2) (5,4) (5,12) (8,0) (9,11) (3,11) (11,6) (10,8) (1,0) (7,12) (7,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph293", "image": "data/cycle/graph_visual/medium/graph293.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (4,2) (9,13) (1,4) (6,3) (0,1) (11,2) (12,11) (11,7) (8,4) (10,1) (3,2) (14,5) (1,5) (13,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph871", "image": "data/cycle/graph_visual/medium/graph871.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (5,17) (16,7) (12,15) (13,8) (0,13) (14,5) (0,3) (1,8) (14,3) (24,13) (3,4) (21,8) (22,24) (14,6) (9,18) (2,18) (23,0) (6,16) (12,16) (15,10) (16,20) (19,9) (15,2) (18,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph527", "image": "data/cycle/graph_visual/medium/graph527.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (7,6) (4,0) (14,9) (5,16) (12,17) (15,10) (12,13) (1,2) (0,15) (8,10) (11,1) (5,0) (18,12) (16,7) (18,3) (16,11) (11,12) (13,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1287", "image": "data/cycle/graph_visual/medium/graph1287.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,13) (8,13) (0,2) (16,5) (9,15) (6,1) (6,8) (1,0) (3,2) (13,11) (8,10) (3,13) (14,4) (1,5) (5,14) (15,12) (1,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph390", "image": "data/cycle/graph_visual/medium/graph390.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (9,16) (0,3) (0,10) (9,8) (8,1) (2,15) (6,8) (5,15) (3,15) (3,9) (0,13) (9,14) (12,2) (4,13) (2,7) (10,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1297", "image": "data/cycle/graph_visual/medium/graph1297.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (6,14) (0,2) (15,12) (13,4) (8,5) (10,2) (15,10) (5,1) (3,1) (9,15) (0,1) (6,0) (0,11) (2,7) (13,8) (16,1) (14,15) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1131", "image": "data/cycle/graph_visual/medium/graph1131.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,0) (10,13) (7,11) (9,1) (0,3) (12,4) (6,5) (7,3) (4,0) (8,9) (7,13) (6,7) (13,4) (2,0) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1513", "image": "data/cycle/graph_visual/medium/graph1513.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,14) (0,16) (7,3) (1,2) (14,3) (0,14) (11,18) (13,17) (9,1) (15,9) (18,16) (8,19) (13,12) (19,11) (5,4) (0,1) (19,10) (11,6) (12,20) (2,0) (19,17) (0,3) (13,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph964", "image": "data/cycle/graph_visual/medium/graph964.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,3) (7,1) (5,7) (6,2) (3,10) (4,7) (1,0) (2,1) (0,6) (9,3) (0,10) (0,8) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph373", "image": "data/cycle/graph_visual/medium/graph373.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,7) (10,14) (4,9) (1,11) (13,5) (9,16) (3,15) (8,7) (7,6) (2,15) (8,13) (9,0) (14,7) (11,0) (12,13) (9,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph291", "image": "data/cycle/graph_visual/medium/graph291.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,12) (4,1) (10,3) (13,8) (2,11) (10,4) (4,0) (10,2) (9,14) (13,3) (14,5) (6,10) (10,12) (14,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1655", "image": "data/cycle/graph_visual/medium/graph1655.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (4,14) (1,0) (19,5) (0,5) (15,9) (3,1) (6,20) (21,3) (7,12) (6,8) (16,22) (15,18) (17,20) (2,0) (5,15) (6,7) (9,14) (13,15) (3,10) (10,11) (21,2) (10,16) (8,22) (8,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph748", "image": "data/cycle/graph_visual/medium/graph748.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (16,5) (2,21) (19,15) (17,16) (1,21) (10,17) (22,21) (12,4) (9,19) (11,1) (7,19) (22,13) (1,14) (13,18) (6,3) (22,6) (6,20) (8,13) (15,4) (20,5) (6,0) (7,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph272", "image": "data/cycle/graph_visual/medium/graph272.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (6,11) (3,5) (11,4) (12,4) (2,13) (14,0) (14,6) (8,10) (0,13) (9,11) (1,4) (10,13) (1,3) (7,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1198", "image": "data/cycle/graph_visual/medium/graph1198.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,2) (9,6) (4,14) (11,10) (11,4) (5,1) (12,3) (6,13) (0,1) (7,0) (13,10) (7,5) (8,4) (7,3) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph568", "image": "data/cycle/graph_visual/medium/graph568.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,9) (12,4) (0,2) (14,0) (1,8) (14,17) (7,0) (8,6) (4,2) (3,17) (13,6) (15,12) (1,12) (19,9) (19,2) (16,18) (0,10) (16,7) (19,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1063", "image": "data/cycle/graph_visual/medium/graph1063.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,5) (8,3) (6,1) (6,12) (4,5) (8,4) (5,0) (7,10) (6,8) (2,1) (7,9) (6,11) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1426", "image": "data/cycle/graph_visual/medium/graph1426.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (10,3) (9,15) (15,16) (8,15) (8,2) (6,14) (13,3) (11,12) (13,5) (11,17) (1,7) (11,15) (0,1) (14,0) (4,18) (10,2) (8,14) (18,8) (1,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1386", "image": "data/cycle/graph_visual/medium/graph1386.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,11) (4,17) (9,8) (15,16) (4,18) (0,2) (15,3) (2,11) (18,5) (2,1) (14,9) (17,2) (13,18) (6,0) (10,11) (8,15) (7,9) (3,0) (1,0) (12,14) (6,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph726", "image": "data/cycle/graph_visual/medium/graph726.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (10,2) (18,13) (4,21) (9,17) (9,16) (0,20) (5,6) (21,7) (4,14) (0,14) (7,19) (4,10) (12,18) (3,7) (17,8) (22,5) (15,22) (18,0) (10,5) (12,8) (1,12) (12,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1696", "image": "data/cycle/graph_visual/medium/graph1696.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,13) (2,18) (21,11) (12,21) (1,20) (3,14) (12,5) (19,22) (15,16) (14,19) (10,0) (8,9) (23,22) (4,8) (10,2) (19,17) (22,5) (7,11) (0,1) (2,0) (1,23) (10,17) (3,0) (6,19) (5,4) (14,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph109", "image": "data/cycle/graph_visual/medium/graph109.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,6) (4,11) (2,1) (3,10) (3,2) (3,9) (4,1) (9,7) (0,6) (2,8) (3,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph583", "image": "data/cycle/graph_visual/medium/graph583.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,18) (8,19) (4,10) (3,2) (8,10) (14,15) (14,3) (16,17) (9,12) (11,3) (16,8) (10,5) (5,14) (16,1) (6,13) (7,3) (6,11) (9,5) (0,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph976", "image": "data/cycle/graph_visual/medium/graph976.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,3) (9,4) (4,0) (8,4) (0,1) (2,0) (8,7) (11,3) (0,7) (5,10) (8,6) (11,6) (3,10) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1687", "image": "data/cycle/graph_visual/medium/graph1687.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (12,1) (13,23) (0,2) (5,19) (14,15) (7,8) (4,21) (12,4) (5,22) (4,0) (3,9) (10,14) (13,0) (17,15) (7,20) (9,6) (23,5) (20,0) (1,10) (2,18) (1,7) (18,9) (21,2) (0,1) (0,3) (16,8) (4,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1716", "image": "data/cycle/graph_visual/medium/graph1716.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (12,9) (8,16) (4,20) (20,21) (7,19) (13,2) (2,4) (0,2) (3,5) (0,22) (17,20) (6,15) (0,1) (0,23) (22,19) (6,14) (13,14) (1,15) (3,20) (18,6) (23,6) (21,11) (17,10) (8,22) (0,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph305", "image": "data/cycle/graph_visual/medium/graph305.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,5) (10,12) (6,7) (0,10) (6,14) (8,4) (13,11) (8,14) (4,11) (1,3) (2,9) (9,15) (12,14) (15,1) (15,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1330", "image": "data/cycle/graph_visual/medium/graph1330.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,1) (6,11) (11,16) (3,0) (8,2) (2,11) (4,5) (14,5) (0,1) (17,3) (3,7) (4,0) (4,9) (11,12) (3,13) (0,15) (15,3) (2,0) (10,12) (3,12) (5,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1303", "image": "data/cycle/graph_visual/medium/graph1303.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,2) (10,6) (15,6) (0,3) (13,4) (9,13) (6,16) (4,6) (7,3) (4,7) (4,1) (5,12) (4,5) (14,8) (12,14) (11,6) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph391", "image": "data/cycle/graph_visual/medium/graph391.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,11) (1,15) (14,0) (3,4) (10,8) (9,15) (6,7) (15,3) (12,8) (3,16) (10,14) (2,16) (5,3) (7,13) (1,14) (11,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1251", "image": "data/cycle/graph_visual/medium/graph1251.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,1) (11,14) (7,8) (4,8) (12,1) (2,10) (6,11) (14,3) (1,10) (0,10) (5,14) (13,2) (5,12) (4,5) (9,0) (15,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1750", "image": "data/cycle/graph_visual/medium/graph1750.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (6,18) (7,2) (16,20) (6,19) (20,22) (8,4) (1,13) (11,4) (0,1) (14,3) (0,15) (15,6) (2,0) (23,2) (9,5) (11,9) (22,24) (14,1) (1,2) (17,6) (1,12) (5,21) (9,17) (4,13) (15,20) (12,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph836", "image": "data/cycle/graph_visual/medium/graph836.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (6,4) (15,19) (14,19) (13,12) (11,19) (9,22) (4,14) (5,22) (19,17) (12,23) (13,16) (3,10) (21,8) (2,1) (3,14) (18,11) (20,15) (0,21) (7,11) (16,0) (1,9) (22,18) (13,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph868", "image": "data/cycle/graph_visual/medium/graph868.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (19,2) (5,6) (7,14) (14,8) (20,17) (3,4) (18,24) (13,11) (1,22) (23,19) (7,6) (0,6) (10,3) (24,9) (21,22) (21,18) (24,7) (7,17) (24,10) (15,21) (12,17) (11,18) (16,12) (18,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph61", "image": "data/cycle/graph_visual/medium/graph61.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,0) (8,5) (11,7) (7,2) (9,11) (10,5) (1,10) (7,1) (2,6) (4,0) (11,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph821", "image": "data/cycle/graph_visual/medium/graph821.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,22) (2,19) (21,6) (17,7) (8,18) (10,20) (13,22) (19,11) (10,2) (7,3) (6,23) (3,11) (18,0) (15,9) (14,16) (6,18) (17,9) (17,1) (4,0) (13,16) (8,20) (15,5) (20,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph34", "image": "data/cycle/graph_visual/medium/graph34.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,1) (0,7) (2,6) (10,2) (8,9) (0,5) (3,5) (10,5) (0,8) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1349", "image": "data/cycle/graph_visual/medium/graph1349.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,12) (11,3) (9,10) (2,0) (0,14) (3,15) (0,1) (3,0) (13,14) (10,5) (17,6) (4,17) (3,13) (16,12) (16,2) (7,0) (16,6) (0,6) (2,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1685", "image": "data/cycle/graph_visual/medium/graph1685.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,17) (21,16) (15,11) (1,0) (8,15) (23,18) (14,2) (16,5) (17,9) (16,19) (0,2) (3,0) (8,6) (20,22) (19,0) (20,6) (4,13) (18,1) (12,0) (17,3) (7,23) (0,4) (20,23) (20,2) (6,19) (10,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1530", "image": "data/cycle/graph_visual/medium/graph1530.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (17,18) (10,0) (3,4) (18,13) (6,2) (13,1) (7,8) (16,19) (12,7) (4,14) (20,19) (16,7) (8,11) (0,2) (6,7) (5,20) (3,0) (0,1) (9,3) (2,15) (3,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1103", "image": "data/cycle/graph_visual/medium/graph1103.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,13) (2,11) (10,12) (0,3) (1,8) (4,9) (5,1) (0,1) (6,13) (3,5) (0,2) (7,12) (3,9) (13,11) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph381", "image": "data/cycle/graph_visual/medium/graph381.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (13,0) (7,5) (1,9) (11,16) (2,14) (2,7) (7,13) (6,14) (10,13) (14,12) (15,10) (9,3) (8,16) (9,14) (14,8) (16,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1279", "image": "data/cycle/graph_visual/medium/graph1279.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,3) (2,11) (11,3) (0,1) (2,7) (4,6) (0,2) (5,12) (4,7) (13,5) (10,5) (1,16) (1,13) (7,8) (10,15) (0,9) (0,14) (1,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph406", "image": "data/cycle/graph_visual/medium/graph406.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,6) (12,5) (13,9) (1,3) (15,11) (3,10) (2,14) (15,5) (16,8) (4,7) (10,15) (5,0) (8,14) (6,15) (6,7) (14,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1147", "image": "data/cycle/graph_visual/medium/graph1147.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,3) (9,8) (11,4) (0,1) (2,3) (7,3) (12,2) (0,2) (5,6) (11,6) (6,0) (4,1) (14,6) (2,9) (12,1) (13,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1573", "image": "data/cycle/graph_visual/medium/graph1573.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (14,18) (0,1) (17,19) (18,11) (21,17) (4,21) (13,17) (2,15) (9,1) (8,0) (2,5) (11,10) (18,3) (15,6) (0,2) (6,13) (16,15) (12,4) (10,0) (8,15) (3,0) (21,20) (8,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph197", "image": "data/cycle/graph_visual/medium/graph197.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,11) (13,7) (13,12) (4,2) (0,8) (12,5) (6,11) (11,3) (10,11) (8,10) (9,1) (5,4) (0,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1237", "image": "data/cycle/graph_visual/medium/graph1237.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,2) (15,6) (10,0) (3,15) (12,7) (0,3) (1,4) (15,4) (0,4) (2,9) (5,4) (7,6) (8,6) (6,14) (10,5) (9,13) (4,13) (1,0) (3,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1293", "image": "data/cycle/graph_visual/medium/graph1293.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (6,9) (0,2) (1,0) (13,15) (12,16) (3,0) (14,13) (2,12) (5,3) (4,2) (4,11) (3,12) (14,6) (0,6) (8,10) (0,7) (8,6) (1,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph503", "image": "data/cycle/graph_visual/medium/graph503.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (12,13) (14,4) (1,2) (5,18) (12,5) (17,13) (3,14) (3,8) (14,13) (11,16) (15,18) (4,6) (16,0) (9,15) (10,0) (1,9) (11,7) (11,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph955", "image": "data/cycle/graph_visual/medium/graph955.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,8) (8,3) (4,2) (9,1) (7,10) (1,0) (3,0) (9,10) (2,0) (5,2) (5,9) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph419", "image": "data/cycle/graph_visual/medium/graph419.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,4) (1,2) (14,16) (4,12) (15,0) (14,7) (4,0) (11,12) (13,7) (11,5) (14,0) (7,10) (3,11) (2,5) (6,9) (9,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1070", "image": "data/cycle/graph_visual/medium/graph1070.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,4) (7,10) (5,12) (12,3) (2,0) (4,8) (1,6) (12,7) (7,1) (0,1) (9,2) (9,12) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1023", "image": "data/cycle/graph_visual/medium/graph1023.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,0) (2,6) (0,6) (8,11) (5,1) (4,0) (5,3) (0,3) (2,0) (8,4) (6,12) (2,3) (9,11) (4,6) (9,7) (10,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1660", "image": "data/cycle/graph_visual/medium/graph1660.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (17,4) (9,15) (5,9) (18,10) (14,19) (14,7) (12,6) (1,15) (15,17) (3,14) (0,5) (2,19) (12,18) (0,4) (6,1) (17,2) (13,7) (12,11) (6,20) (21,14) (22,17) (0,3) (10,16) (15,8) (2,0) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1365", "image": "data/cycle/graph_visual/medium/graph1365.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (3,16) (8,2) (15,2) (14,0) (0,4) (0,10) (10,12) (11,9) (3,9) (1,17) (15,9) (0,3) (4,8) (1,0) (0,5) (6,15) (7,8) (13,2) (1,9) (0,2) (13,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1336", "image": "data/cycle/graph_visual/medium/graph1336.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,2) (3,0) (17,11) (4,12) (0,7) (4,1) (9,8) (13,8) (15,6) (0,1) (14,6) (13,1) (3,10) (2,6) (5,11) (16,0) (17,12) (3,9) (15,12) (7,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1392", "image": "data/cycle/graph_visual/medium/graph1392.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (6,17) (11,9) (11,8) (7,16) (18,2) (2,0) (17,0) (11,5) (12,15) (9,4) (2,14) (3,5) (0,1) (0,14) (1,2) (14,7) (7,10) (4,12) (4,0) (13,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1575", "image": "data/cycle/graph_visual/medium/graph1575.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (16,0) (19,16) (0,1) (4,0) (20,17) (12,17) (1,8) (7,10) (0,3) (15,9) (10,2) (21,18) (4,7) (21,15) (11,6) (8,0) (17,4) (5,6) (13,19) (0,2) (0,15) (3,6) (20,8) (3,9) (7,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1472", "image": "data/cycle/graph_visual/medium/graph1472.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,1) (13,3) (1,10) (18,14) (19,18) (16,6) (1,8) (17,6) (12,2) (0,6) (2,0) (3,18) (11,8) (16,19) (0,3) (1,0) (0,4) (15,7) (9,18) (15,3) (13,12) (9,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph564", "image": "data/cycle/graph_visual/medium/graph564.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,9) (11,18) (4,5) (1,14) (19,7) (13,18) (4,12) (2,13) (1,6) (11,3) (17,13) (2,1) (7,2) (10,0) (12,3) (17,10) (6,16) (8,1) (15,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1270", "image": "data/cycle/graph_visual/medium/graph1270.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,12) (0,7) (8,6) (0,3) (0,15) (2,3) (4,6) (14,8) (1,9) (0,4) (16,12) (14,16) (7,14) (9,5) (13,11) (4,11) (13,9) (0,2) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph922", "image": "data/cycle/graph_visual/medium/graph922.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,10) (1,5) (9,8) (5,3) (7,4) (9,6) (8,4) (6,2) (3,2) (0,4) (0,1) (2,0) (3,0) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph501", "image": "data/cycle/graph_visual/medium/graph501.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,3) (3,1) (3,11) (8,16) (16,0) (11,6) (9,7) (13,14) (2,10) (5,10) (16,15) (9,5) (10,8) (12,6) (3,4) (8,18) (14,5) (17,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1742", "image": "data/cycle/graph_visual/medium/graph1742.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (9,18) (8,16) (23,5) (18,2) (20,0) (14,15) (3,0) (1,10) (5,4) (23,13) (12,22) (15,17) (4,24) (21,4) (8,7) (1,12) (9,6) (0,1) (7,20) (7,1) (10,14) (3,9) (11,4) (5,19) (13,0) (21,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1163", "image": "data/cycle/graph_visual/medium/graph1163.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,0) (9,3) (5,2) (9,0) (13,1) (8,2) (9,10) (4,3) (10,7) (8,6) (9,11) (9,1) (1,0) (7,12) (14,5) (0,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph260", "image": "data/cycle/graph_visual/medium/graph260.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,14) (1,12) (0,2) (8,3) (8,12) (13,10) (5,11) (6,8) (4,8) (11,2) (12,2) (13,7) (7,0) (14,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1123", "image": "data/cycle/graph_visual/medium/graph1123.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (4,0) (11,7) (5,0) (0,1) (10,13) (7,3) (6,0) (7,6) (13,4) (9,1) (9,0) (0,3) (8,9) (6,5) (7,13) (4,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph192", "image": "data/cycle/graph_visual/medium/graph192.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,1) (3,6) (4,5) (6,8) (11,12) (2,5) (3,1) (0,10) (13,0) (11,0) (9,5) (10,7) (12,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1632", "image": "data/cycle/graph_visual/medium/graph1632.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,13) (1,0) (2,7) (1,2) (5,9) (4,13) (2,21) (0,2) (8,4) (6,19) (6,17) (15,6) (12,1) (6,18) (20,5) (16,20) (12,10) (14,3) (1,14) (11,9) (17,9) (15,22) (15,0) (4,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph738", "image": "data/cycle/graph_visual/medium/graph738.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (11,12) (15,1) (9,15) (17,4) (14,3) (12,6) (21,14) (7,13) (9,5) (4,0) (17,15) (20,6) (1,6) (22,17) (10,16) (7,14) (14,19) (19,2) (12,18) (10,18) (15,8) (2,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1623", "image": "data/cycle/graph_visual/medium/graph1623.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (18,20) (19,16) (1,13) (2,0) (0,1) (10,0) (4,3) (7,6) (6,2) (17,15) (8,7) (22,0) (5,20) (3,21) (19,0) (18,13) (8,11) (9,3) (4,14) (2,17) (21,2) (3,0) (12,7) (7,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1335", "image": "data/cycle/graph_visual/medium/graph1335.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,1) (6,1) (6,2) (11,2) (5,9) (12,14) (17,10) (8,2) (2,0) (7,5) (4,3) (17,11) (0,3) (15,9) (12,10) (13,12) (16,15) (12,16) (9,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph418", "image": "data/cycle/graph_visual/medium/graph418.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,7) (0,15) (7,3) (0,2) (4,12) (3,11) (4,8) (4,1) (16,7) (10,4) (9,1) (1,15) (12,6) (1,14) (5,3) (13,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph776", "image": "data/cycle/graph_visual/medium/graph776.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (3,21) (7,21) (11,14) (19,5) (9,19) (15,1) (13,14) (4,14) (21,0) (18,16) (20,8) (21,19) (12,9) (14,20) (6,2) (17,11) (13,12) (16,3) (16,10) (22,4) (2,19) (1,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph112", "image": "data/cycle/graph_visual/medium/graph112.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,10) (2,6) (2,10) (10,4) (9,10) (3,2) (4,0) (8,3) (4,1) (10,5) (11,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph310", "image": "data/cycle/graph_visual/medium/graph310.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,3) (10,11) (12,10) (14,2) (14,15) (4,15) (6,12) (5,15) (14,7) (6,1) (7,9) (0,4) (1,15) (6,13) (12,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1191", "image": "data/cycle/graph_visual/medium/graph1191.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,12) (2,0) (2,10) (4,6) (13,10) (8,3) (6,9) (11,14) (2,7) (0,11) (2,3) (2,9) (1,10) (1,0) (13,5) (11,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1233", "image": "data/cycle/graph_visual/medium/graph1233.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,6) (1,0) (9,11) (5,7) (10,5) (4,2) (8,14) (0,6) (15,3) (14,15) (11,2) (7,15) (13,4) (1,4) (12,7) (11,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph54", "image": "data/cycle/graph_visual/medium/graph54.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (8,2) (9,0) (9,6) (10,2) (3,10) (9,8) (0,5) (1,4) (3,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph280", "image": "data/cycle/graph_visual/medium/graph280.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (6,12) (7,1) (7,14) (13,11) (3,6) (12,10) (13,7) (0,5) (8,9) (0,11) (9,2) (8,10) (14,10) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph350", "image": "data/cycle/graph_visual/medium/graph350.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (6,2) (4,10) (6,13) (8,13) (13,14) (1,5) (13,5) (4,15) (6,0) (15,7) (12,7) (1,11) (9,1) (7,0) (3,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph925", "image": "data/cycle/graph_visual/medium/graph925.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,10) (4,1) (7,3) (8,3) (3,6) (4,0) (5,0) (5,9) (1,5) (3,0) (7,5) (0,2) (0,1) (9,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph672", "image": "data/cycle/graph_visual/medium/graph672.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (8,7) (16,14) (15,11) (3,21) (6,12) (20,6) (6,7) (4,21) (18,1) (13,14) (2,0) (12,5) (5,9) (5,2) (19,18) (14,17) (14,8) (19,11) (10,14) (6,15) (12,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph58", "image": "data/cycle/graph_visual/medium/graph58.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,2) (5,4) (1,7) (8,3) (0,7) (6,2) (5,0) (3,5) (7,10) (9,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph376", "image": "data/cycle/graph_visual/medium/graph376.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,8) (0,12) (14,16) (7,3) (15,7) (5,14) (6,10) (11,16) (13,4) (12,1) (5,4) (14,10) (3,4) (2,6) (0,10) (9,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1558", "image": "data/cycle/graph_visual/medium/graph1558.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,1) (7,0) (4,2) (0,20) (19,9) (0,14) (1,12) (18,4) (19,16) (11,19) (12,17) (16,7) (1,8) (2,14) (8,6) (12,20) (6,15) (20,13) (0,10) (9,5) (3,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1704", "image": "data/cycle/graph_visual/medium/graph1704.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,0) (0,2) (17,18) (10,3) (9,7) (11,0) (9,23) (0,5) (3,21) (8,22) (1,0) (20,14) (13,18) (2,20) (14,15) (19,23) (16,0) (0,4) (11,8) (17,1) (11,6) (5,13) (12,1) (21,15) (4,6) (10,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1075", "image": "data/cycle/graph_visual/medium/graph1075.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,6) (10,1) (1,2) (6,2) (3,6) (3,12) (4,0) (11,4) (1,0) (0,3) (2,0) (11,8) (8,9) (7,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1410", "image": "data/cycle/graph_visual/medium/graph1410.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,2) (15,1) (6,16) (1,0) (13,10) (17,3) (17,18) (14,7) (18,10) (9,4) (8,15) (5,15) (17,15) (6,12) (12,14) (4,0) (1,6) (11,7) (12,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph995", "image": "data/cycle/graph_visual/medium/graph995.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,5) (3,10) (3,0) (1,0) (2,7) (6,8) (2,1) (0,4) (9,5) (11,6) (5,0) (8,5) (1,9) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph786", "image": "data/cycle/graph_visual/medium/graph786.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,10) (20,12) (3,16) (3,12) (23,15) (18,0) (22,6) (23,9) (6,23) (23,7) (0,8) (13,3) (5,10) (14,0) (0,1) (18,6) (2,22) (20,17) (14,13) (21,16) (4,17) (16,11) (9,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph281", "image": "data/cycle/graph_visual/medium/graph281.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,12) (9,12) (11,14) (9,7) (12,4) (8,4) (9,2) (10,13) (8,3) (5,8) (1,8) (10,12) (6,0) (6,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph560", "image": "data/cycle/graph_visual/medium/graph560.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (6,0) (2,12) (4,16) (13,14) (2,4) (12,7) (17,9) (8,6) (15,8) (10,0) (2,18) (12,0) (11,6) (5,3) (13,17) (3,19) (14,6) (19,0) (1,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1683", "image": "data/cycle/graph_visual/medium/graph1683.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (10,5) (11,6) (20,8) (8,10) (12,3) (3,11) (3,14) (4,3) (13,9) (18,16) (14,17) (7,10) (9,5) (0,22) (19,1) (0,1) (16,8) (2,0) (16,19) (0,19) (22,23) (15,6) (14,5) (2,16) (21,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph956", "image": "data/cycle/graph_visual/medium/graph956.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,0) (0,5) (6,1) (2,10) (0,2) (0,1) (10,5) (8,0) (9,8) (0,7) (4,3) (5,3) (2,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1277", "image": "data/cycle/graph_visual/medium/graph1277.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,10) (16,0) (5,7) (8,15) (6,8) (12,11) (3,5) (0,1) (12,0) (12,7) (16,13) (4,7) (14,9) (14,10) (2,16) (8,12) (7,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph216", "image": "data/cycle/graph_visual/medium/graph216.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,6) (1,7) (11,13) (5,0) (10,7) (10,8) (4,7) (8,9) (10,12) (0,11) (12,6) (9,2) (13,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1634", "image": "data/cycle/graph_visual/medium/graph1634.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (22,1) (14,18) (15,12) (10,3) (22,14) (2,19) (7,11) (11,9) (5,6) (19,18) (21,13) (10,18) (19,21) (8,14) (7,21) (6,0) (17,7) (12,17) (3,4) (0,1) (6,7) (16,17) (18,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1698", "image": "data/cycle/graph_visual/medium/graph1698.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (1,0) (23,10) (5,9) (15,17) (3,0) (21,16) (0,2) (8,23) (23,11) (6,9) (9,2) (7,2) (10,12) (13,23) (12,17) (23,4) (19,15) (22,13) (11,2) (6,1) (14,5) (12,20) (16,12) (21,18) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1205", "image": "data/cycle/graph_visual/medium/graph1205.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,7) (6,10) (9,13) (15,6) (1,0) (4,6) (14,12) (7,4) (4,1) (8,14) (5,2) (0,2) (6,11) (3,0) (4,0) (12,5) (4,13) (5,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph752", "image": "data/cycle/graph_visual/medium/graph752.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (3,21) (11,3) (12,15) (19,21) (7,10) (1,8) (7,22) (2,14) (10,16) (10,13) (17,2) (9,22) (20,17) (4,2) (11,10) (20,6) (7,18) (7,8) (17,15) (0,15) (4,11) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1295", "image": "data/cycle/graph_visual/medium/graph1295.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,0) (0,15) (2,1) (2,9) (15,6) (13,4) (12,10) (5,6) (1,12) (16,4) (3,14) (13,1) (11,1) (5,9) (7,2) (8,4) (14,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph243", "image": "data/cycle/graph_visual/medium/graph243.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (4,1) (7,10) (11,7) (13,0) (2,4) (0,14) (4,3) (12,5) (9,2) (9,8) (14,5) (7,14) (3,12) (6,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph505", "image": "data/cycle/graph_visual/medium/graph505.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,17) (12,2) (5,10) (10,9) (15,11) (10,18) (6,7) (11,2) (4,17) (15,1) (0,15) (13,0) (8,9) (14,12) (16,11) (10,14) (3,5) (6,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph265", "image": "data/cycle/graph_visual/medium/graph265.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,7) (9,0) (7,10) (5,14) (9,1) (8,2) (3,9) (9,11) (5,2) (0,14) (9,10) (6,8) (1,13) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph808", "image": "data/cycle/graph_visual/medium/graph808.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (13,20) (23,12) (7,5) (1,18) (13,5) (22,16) (21,18) (5,21) (9,15) (11,2) (11,16) (8,9) (11,23) (20,12) (0,1) (8,19) (19,6) (23,10) (21,14) (3,2) (4,2) (1,19) (17,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1009", "image": "data/cycle/graph_visual/medium/graph1009.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,1) (7,0) (2,0) (0,1) (0,5) (8,2) (6,11) (4,0) (0,3) (3,2) (11,10) (9,0) (8,5) (10,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph402", "image": "data/cycle/graph_visual/medium/graph402.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,5) (4,16) (15,10) (1,9) (14,6) (14,8) (16,11) (14,12) (9,14) (2,7) (7,13) (13,0) (2,14) (9,3) (8,16) (10,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph899", "image": "data/cycle/graph_visual/medium/graph899.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (6,13) (8,9) (16,4) (23,13) (19,14) (23,3) (2,20) (9,1) (17,8) (15,18) (2,0) (17,3) (22,2) (4,22) (21,11) (23,24) (5,22) (14,7) (23,11) (9,12) (10,7) (15,5) (14,16) (5,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1376", "image": "data/cycle/graph_visual/medium/graph1376.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (8,2) (8,11) (9,2) (15,7) (7,16) (11,12) (2,6) (15,0) (12,5) (1,8) (8,10) (7,5) (10,14) (0,1) (3,9) (17,15) (13,17) (0,2) (6,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph110", "image": "data/cycle/graph_visual/medium/graph110.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,10) (1,2) (8,5) (6,11) (0,4) (10,3) (9,5) (1,0) (6,8) (9,1) (7,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph130", "image": "data/cycle/graph_visual/medium/graph130.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,11) (7,2) (11,5) (8,1) (11,0) (4,11) (6,7) (7,12) (8,10) (9,1) (9,3) (3,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph457", "image": "data/cycle/graph_visual/medium/graph457.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,0) (5,1) (12,10) (11,6) (11,2) (15,3) (11,12) (4,5) (3,12) (16,11) (3,17) (1,17) (9,4) (14,5) (13,3) (7,3) (2,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1555", "image": "data/cycle/graph_visual/medium/graph1555.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (9,5) (15,3) (14,0) (10,9) (10,4) (11,1) (14,12) (20,16) (15,13) (19,20) (18,9) (8,13) (4,0) (15,2) (0,2) (0,3) (1,0) (9,0) (19,4) (11,7) (7,17) (6,13) (0,7) (7,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph948", "image": "data/cycle/graph_visual/medium/graph948.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,10) (6,5) (1,0) (3,9) (1,7) (0,4) (3,6) (8,5) (10,2) (8,0) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph682", "image": "data/cycle/graph_visual/medium/graph682.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (3,6) (8,0) (14,17) (8,7) (15,18) (10,9) (3,10) (19,2) (16,15) (11,3) (2,21) (5,17) (1,4) (4,6) (12,8) (17,10) (2,12) (21,20) (20,13) (19,16) (0,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1644", "image": "data/cycle/graph_visual/medium/graph1644.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (5,0) (2,21) (15,10) (3,4) (6,22) (16,10) (21,8) (13,20) (10,4) (14,18) (13,14) (7,4) (9,8) (20,11) (3,12) (21,1) (15,18) (5,19) (13,6) (13,0) (18,17) (2,3) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1317", "image": "data/cycle/graph_visual/medium/graph1317.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,16) (0,1) (11,4) (8,1) (12,1) (12,14) (13,0) (10,12) (3,0) (0,5) (0,4) (0,6) (4,2) (2,0) (7,0) (3,9) (8,6) (16,2) (15,7) (6,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph317", "image": "data/cycle/graph_visual/medium/graph317.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,11) (15,12) (14,5) (2,3) (6,1) (7,13) (4,14) (13,8) (9,1) (0,2) (8,6) (10,8) (1,15) (5,9) (3,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1640", "image": "data/cycle/graph_visual/medium/graph1640.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (16,18) (0,17) (2,8) (16,5) (3,12) (7,5) (17,4) (19,21) (10,11) (22,18) (12,17) (7,20) (2,0) (12,14) (13,17) (8,13) (19,1) (7,12) (22,6) (11,9) (0,1) (11,0) (15,11) (12,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1672", "image": "data/cycle/graph_visual/medium/graph1672.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,22) (0,1) (15,14) (1,17) (14,19) (14,4) (15,7) (10,2) (3,0) (11,3) (9,7) (6,9) (0,2) (6,8) (16,9) (5,12) (9,18) (11,1) (10,17) (13,12) (21,9) (2,20) (7,13) (7,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1763", "image": "data/cycle/graph_visual/medium/graph1763.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (19,12) (15,22) (4,20) (2,11) (0,1) (14,5) (22,21) (10,13) (2,10) (8,16) (23,6) (0,19) (21,10) (2,0) (18,5) (19,14) (24,7) (8,4) (9,22) (2,1) (13,4) (17,11) (24,3) (9,6) (7,0) (18,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph779", "image": "data/cycle/graph_visual/medium/graph779.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (22,21) (15,22) (9,0) (5,14) (1,10) (0,19) (3,16) (7,2) (5,19) (12,14) (17,5) (7,4) (8,7) (22,13) (3,20) (4,6) (13,20) (8,1) (19,10) (17,21) (18,11) (2,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1085", "image": "data/cycle/graph_visual/medium/graph1085.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,2) (6,7) (11,10) (4,3) (0,4) (13,10) (0,2) (1,0) (13,2) (5,0) (3,0) (10,12) (5,1) (5,9) (2,7) (4,11) (7,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph107", "image": "data/cycle/graph_visual/medium/graph107.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,1) (4,9) (3,10) (7,4) (2,0) (8,7) (8,11) (3,7) (6,10) (11,2) (5,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1769", "image": "data/cycle/graph_visual/medium/graph1769.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,13) (14,19) (0,2) (15,13) (13,12) (19,7) (6,1) (18,21) (17,23) (3,1) (18,14) (9,10) (17,14) (10,16) (2,24) (12,2) (14,4) (17,10) (11,17) (11,8) (16,22) (3,5) (5,2) (0,21) (13,20) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1388", "image": "data/cycle/graph_visual/medium/graph1388.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,4) (1,0) (5,3) (17,8) (0,2) (1,18) (5,14) (0,3) (0,5) (13,5) (0,15) (16,12) (9,10) (7,2) (5,8) (11,5) (18,15) (0,4) (14,7) (6,2) (16,0) (11,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1755", "image": "data/cycle/graph_visual/medium/graph1755.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (9,3) (19,24) (22,15) (0,7) (14,13) (6,22) (1,0) (20,1) (17,12) (23,10) (9,21) (7,23) (12,15) (20,21) (16,4) (8,11) (3,5) (23,8) (12,18) (2,6) (1,13) (4,20) (6,21) (23,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph782", "image": "data/cycle/graph_visual/medium/graph782.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (9,19) (19,17) (23,22) (7,23) (5,20) (4,15) (19,13) (18,16) (20,7) (0,23) (17,10) (12,4) (22,13) (6,2) (21,15) (13,6) (23,1) (21,13) (14,1) (5,16) (3,21) (11,1) (6,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1391", "image": "data/cycle/graph_visual/medium/graph1391.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,7) (3,0) (12,0) (5,13) (11,8) (4,0) (8,17) (2,14) (16,1) (0,1) (18,9) (4,6) (18,10) (10,3) (13,17) (3,15) (0,11) (11,6) (14,15) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph717", "image": "data/cycle/graph_visual/medium/graph717.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (9,13) (19,21) (0,12) (1,16) (3,10) (3,8) (8,11) (3,4) (7,0) (4,16) (14,0) (11,19) (7,15) (18,16) (10,9) (2,17) (11,5) (12,11) (13,2) (18,20) (6,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph269", "image": "data/cycle/graph_visual/medium/graph269.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,1) (8,1) (4,2) (7,4) (12,8) (14,6) (7,10) (1,0) (3,9) (13,4) (3,12) (12,13) (5,6) (4,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1274", "image": "data/cycle/graph_visual/medium/graph1274.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,16) (13,15) (2,0) (8,6) (11,4) (6,9) (0,6) (12,2) (1,0) (0,7) (8,10) (12,3) (6,14) (1,15) (4,2) (14,13) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1137", "image": "data/cycle/graph_visual/medium/graph1137.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,4) (12,1) (13,7) (0,12) (1,0) (8,11) (6,8) (12,2) (3,12) (3,0) (2,0) (8,13) (5,0) (9,5) (11,5) (10,0) (1,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph348", "image": "data/cycle/graph_visual/medium/graph348.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,12) (10,0) (11,8) (2,15) (9,0) (5,11) (13,6) (3,8) (5,0) (1,6) (7,6) (2,9) (7,12) (8,14) (12,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph702", "image": "data/cycle/graph_visual/medium/graph702.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (8,11) (21,7) (2,20) (1,9) (13,5) (0,1) (10,3) (11,0) (13,0) (17,16) (18,12) (4,6) (14,15) (0,2) (10,7) (17,1) (20,3) (6,11) (8,18) (21,15) (14,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1378", "image": "data/cycle/graph_visual/medium/graph1378.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,5) (0,1) (2,0) (17,16) (9,4) (4,0) (7,14) (11,6) (5,6) (17,2) (9,14) (12,16) (4,2) (16,10) (14,8) (15,13) (1,17) (3,5) (0,14) (3,14) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1779", "image": "data/cycle/graph_visual/medium/graph1779.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (5,3) (14,8) (19,11) (14,13) (10,5) (12,5) (15,11) (9,21) (1,0) (21,4) (22,6) (23,2) (24,12) (15,6) (24,2) (19,21) (12,6) (17,14) (1,18) (8,7) (7,6) (23,16) (20,14) (14,18) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1102", "image": "data/cycle/graph_visual/medium/graph1102.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,8) (10,8) (13,7) (1,0) (8,5) (4,7) (1,8) (2,12) (7,6) (2,0) (9,5) (2,13) (13,3) (0,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph946", "image": "data/cycle/graph_visual/medium/graph946.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,7) (2,7) (7,5) (8,2) (9,10) (1,0) (0,4) (6,9) (1,8) (9,4) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph482", "image": "data/cycle/graph_visual/medium/graph482.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,18) (17,13) (2,6) (11,4) (1,16) (4,7) (6,3) (7,0) (1,14) (6,0) (16,7) (6,13) (13,5) (15,12) (10,1) (17,9) (8,13) (5,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1114", "image": "data/cycle/graph_visual/medium/graph1114.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,7) (6,1) (11,10) (6,2) (12,8) (5,3) (0,11) (9,8) (13,5) (0,1) (13,0) (4,3) (5,12) (10,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1318", "image": "data/cycle/graph_visual/medium/graph1318.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (15,10) (10,7) (12,16) (15,14) (15,1) (3,0) (16,8) (9,2) (0,2) (5,0) (9,6) (1,3) (1,0) (12,14) (11,13) (4,11) (16,0) (14,6) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph892", "image": "data/cycle/graph_visual/medium/graph892.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (24,21) (3,22) (22,8) (4,14) (15,13) (16,21) (20,6) (16,10) (14,8) (20,17) (6,8) (11,10) (5,15) (19,5) (23,24) (9,14) (12,7) (10,3) (9,15) (1,3) (2,21) (0,5) (18,15) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1662", "image": "data/cycle/graph_visual/medium/graph1662.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (3,9) (11,8) (3,0) (15,7) (20,1) (0,10) (9,20) (0,1) (19,2) (15,17) (4,8) (22,8) (2,16) (13,9) (12,2) (9,18) (10,14) (19,1) (15,0) (0,2) (6,13) (5,8) (21,3) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph944", "image": "data/cycle/graph_visual/medium/graph944.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,6) (9,5) (4,7) (1,8) (3,7) (0,4) (0,1) (1,10) (8,6) (0,3) (6,2) (2,0) (7,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1737", "image": "data/cycle/graph_visual/medium/graph1737.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,4) (23,7) (19,9) (2,0) (21,19) (14,13) (11,14) (15,1) (12,23) (16,3) (12,9) (0,3) (1,0) (1,20) (21,6) (18,16) (4,19) (14,20) (17,11) (3,21) (14,23) (22,13) (16,10) (0,21) (2,5) (20,8) (2,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph118", "image": "data/cycle/graph_visual/medium/graph118.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (8,2) (11,3) (1,6) (6,5) (0,4) (7,5) (10,8) (5,9) (8,6) (6,4) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1351", "image": "data/cycle/graph_visual/medium/graph1351.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,5) (6,8) (11,6) (2,0) (4,2) (0,3) (9,4) (12,2) (14,15) (6,5) (16,0) (12,1) (5,10) (9,0) (14,13) (7,5) (1,0) (14,3) (5,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1413", "image": "data/cycle/graph_visual/medium/graph1413.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (13,12) (4,6) (4,11) (14,7) (9,10) (8,14) (11,15) (18,5) (0,2) (12,16) (3,2) (8,6) (13,9) (14,0) (17,7) (16,0) (1,0) (1,9) (0,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1651", "image": "data/cycle/graph_visual/medium/graph1651.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (3,9) (19,0) (3,4) (16,7) (6,7) (18,20) (19,16) (13,1) (10,0) (1,0) (14,4) (12,7) (0,2) (22,0) (5,20) (2,17) (17,15) (2,21) (21,3) (11,8) (2,6) (7,8) (13,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph854", "image": "data/cycle/graph_visual/medium/graph854.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (3,23) (0,20) (11,15) (13,17) (11,9) (19,2) (21,17) (7,12) (14,19) (4,12) (11,5) (7,10) (20,4) (22,21) (4,19) (2,1) (8,22) (22,16) (0,24) (22,23) (6,5) (9,23) (18,19) (22,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1394", "image": "data/cycle/graph_visual/medium/graph1394.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,12) (15,18) (4,3) (0,1) (18,3) (9,10) (10,3) (18,6) (16,1) (16,17) (2,11) (12,0) (0,3) (4,16) (14,7) (8,0) (2,13) (9,13) (2,0) (7,0) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1037", "image": "data/cycle/graph_visual/medium/graph1037.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,12) (5,4) (5,1) (3,9) (8,1) (10,7) (3,11) (1,0) (0,7) (4,2) (10,6) (5,11) (7,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph185", "image": "data/cycle/graph_visual/medium/graph185.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,12) (10,13) (11,9) (3,8) (7,5) (0,1) (0,9) (8,5) (3,0) (5,2) (7,4) (10,6) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph631", "image": "data/cycle/graph_visual/medium/graph631.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,14) (16,8) (13,18) (17,9) (7,3) (4,10) (2,10) (11,12) (5,10) (17,0) (7,0) (5,6) (18,12) (8,12) (20,5) (18,7) (4,19) (9,15) (1,12) (0,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1366", "image": "data/cycle/graph_visual/medium/graph1366.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (3,0) (8,12) (6,13) (4,7) (2,0) (4,2) (2,1) (16,7) (14,17) (6,12) (9,4) (0,1) (0,14) (16,15) (15,14) (7,3) (6,10) (5,11) (1,11) (0,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph812", "image": "data/cycle/graph_visual/medium/graph812.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (21,14) (10,14) (16,20) (15,9) (3,7) (3,6) (8,14) (19,0) (4,18) (8,23) (22,23) (13,12) (3,15) (0,22) (4,1) (2,8) (11,15) (20,12) (6,18) (5,2) (12,17) (13,19) (0,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1367", "image": "data/cycle/graph_visual/medium/graph1367.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,10) (13,15) (17,4) (7,16) (16,4) (5,8) (17,9) (0,3) (4,0) (5,1) (5,11) (12,5) (15,3) (13,1) (2,0) (0,1) (5,0) (8,14) (6,3) (15,2) (6,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph263", "image": "data/cycle/graph_visual/medium/graph263.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,8) (9,14) (5,14) (10,2) (3,13) (10,3) (2,11) (1,4) (0,4) (4,10) (12,10) (7,12) (6,10) (2,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1638", "image": "data/cycle/graph_visual/medium/graph1638.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (5,3) (11,5) (2,1) (20,0) (6,22) (4,0) (20,4) (19,13) (7,10) (0,2) (3,0) (10,21) (12,7) (19,16) (1,0) (22,18) (19,2) (15,21) (14,11) (22,9) (22,19) (22,0) (17,4) (9,11) (4,12) (8,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1273", "image": "data/cycle/graph_visual/medium/graph1273.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,14) (15,12) (16,7) (2,0) (7,9) (11,4) (0,14) (1,0) (8,2) (16,6) (0,8) (3,12) (1,5) (5,3) (15,11) (1,10) (7,3) (13,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1714", "image": "data/cycle/graph_visual/medium/graph1714.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (7,0) (19,3) (16,11) (22,12) (6,9) (18,2) (1,0) (11,2) (23,7) (18,5) (10,2) (13,4) (20,6) (21,10) (8,4) (13,10) (22,21) (4,17) (14,19) (9,22) (1,2) (0,2) (0,19) (15,8) (5,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph439", "image": "data/cycle/graph_visual/medium/graph439.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,5) (10,11) (9,16) (15,7) (12,14) (11,15) (1,8) (6,16) (3,14) (1,0) (17,1) (6,2) (14,5) (4,8) (5,1) (4,11) (13,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph500", "image": "data/cycle/graph_visual/medium/graph500.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,2) (13,12) (5,12) (11,17) (10,0) (8,3) (14,3) (13,14) (17,13) (18,5) (11,7) (1,9) (4,6) (9,15) (15,18) (0,16) (11,16) (14,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1633", "image": "data/cycle/graph_visual/medium/graph1633.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,15) (19,18) (8,20) (0,17) (3,21) (16,14) (8,2) (10,4) (19,22) (4,12) (6,21) (11,15) (16,5) (1,0) (11,9) (20,7) (21,0) (19,21) (1,15) (0,12) (11,13) (22,14) (17,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph302", "image": "data/cycle/graph_visual/medium/graph302.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (8,14) (10,11) (7,12) (6,8) (0,12) (10,13) (7,1) (5,2) (11,12) (0,3) (7,4) (7,5) (3,15) (12,8) (9,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph592", "image": "data/cycle/graph_visual/medium/graph592.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,1) (18,1) (8,13) (18,3) (9,17) (18,2) (16,6) (15,5) (11,17) (3,8) (1,10) (17,10) (16,14) (12,18) (18,7) (4,13) (2,5) (0,19) (16,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph787", "image": "data/cycle/graph_visual/medium/graph787.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (18,16) (18,8) (9,23) (1,16) (21,0) (3,10) (7,16) (6,12) (4,17) (11,16) (8,20) (9,15) (9,10) (12,11) (13,10) (19,4) (6,14) (19,3) (5,3) (8,3) (22,8) (13,21) (1,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph998", "image": "data/cycle/graph_visual/medium/graph998.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,7) (7,4) (7,3) (1,0) (9,0) (6,5) (10,7) (2,0) (9,1) (4,11) (3,0) (8,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph311", "image": "data/cycle/graph_visual/medium/graph311.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,15) (0,6) (8,9) (14,10) (15,1) (15,5) (2,11) (3,2) (11,8) (4,2) (12,9) (11,7) (8,14) (9,6) (1,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1360", "image": "data/cycle/graph_visual/medium/graph1360.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,7) (3,8) (4,11) (7,16) (2,0) (15,10) (15,17) (9,14) (12,3) (16,17) (12,0) (5,7) (2,13) (2,4) (12,17) (1,9) (1,0) (6,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1281", "image": "data/cycle/graph_visual/medium/graph1281.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,16) (15,4) (2,9) (7,1) (5,7) (15,11) (15,2) (8,10) (16,6) (9,14) (0,5) (16,5) (12,14) (3,8) (13,16) (0,3) (9,13) (2,0) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph968", "image": "data/cycle/graph_visual/medium/graph968.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,0) (7,9) (0,2) (11,2) (0,3) (5,10) (9,4) (4,10) (6,10) (3,1) (9,8) (1,7) (0,1) (5,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1017", "image": "data/cycle/graph_visual/medium/graph1017.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,7) (10,1) (3,8) (1,0) (4,7) (5,6) (2,0) (3,7) (3,5) (10,9) (1,2) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1057", "image": "data/cycle/graph_visual/medium/graph1057.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,12) (11,8) (0,5) (0,3) (12,8) (12,2) (6,8) (12,3) (5,11) (0,2) (7,5) (4,0) (1,10) (0,1) (9,0) (1,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph681", "image": "data/cycle/graph_visual/medium/graph681.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,2) (10,1) (4,16) (19,21) (4,8) (18,1) (13,7) (15,4) (7,17) (4,1) (7,4) (17,3) (6,12) (9,21) (21,14) (3,12) (15,0) (17,14) (11,4) (20,1) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph186", "image": "data/cycle/graph_visual/medium/graph186.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,11) (2,9) (2,7) (10,2) (11,3) (12,10) (4,6) (6,9) (13,5) (2,3) (8,3) (10,1) (1,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph124", "image": "data/cycle/graph_visual/medium/graph124.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,5) (9,7) (6,1) (4,5) (6,11) (10,7) (12,6) (5,9) (8,3) (2,1) (4,8) (8,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1524", "image": "data/cycle/graph_visual/medium/graph1524.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,0) (0,1) (13,8) (11,18) (14,3) (2,0) (11,19) (16,1) (4,18) (7,1) (6,14) (13,20) (15,8) (16,8) (0,3) (13,5) (17,15) (8,2) (10,3) (11,12) (19,15) (2,10) (15,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph830", "image": "data/cycle/graph_visual/medium/graph830.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (16,21) (12,0) (3,6) (6,15) (8,23) (15,19) (20,22) (5,10) (1,12) (5,7) (13,6) (22,23) (11,7) (19,2) (12,16) (2,4) (7,4) (13,23) (12,18) (9,19) (17,2) (14,8) (21,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph227", "image": "data/cycle/graph_visual/medium/graph227.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,1) (10,12) (13,9) (10,4) (3,2) (2,8) (11,7) (10,5) (13,7) (2,6) (11,12) (7,6) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1086", "image": "data/cycle/graph_visual/medium/graph1086.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,9) (5,4) (0,5) (11,5) (1,0) (8,4) (8,3) (6,8) (6,1) (7,10) (9,7) (9,6) (6,12) (2,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph916", "image": "data/cycle/graph_visual/medium/graph916.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,0) (8,0) (7,1) (3,9) (5,6) (3,6) (1,0) (4,0) (10,8) (3,0) (5,8) (1,8) (2,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph223", "image": "data/cycle/graph_visual/medium/graph223.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,9) (11,3) (10,7) (2,4) (12,7) (8,11) (1,11) (8,5) (10,2) (3,2) (2,9) (0,1) (12,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1591", "image": "data/cycle/graph_visual/medium/graph1591.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (18,11) (3,2) (9,19) (5,17) (15,9) (10,11) (15,21) (0,2) (19,10) (13,4) (6,13) (13,11) (14,12) (0,20) (7,3) (10,8) (18,5) (1,14) (1,0) (20,8) (16,21) (19,1) (11,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph657", "image": "data/cycle/graph_visual/medium/graph657.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,6) (16,17) (18,8) (14,19) (5,14) (3,2) (3,14) (11,6) (16,8) (5,9) (12,9) (14,15) (10,4) (16,20) (10,5) (3,11) (3,7) (10,8) (16,1) (19,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph199", "image": "data/cycle/graph_visual/medium/graph199.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,6) (4,11) (5,6) (12,4) (6,0) (7,2) (9,0) (8,4) (3,4) (10,3) (1,5) (13,12) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph528", "image": "data/cycle/graph_visual/medium/graph528.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,0) (14,13) (17,4) (6,18) (3,11) (16,6) (17,6) (12,9) (0,14) (0,18) (13,3) (12,16) (7,0) (2,16) (3,15) (10,9) (10,5) (8,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1079", "image": "data/cycle/graph_visual/medium/graph1079.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,7) (7,10) (8,4) (0,1) (5,6) (4,7) (3,12) (11,12) (6,1) (10,6) (2,11) (0,2) (3,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1682", "image": "data/cycle/graph_visual/medium/graph1682.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (12,0) (0,1) (17,21) (6,3) (8,23) (6,15) (19,15) (13,23) (14,8) (4,7) (4,2) (12,16) (16,21) (17,2) (23,22) (10,5) (11,7) (22,20) (1,12) (12,18) (6,13) (19,2) (9,19) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1241", "image": "data/cycle/graph_visual/medium/graph1241.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,12) (15,9) (4,8) (0,1) (13,11) (10,0) (0,5) (10,15) (0,3) (15,1) (1,3) (11,4) (8,14) (7,6) (2,9) (12,14) (2,0) (14,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1092", "image": "data/cycle/graph_visual/medium/graph1092.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,2) (7,4) (6,4) (0,9) (3,12) (12,6) (4,9) (3,0) (1,11) (10,13) (8,5) (5,2) (13,2) (8,6) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1743", "image": "data/cycle/graph_visual/medium/graph1743.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,1) (6,9) (20,12) (13,17) (23,4) (0,2) (6,1) (0,3) (19,15) (5,14) (16,12) (21,18) (7,2) (9,2) (23,13) (24,17) (2,11) (0,4) (3,4) (23,11) (23,10) (5,9) (8,23) (12,21) (22,16) (17,15) (12,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph764", "image": "data/cycle/graph_visual/medium/graph764.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (6,12) (14,12) (2,1) (14,0) (4,9) (20,17) (7,4) (1,13) (18,22) (6,10) (20,15) (2,4) (15,12) (6,16) (18,15) (7,16) (7,3) (0,19) (14,21) (5,11) (8,12) (22,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1047", "image": "data/cycle/graph_visual/medium/graph1047.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,12) (12,5) (2,5) (11,10) (1,5) (10,7) (1,0) (4,5) (11,0) (3,1) (0,9) (6,8) (6,3) (0,2) (0,3) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph201", "image": "data/cycle/graph_visual/medium/graph201.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,6) (11,3) (12,5) (5,7) (9,8) (2,8) (6,0) (4,13) (6,4) (9,0) (3,0) (1,5) (10,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph372", "image": "data/cycle/graph_visual/medium/graph372.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,13) (7,8) (7,0) (9,15) (14,10) (7,14) (1,11) (15,3) (16,9) (13,12) (2,15) (4,9) (6,7) (5,13) (9,0) (0,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1176", "image": "data/cycle/graph_visual/medium/graph1176.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,8) (1,11) (0,2) (5,8) (2,10) (9,11) (12,6) (2,11) (7,12) (2,3) (0,3) (3,13) (0,1) (7,10) (6,14) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph535", "image": "data/cycle/graph_visual/medium/graph535.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (13,18) (17,14) (10,15) (4,10) (8,10) (4,1) (18,9) (3,7) (2,3) (15,18) (0,5) (8,6) (3,4) (12,13) (13,0) (13,14) (11,5) (16,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph886", "image": "data/cycle/graph_visual/medium/graph886.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,20) (15,1) (18,6) (3,20) (5,3) (17,24) (15,8) (11,21) (22,19) (12,9) (16,20) (12,0) (23,6) (8,22) (19,7) (23,24) (17,10) (13,2) (4,2) (24,21) (22,20) (6,14) (0,6) (14,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1405", "image": "data/cycle/graph_visual/medium/graph1405.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,1) (16,15) (10,2) (14,17) (18,8) (2,0) (0,16) (10,5) (6,11) (7,9) (4,0) (5,14) (14,3) (3,11) (10,8) (4,3) (13,14) (5,9) (6,12) (0,3) (3,1) (8,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph724", "image": "data/cycle/graph_visual/medium/graph724.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (14,18) (6,7) (0,6) (18,10) (3,4) (3,10) (12,15) (7,11) (11,9) (22,14) (1,22) (5,6) (21,13) (7,21) (20,18) (7,17) (12,17) (2,19) (14,8) (21,19) (19,18) (17,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph759", "image": "data/cycle/graph_visual/medium/graph759.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (15,11) (14,16) (3,5) (4,21) (22,2) (6,15) (13,14) (6,7) (2,12) (12,6) (17,14) (19,20) (18,1) (5,12) (6,21) (7,8) (5,10) (14,18) (0,2) (14,8) (19,11) (21,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1074", "image": "data/cycle/graph_visual/medium/graph1074.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,4) (4,0) (1,8) (3,12) (11,8) (12,1) (5,6) (10,4) (0,2) (2,4) (7,9) (3,0) (7,4) (6,3) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1179", "image": "data/cycle/graph_visual/medium/graph1179.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,14) (5,14) (8,4) (0,1) (8,11) (0,6) (13,5) (4,1) (3,9) (3,7) (6,13) (10,7) (7,12) (2,4) (8,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1339", "image": "data/cycle/graph_visual/medium/graph1339.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (10,17) (11,1) (0,9) (9,16) (15,7) (14,11) (13,14) (0,1) (8,7) (0,12) (15,3) (10,9) (9,4) (2,15) (5,13) (8,13) (0,7) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph115", "image": "data/cycle/graph_visual/medium/graph115.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,2) (5,8) (1,5) (3,2) (0,8) (2,4) (9,11) (7,11) (4,6) (4,9) (10,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph78", "image": "data/cycle/graph_visual/medium/graph78.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,7) (4,2) (1,4) (7,8) (6,0) (8,11) (3,5) (8,4) (6,7) (8,9) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph267", "image": "data/cycle/graph_visual/medium/graph267.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (6,3) (9,11) (12,4) (4,2) (11,6) (10,12) (3,1) (0,7) (13,3) (10,0) (4,14) (3,8) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1319", "image": "data/cycle/graph_visual/medium/graph1319.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,15) (8,7) (13,6) (0,3) (14,11) (2,15) (2,0) (15,4) (11,10) (6,15) (10,0) (4,0) (1,9) (0,1) (2,5) (16,3) (0,8) (13,3) (12,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph489", "image": "data/cycle/graph_visual/medium/graph489.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (10,9) (4,6) (4,11) (16,12) (11,15) (9,1) (8,6) (3,2) (14,7) (18,5) (0,2) (16,0) (18,0) (14,8) (13,12) (0,14) (13,9) (7,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph477", "image": "data/cycle/graph_visual/medium/graph477.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (14,7) (4,0) (14,8) (12,5) (3,2) (14,2) (14,4) (17,15) (1,6) (5,9) (1,8) (12,16) (6,17) (13,11) (13,3) (16,3) (10,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph324", "image": "data/cycle/graph_visual/medium/graph324.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,7) (1,9) (1,4) (4,12) (3,11) (12,6) (4,7) (4,8) (10,4) (1,14) (3,5) (15,0) (1,13) (2,0) (15,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph504", "image": "data/cycle/graph_visual/medium/graph504.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,18) (14,11) (9,17) (0,12) (12,10) (4,3) (15,13) (9,12) (6,15) (8,1) (18,3) (5,1) (9,4) (16,6) (16,7) (16,4) (15,8) (13,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph933", "image": "data/cycle/graph_visual/medium/graph933.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,9) (7,0) (2,10) (5,0) (8,0) (5,3) (1,0) (2,0) (5,10) (3,4) (2,6) (1,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1473", "image": "data/cycle/graph_visual/medium/graph1473.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (17,14) (0,15) (6,12) (3,5) (13,4) (4,8) (16,1) (0,1) (3,17) (1,9) (0,3) (19,14) (0,2) (10,4) (15,4) (0,4) (11,3) (7,17) (1,4) (18,1) (12,7) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph323", "image": "data/cycle/graph_visual/medium/graph323.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,10) (9,4) (9,7) (11,3) (8,4) (5,12) (8,3) (12,8) (8,10) (1,0) (13,14) (3,15) (6,2) (1,3) (11,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph953", "image": "data/cycle/graph_visual/medium/graph953.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,1) (0,2) (10,8) (0,1) (7,6) (7,4) (5,1) (2,6) (0,3) (0,9) (1,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph50", "image": "data/cycle/graph_visual/medium/graph50.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,9) (2,1) (2,7) (6,0) (5,3) (3,2) (10,1) (3,8) (3,9) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph104", "image": "data/cycle/graph_visual/medium/graph104.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,11) (6,5) (7,11) (4,2) (0,1) (3,9) (6,2) (1,2) (4,8) (9,5) (1,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph768", "image": "data/cycle/graph_visual/medium/graph768.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (4,14) (10,5) (7,3) (1,12) (18,0) (4,10) (22,5) (15,22) (12,11) (2,10) (5,6) (14,0) (18,13) (7,19) (8,17) (21,7) (18,12) (0,20) (12,8) (9,16) (17,9) (21,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph522", "image": "data/cycle/graph_visual/medium/graph522.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,6) (14,0) (16,12) (14,8) (8,6) (5,18) (4,11) (9,1) (0,2) (13,12) (18,0) (16,0) (14,7) (2,3) (13,9) (9,10) (11,15) (17,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph751", "image": "data/cycle/graph_visual/medium/graph751.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,3) (2,3) (7,20) (21,22) (2,22) (9,13) (18,0) (14,8) (12,13) (19,14) (5,2) (9,17) (9,1) (11,4) (19,7) (6,4) (11,16) (0,14) (16,12) (0,10) (18,15) (6,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph314", "image": "data/cycle/graph_visual/medium/graph314.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,12) (3,2) (12,7) (0,15) (13,14) (7,14) (14,8) (1,6) (5,6) (4,10) (3,0) (6,7) (7,10) (11,9) (13,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1048", "image": "data/cycle/graph_visual/medium/graph1048.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (10,4) (1,5) (11,10) (5,9) (8,2) (0,3) (0,1) (0,2) (7,12) (12,6) (9,12) (10,1) (10,3) (0,11) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph81", "image": "data/cycle/graph_visual/medium/graph81.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,11) (6,4) (0,5) (1,3) (3,6) (9,0) (8,3) (2,4) (11,6) (9,10) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1721", "image": "data/cycle/graph_visual/medium/graph1721.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (5,14) (20,23) (17,4) (20,2) (4,0) (12,5) (3,15) (13,15) (8,5) (18,21) (9,17) (9,6) (0,2) (10,16) (1,0) (15,7) (16,21) (9,11) (3,18) (3,0) (4,3) (13,1) (0,5) (6,22) (15,2) (8,19) (5,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph173", "image": "data/cycle/graph_visual/medium/graph173.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,4) (0,7) (9,10) (2,4) (6,7) (8,2) (0,11) (1,3) (9,12) (1,10) (5,3) (10,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1568", "image": "data/cycle/graph_visual/medium/graph1568.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (21,10) (14,17) (21,16) (13,14) (0,10) (13,10) (0,2) (2,6) (11,0) (8,5) (16,12) (12,1) (19,5) (14,5) (20,7) (19,4) (20,9) (18,4) (0,15) (10,6) (7,3) (3,4) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph544", "image": "data/cycle/graph_visual/medium/graph544.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,4) (7,0) (7,5) (12,8) (16,10) (17,14) (1,16) (17,2) (16,17) (15,14) (18,10) (6,17) (18,11) (12,9) (5,3) (7,8) (13,17) (11,12) (19,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph122", "image": "data/cycle/graph_visual/medium/graph122.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,0) (9,0) (12,11) (2,7) (4,3) (7,3) (10,4) (1,5) (3,6) (4,8) (6,5) (12,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph931", "image": "data/cycle/graph_visual/medium/graph931.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,4) (4,6) (1,0) (2,9) (7,10) (3,5) (0,2) (10,2) (0,6) (0,3) (0,4) (1,3) (0,10) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1648", "image": "data/cycle/graph_visual/medium/graph1648.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,15) (14,6) (0,6) (13,2) (22,0) (3,20) (20,21) (0,2) (7,19) (10,17) (21,11) (3,0) (13,14) (6,18) (5,3) (8,16) (0,12) (22,19) (12,9) (4,20) (1,0) (6,15) (4,2) (17,20) (8,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph991", "image": "data/cycle/graph_visual/medium/graph991.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,0) (2,0) (4,11) (8,1) (3,10) (1,9) (4,8) (8,5) (2,10) (0,1) (8,0) (0,7) (6,3) (5,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1517", "image": "data/cycle/graph_visual/medium/graph1517.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,11) (0,3) (17,5) (9,11) (10,20) (12,7) (18,13) (16,1) (12,19) (6,9) (8,13) (13,2) (4,12) (16,10) (15,8) (17,3) (0,7) (4,20) (0,1) (0,2) (16,8) (5,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph667", "image": "data/cycle/graph_visual/medium/graph667.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (9,18) (12,16) (0,3) (4,11) (1,18) (15,21) (13,21) (3,20) (8,0) (17,12) (17,6) (13,1) (0,19) (2,5) (10,11) (16,14) (19,12) (14,7) (10,8) (8,15) (13,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1705", "image": "data/cycle/graph_visual/medium/graph1705.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (6,13) (3,6) (22,23) (18,12) (10,5) (16,21) (7,11) (12,16) (0,12) (1,12) (21,17) (0,1) (2,4) (8,14) (5,7) (19,2) (2,0) (3,0) (9,19) (22,20) (17,2) (23,8) (6,15) (4,0) (15,19) (23,13) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph846", "image": "data/cycle/graph_visual/medium/graph846.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (17,9) (24,21) (14,6) (4,9) (18,23) (18,10) (20,12) (24,9) (15,0) (15,12) (22,11) (16,19) (0,13) (5,23) (1,7) (19,0) (21,10) (22,5) (15,17) (0,7) (2,20) (8,4) (21,14) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph794", "image": "data/cycle/graph_visual/medium/graph794.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (17,12) (18,0) (11,10) (14,12) (13,17) (11,9) (0,23) (18,16) (19,22) (7,5) (16,5) (12,7) (11,0) (15,11) (8,13) (19,1) (12,1) (3,12) (20,17) (7,21) (4,17) (6,22) (2,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph980", "image": "data/cycle/graph_visual/medium/graph980.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,2) (2,4) (1,7) (5,0) (7,4) (8,11) (1,0) (6,5) (10,0) (9,2) (9,3) (5,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1492", "image": "data/cycle/graph_visual/medium/graph1492.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (8,12) (8,11) (15,5) (14,11) (3,10) (0,4) (0,16) (2,0) (0,6) (0,1) (14,10) (7,3) (8,19) (1,13) (4,11) (7,5) (6,2) (3,0) (16,9) (7,17) (1,4) (12,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1739", "image": "data/cycle/graph_visual/medium/graph1739.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (10,21) (0,3) (21,2) (1,8) (22,9) (17,2) (5,4) (20,12) (7,18) (6,23) (7,20) (13,4) (23,4) (8,21) (1,0) (4,16) (19,23) (5,11) (6,17) (13,0) (15,21) (0,2) (14,7) (5,20) (9,0) (9,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph432", "image": "data/cycle/graph_visual/medium/graph432.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,12) (5,12) (0,7) (10,2) (14,0) (14,4) (7,15) (4,10) (3,7) (1,12) (4,16) (17,10) (8,13) (6,5) (12,8) (11,9) (9,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph276", "image": "data/cycle/graph_visual/medium/graph276.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,5) (11,14) (9,2) (2,3) (1,10) (12,3) (8,3) (11,0) (13,10) (4,6) (6,9) (2,10) (11,1) (2,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1506", "image": "data/cycle/graph_visual/medium/graph1506.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (12,13) (8,11) (14,11) (17,10) (17,7) (17,0) (12,1) (1,19) (20,16) (18,19) (1,0) (0,11) (9,11) (0,4) (12,3) (15,12) (0,2) (7,12) (17,4) (3,0) (6,13) (5,16) (2,8) (7,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1139", "image": "data/cycle/graph_visual/medium/graph1139.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,9) (4,1) (0,1) (13,8) (11,1) (13,3) (4,12) (3,0) (13,7) (3,6) (2,0) (10,8) (0,4) (11,2) (5,12) (5,10) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1166", "image": "data/cycle/graph_visual/medium/graph1166.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,13) (9,2) (0,2) (5,14) (1,5) (8,9) (7,2) (7,11) (6,5) (4,7) (1,2) (11,3) (3,10) (0,1) (3,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph934", "image": "data/cycle/graph_visual/medium/graph934.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,3) (8,6) (3,0) (1,4) (1,7) (0,1) (0,2) (10,5) (9,0) (2,4) (8,5) (3,2) (1,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph158", "image": "data/cycle/graph_visual/medium/graph158.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,4) (10,11) (2,12) (5,4) (8,12) (11,8) (12,3) (1,6) (8,0) (6,4) (9,11) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1658", "image": "data/cycle/graph_visual/medium/graph1658.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (15,3) (4,5) (18,22) (17,11) (4,2) (12,9) (20,15) (13,19) (22,17) (1,0) (6,7) (9,16) (3,21) (13,5) (16,6) (7,20) (10,1) (10,22) (8,17) (16,17) (17,0) (6,14) (4,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1788", "image": "data/cycle/graph_visual/medium/graph1788.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (10,1) (2,0) (1,7) (17,15) (6,9) (18,2) (4,5) (14,10) (5,23) (5,19) (9,3) (8,7) (21,2) (1,0) (12,1) (20,0) (20,7) (15,14) (22,12) (23,13) (18,9) (4,24) (16,8) (11,4) (0,13) (0,3) (4,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph19", "image": "data/cycle/graph_visual/medium/graph19.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,10) (0,9) (4,8) (5,2) (7,0) (3,8) (7,6) (8,2) (8,1) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1510", "image": "data/cycle/graph_visual/medium/graph1510.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,0) (0,2) (3,2) (6,1) (7,11) (18,8) (20,4) (10,20) (5,0) (19,1) (0,17) (17,15) (18,9) (16,12) (7,20) (3,0) (1,16) (4,13) (0,4) (2,18) (1,0) (10,2) (5,12) (18,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph438", "image": "data/cycle/graph_visual/medium/graph438.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,9) (9,7) (16,0) (16,3) (6,14) (2,14) (12,4) (14,17) (10,7) (4,1) (1,6) (1,5) (11,13) (8,11) (8,14) (16,4) (0,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph571", "image": "data/cycle/graph_visual/medium/graph571.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,0) (2,15) (12,11) (1,8) (3,9) (2,6) (13,8) (17,14) (15,7) (18,2) (19,18) (10,16) (4,6) (8,10) (5,7) (9,2) (11,8) (7,17) (12,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1296", "image": "data/cycle/graph_visual/medium/graph1296.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,1) (10,3) (15,2) (1,0) (16,11) (0,2) (5,13) (4,11) (9,12) (10,11) (7,10) (8,2) (5,0) (3,6) (6,12) (0,3) (13,10) (8,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1010", "image": "data/cycle/graph_visual/medium/graph1010.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,8) (0,1) (3,0) (2,11) (5,7) (5,6) (1,4) (8,9) (4,11) (5,0) (0,6) (2,0) (10,2) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1242", "image": "data/cycle/graph_visual/medium/graph1242.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,0) (9,0) (7,8) (5,13) (0,4) (3,15) (14,7) (0,2) (15,2) (15,9) (0,7) (1,0) (7,6) (1,11) (11,0) (9,4) (8,13) (13,12) (10,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1496", "image": "data/cycle/graph_visual/medium/graph1496.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,11) (0,19) (14,19) (1,10) (11,12) (0,3) (8,16) (0,2) (4,0) (9,13) (17,13) (6,14) (6,1) (5,0) (18,2) (8,14) (9,18) (4,6) (5,6) (0,1) (7,6) (12,15) (18,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1346", "image": "data/cycle/graph_visual/medium/graph1346.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (8,9) (1,0) (6,1) (7,5) (11,15) (13,12) (10,9) (2,0) (2,11) (6,8) (4,2) (17,11) (14,17) (13,5) (14,16) (5,1) (16,12) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph918", "image": "data/cycle/graph_visual/medium/graph918.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,3) (5,1) (0,3) (7,5) (2,0) (4,2) (8,10) (1,0) (0,7) (4,5) (8,1) (10,6) (3,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1329", "image": "data/cycle/graph_visual/medium/graph1329.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (12,0) (10,0) (1,12) (15,4) (6,2) (5,4) (13,17) (7,3) (13,14) (3,4) (9,0) (10,14) (10,6) (5,14) (16,7) (11,16) (8,5) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph214", "image": "data/cycle/graph_visual/medium/graph214.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,13) (9,13) (2,3) (0,1) (10,4) (5,10) (12,10) (6,2) (2,8) (6,7) (11,12) (1,9) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph936", "image": "data/cycle/graph_visual/medium/graph936.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,0) (4,1) (2,0) (10,9) (0,3) (5,10) (9,1) (2,10) (8,7) (10,0) (0,1) (9,3) (10,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1455", "image": "data/cycle/graph_visual/medium/graph1455.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,2) (10,18) (12,14) (0,6) (1,7) (5,9) (15,12) (14,2) (9,16) (5,19) (8,0) (7,4) (17,15) (3,2) (0,1) (0,13) (10,5) (0,4) (19,11) (4,9) (0,15) (3,0) (17,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph73", "image": "data/cycle/graph_visual/medium/graph73.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,1) (9,5) (0,3) (11,2) (7,3) (3,10) (5,7) (1,5) (8,3) (11,9) (4,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph754", "image": "data/cycle/graph_visual/medium/graph754.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (15,6) (8,21) (4,6) (3,0) (7,20) (11,9) (9,13) (19,13) (11,12) (6,5) (17,14) (9,18) (8,14) (16,1) (1,6) (20,12) (15,0) (18,2) (22,6) (14,19) (18,3) (10,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1571", "image": "data/cycle/graph_visual/medium/graph1571.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (6,13) (6,20) (2,0) (6,16) (3,17) (19,8) (2,4) (5,9) (4,5) (4,7) (1,3) (5,12) (0,3) (18,12) (14,13) (19,4) (15,14) (0,6) (0,1) (6,19) (7,10) (4,17) (20,11) (0,4) (21,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1744", "image": "data/cycle/graph_visual/medium/graph1744.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,14) (3,2) (21,1) (16,13) (11,13) (14,23) (5,15) (12,23) (19,11) (7,14) (6,10) (0,4) (8,1) (3,17) (18,12) (20,21) (0,1) (2,0) (3,16) (9,24) (14,8) (10,24) (5,22) (6,20) (22,17) (2,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1390", "image": "data/cycle/graph_visual/medium/graph1390.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,8) (0,2) (5,9) (15,6) (0,4) (3,14) (0,3) (17,2) (11,4) (0,1) (5,6) (6,16) (1,13) (0,15) (9,18) (1,2) (14,1) (13,4) (10,12) (1,12) (7,2) (9,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph939", "image": "data/cycle/graph_visual/medium/graph939.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,1) (0,3) (5,1) (6,5) (9,7) (2,8) (0,1) (3,9) (6,0) (0,8) (5,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph480", "image": "data/cycle/graph_visual/medium/graph480.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,18) (16,3) (0,14) (8,10) (2,16) (8,13) (11,5) (1,17) (5,17) (14,10) (11,15) (1,3) (7,13) (12,15) (3,4) (6,18) (7,9) (17,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph845", "image": "data/cycle/graph_visual/medium/graph845.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (10,6) (4,0) (5,17) (9,23) (12,3) (13,14) (17,23) (3,16) (2,22) (18,24) (0,8) (9,20) (0,18) (21,12) (19,20) (24,23) (7,23) (15,16) (14,0) (11,2) (10,24) (22,16) (24,1) (13,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph990", "image": "data/cycle/graph_visual/medium/graph990.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,10) (0,1) (0,8) (4,6) (2,4) (2,0) (5,2) (3,2) (9,4) (8,5) (5,1) (11,9) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1265", "image": "data/cycle/graph_visual/medium/graph1265.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,3) (3,0) (4,16) (5,4) (8,16) (4,15) (2,0) (6,16) (13,10) (4,1) (9,6) (0,1) (13,7) (16,14) (0,10) (5,11) (15,3) (7,6) (2,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph912", "image": "data/cycle/graph_visual/medium/graph912.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,1) (4,8) (9,1) (8,10) (3,7) (10,0) (2,0) (0,3) (0,1) (4,5) (2,7) (4,6) (1,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1004", "image": "data/cycle/graph_visual/medium/graph1004.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,3) (4,1) (7,4) (4,2) (11,6) (0,1) (1,11) (2,3) (2,10) (2,0) (11,9) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1531", "image": "data/cycle/graph_visual/medium/graph1531.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,0) (10,7) (4,7) (1,8) (9,3) (17,12) (13,19) (15,0) (19,8) (20,17) (0,8) (0,3) (18,16) (6,11) (15,20) (2,0) (10,2) (6,3) (16,0) (17,4) (7,14) (9,15) (0,1) (5,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1371", "image": "data/cycle/graph_visual/medium/graph1371.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,16) (11,9) (15,2) (6,16) (14,6) (1,8) (15,8) (3,0) (3,4) (14,3) (2,9) (14,5) (10,5) (1,0) (0,17) (16,12) (7,16) (12,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1116", "image": "data/cycle/graph_visual/medium/graph1116.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,6) (11,4) (2,9) (8,3) (3,7) (0,11) (13,5) (2,0) (11,12) (1,5) (0,1) (10,3) (0,7) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph954", "image": "data/cycle/graph_visual/medium/graph954.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,2) (3,0) (8,10) (7,4) (1,6) (1,0) (5,10) (3,9) (0,2) (6,4) (3,7) (8,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1035", "image": "data/cycle/graph_visual/medium/graph1035.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,1) (0,1) (6,11) (11,7) (2,0) (2,6) (3,6) (0,10) (7,5) (12,4) (3,0) (1,8) (1,5) (11,10) (5,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1684", "image": "data/cycle/graph_visual/medium/graph1684.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (4,8) (22,1) (22,10) (5,19) (2,21) (8,2) (10,3) (16,0) (0,3) (21,14) (10,11) (7,11) (13,5) (10,20) (1,17) (15,12) (6,3) (0,23) (20,13) (10,9) (0,2) (6,12) (18,0) (11,8) (16,4) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph900", "image": "data/cycle/graph_visual/medium/graph900.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,0) (6,4) (0,1) (1,5) (7,9) (1,8) (0,5) (5,7) (3,6) (1,6) (0,10) (2,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1106", "image": "data/cycle/graph_visual/medium/graph1106.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,7) (1,13) (12,6) (2,13) (2,3) (7,8) (3,9) (4,8) (1,0) (0,2) (7,10) (0,3) (9,12) (13,8) (11,7) (13,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph374", "image": "data/cycle/graph_visual/medium/graph374.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,0) (5,1) (7,9) (5,3) (6,14) (4,2) (11,16) (9,11) (0,14) (12,5) (0,3) (5,13) (5,10) (8,15) (5,8) (2,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph648", "image": "data/cycle/graph_visual/medium/graph648.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,17) (13,12) (12,16) (14,0) (9,14) (6,3) (20,11) (10,15) (2,8) (0,15) (1,4) (4,18) (12,18) (3,15) (2,5) (14,20) (19,13) (3,7) (15,8) (0,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph46", "image": "data/cycle/graph_visual/medium/graph46.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,7) (10,9) (7,1) (7,10) (2,9) (8,7) (3,1) (5,4) (4,1) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1401", "image": "data/cycle/graph_visual/medium/graph1401.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (12,7) (0,3) (1,15) (4,14) (4,0) (0,5) (17,7) (15,0) (7,4) (4,10) (18,17) (13,4) (5,3) (1,0) (9,1) (2,0) (11,3) (8,4) (12,6) (1,16) (4,1) (3,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1188", "image": "data/cycle/graph_visual/medium/graph1188.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,10) (10,3) (12,14) (13,11) (5,8) (7,2) (0,4) (14,5) (13,12) (1,2) (0,1) (9,1) (9,5) (12,6) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1777", "image": "data/cycle/graph_visual/medium/graph1777.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (13,22) (10,5) (7,6) (2,24) (0,20) (3,0) (22,16) (1,0) (0,17) (3,5) (9,8) (17,4) (12,21) (2,11) (15,1) (10,6) (0,2) (22,2) (15,11) (14,10) (11,19) (5,23) (0,16) (9,10) (20,10) (12,14) (15,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph570", "image": "data/cycle/graph_visual/medium/graph570.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,18) (18,8) (16,2) (6,0) (11,19) (9,14) (0,4) (15,5) (1,17) (17,9) (11,3) (13,7) (7,3) (2,10) (8,10) (17,6) (12,16) (15,13) (19,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1572", "image": "data/cycle/graph_visual/medium/graph1572.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,0) (6,2) (0,17) (10,20) (11,19) (10,1) (4,21) (15,11) (9,8) (12,0) (5,2) (15,16) (7,15) (6,4) (3,0) (0,19) (3,14) (1,0) (16,1) (3,10) (4,17) (18,16) (1,13) (7,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph861", "image": "data/cycle/graph_visual/medium/graph861.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (11,10) (23,3) (22,12) (2,4) (8,1) (10,7) (19,10) (11,4) (9,7) (24,6) (14,24) (8,20) (15,13) (2,17) (17,21) (7,20) (22,21) (15,0) (15,10) (11,5) (11,3) (2,16) (17,18) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1395", "image": "data/cycle/graph_visual/medium/graph1395.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,13) (8,12) (18,10) (14,17) (11,17) (6,17) (0,7) (11,12) (5,3) (17,2) (5,7) (15,16) (0,2) (0,1) (1,16) (16,10) (18,12) (8,7) (9,17) (7,4) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1027", "image": "data/cycle/graph_visual/medium/graph1027.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,1) (11,7) (8,4) (0,2) (12,7) (12,3) (1,7) (2,9) (1,0) (5,12) (12,9) (7,10) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph410", "image": "data/cycle/graph_visual/medium/graph410.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,12) (1,12) (5,16) (7,5) (7,13) (11,6) (9,12) (16,15) (11,0) (8,11) (3,12) (10,11) (4,13) (14,1) (0,12) (2,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph935", "image": "data/cycle/graph_visual/medium/graph935.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,2) (10,8) (8,0) (5,0) (0,6) (2,0) (2,9) (7,4) (5,3) (1,0) (3,0) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1289", "image": "data/cycle/graph_visual/medium/graph1289.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,3) (2,16) (8,1) (6,9) (1,0) (0,13) (7,15) (5,0) (7,0) (1,12) (2,0) (12,10) (14,12) (9,3) (8,6) (4,2) (4,11) (14,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph739", "image": "data/cycle/graph_visual/medium/graph739.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (15,13) (15,2) (12,22) (16,17) (11,3) (12,0) (1,18) (7,11) (4,18) (14,9) (15,6) (1,10) (1,20) (12,6) (1,5) (11,0) (19,22) (20,11) (8,13) (9,21) (2,17) (21,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1537", "image": "data/cycle/graph_visual/medium/graph1537.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,10) (1,8) (17,3) (5,12) (19,6) (14,2) (7,20) (4,14) (1,20) (16,3) (11,12) (18,17) (8,14) (4,0) (2,0) (7,10) (13,16) (11,13) (2,3) (0,1) (15,5) (14,9) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph166", "image": "data/cycle/graph_visual/medium/graph166.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,8) (6,7) (6,5) (3,8) (2,6) (10,5) (0,12) (5,0) (4,1) (9,5) (4,11) (11,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1719", "image": "data/cycle/graph_visual/medium/graph1719.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (5,16) (1,15) (1,0) (2,0) (0,6) (14,22) (8,23) (4,0) (7,3) (3,10) (8,11) (11,21) (11,19) (5,7) (23,13) (10,14) (22,12) (16,9) (21,1) (22,4) (0,17) (7,20) (3,0) (18,4) (6,2) (12,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph984", "image": "data/cycle/graph_visual/medium/graph984.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,0) (1,3) (0,3) (7,3) (2,4) (2,0) (6,11) (10,9) (1,0) (4,6) (8,3) (3,6) (0,5) (9,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1024", "image": "data/cycle/graph_visual/medium/graph1024.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,7) (0,3) (3,2) (8,2) (10,4) (1,0) (1,9) (7,11) (6,2) (11,10) (2,0) (7,6) (5,0) (9,12) (0,4) (10,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1549", "image": "data/cycle/graph_visual/medium/graph1549.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,15) (18,10) (18,7) (2,18) (12,18) (9,17) (6,16) (5,2) (1,19) (17,11) (4,13) (20,0) (5,15) (16,14) (17,20) (18,3) (10,1) (8,3) (0,1) (8,13) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph888", "image": "data/cycle/graph_visual/medium/graph888.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (16,20) (6,0) (14,13) (3,5) (4,2) (20,4) (8,22) (19,7) (11,21) (6,18) (19,22) (0,12) (17,10) (24,23) (22,20) (2,13) (6,23) (15,1) (3,20) (8,15) (12,9) (24,21) (24,17) (6,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1284", "image": "data/cycle/graph_visual/medium/graph1284.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,7) (15,2) (10,16) (0,2) (15,11) (16,6) (13,16) (2,9) (15,4) (9,13) (8,10) (5,7) (0,5) (12,14) (3,8) (5,16) (9,14) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1428", "image": "data/cycle/graph_visual/medium/graph1428.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,0) (13,5) (0,3) (2,7) (0,1) (5,3) (10,9) (5,14) (18,1) (6,2) (11,9) (5,11) (12,16) (2,0) (16,0) (17,8) (5,8) (0,15) (18,15) (14,7) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph585", "image": "data/cycle/graph_visual/medium/graph585.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,12) (2,18) (18,13) (14,17) (6,1) (18,8) (18,9) (11,7) (15,1) (2,3) (4,0) (1,0) (10,1) (7,16) (2,10) (4,17) (16,0) (12,5) (19,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph784", "image": "data/cycle/graph_visual/medium/graph784.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,10) (2,13) (8,11) (9,13) (15,7) (1,16) (12,11) (11,19) (0,4) (0,19) (18,21) (22,3) (18,16) (12,17) (0,7) (4,16) (14,0) (8,3) (10,9) (20,2) (4,23) (6,18) (5,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph750", "image": "data/cycle/graph_visual/medium/graph750.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (14,8) (9,3) (15,22) (7,2) (1,9) (13,21) (7,5) (14,9) (19,10) (20,6) (10,20) (12,16) (20,15) (17,14) (13,7) (11,14) (0,13) (17,2) (16,14) (8,6) (16,4) (17,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph838", "image": "data/cycle/graph_visual/medium/graph838.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (18,11) (3,14) (11,3) (4,5) (2,1) (8,20) (17,13) (0,10) (6,1) (13,20) (7,2) (4,12) (10,2) (17,2) (17,12) (19,13) (6,16) (23,13) (21,2) (1,9) (16,18) (15,1) (22,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph363", "image": "data/cycle/graph_visual/medium/graph363.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,7) (16,8) (1,3) (0,5) (5,15) (8,6) (8,14) (11,15) (10,3) (9,14) (14,2) (10,15) (12,5) (6,7) (9,13) (15,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph513", "image": "data/cycle/graph_visual/medium/graph513.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (9,10) (8,1) (17,2) (12,4) (16,14) (9,12) (11,7) (7,18) (11,0) (15,14) (9,7) (6,9) (2,10) (6,5) (13,9) (7,15) (13,1) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1271", "image": "data/cycle/graph_visual/medium/graph1271.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,7) (0,1) (0,2) (1,11) (0,11) (10,14) (13,12) (2,15) (9,4) (7,8) (3,15) (16,9) (15,9) (7,0) (9,0) (13,5) (13,8) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph344", "image": "data/cycle/graph_visual/medium/graph344.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (6,10) (15,13) (4,9) (12,0) (7,6) (14,0) (8,12) (14,15) (11,1) (2,4) (4,7) (7,3) (11,5) (12,6) (1,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph150", "image": "data/cycle/graph_visual/medium/graph150.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,3) (8,1) (12,9) (2,9) (8,5) (6,0) (10,12) (4,12) (7,9) (6,12) (8,4) (11,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1458", "image": "data/cycle/graph_visual/medium/graph1458.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,16) (6,19) (6,1) (18,3) (9,6) (12,7) (15,11) (11,8) (7,9) (19,14) (16,4) (8,14) (13,4) (1,4) (18,14) (0,2) (0,16) (1,0) (1,10) (2,14) (17,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1403", "image": "data/cycle/graph_visual/medium/graph1403.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,6) (12,7) (14,8) (18,3) (17,0) (10,1) (6,14) (6,9) (16,4) (13,4) (16,0) (14,18) (14,2) (1,0) (7,9) (11,8) (5,16) (11,15) (1,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph11", "image": "data/cycle/graph_visual/medium/graph11.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,10) (3,4) (0,9) (10,6) (8,7) (8,9) (10,8) (3,5) (2,1) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph14", "image": "data/cycle/graph_visual/medium/graph14.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,4) (8,6) (0,1) (9,2) (4,3) (4,1) (4,9) (10,1) (10,5) (3,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph6", "image": "data/cycle/graph_visual/medium/graph6.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,6) (8,5) (4,0) (8,0) (8,1) (8,10) (1,7) (10,2) (9,3) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1754", "image": "data/cycle/graph_visual/medium/graph1754.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,23) (17,10) (19,16) (10,15) (0,8) (0,1) (21,0) (2,1) (23,12) (20,24) (19,11) (18,12) (9,13) (18,4) (13,20) (12,3) (15,9) (16,7) (22,5) (11,12) (3,20) (5,16) (6,19) (11,1) (14,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph5", "image": "data/cycle/graph_visual/medium/graph5.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,4) (0,4) (2,8) (1,8) (6,9) (2,7) (5,7) (10,9) (3,1) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph62", "image": "data/cycle/graph_visual/medium/graph62.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,3) (5,4) (3,0) (5,10) (0,6) (8,2) (1,5) (8,0) (6,1) (9,7) (11,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph981", "image": "data/cycle/graph_visual/medium/graph981.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,1) (5,7) (0,4) (8,2) (4,6) (10,8) (5,6) (5,9) (8,6) (0,1) (2,0) (11,5) (11,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1187", "image": "data/cycle/graph_visual/medium/graph1187.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,13) (11,2) (11,12) (3,0) (9,4) (3,10) (4,0) (0,1) (12,7) (7,3) (12,13) (1,8) (0,2) (13,6) (5,1) (14,5) (9,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph180", "image": "data/cycle/graph_visual/medium/graph180.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,1) (8,7) (6,5) (3,13) (3,10) (2,4) (3,11) (12,0) (4,1) (3,5) (9,8) (4,7) (9,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1594", "image": "data/cycle/graph_visual/medium/graph1594.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,21) (16,14) (10,1) (18,6) (5,15) (3,0) (20,1) (16,4) (0,1) (8,21) (2,0) (13,0) (13,3) (15,16) (5,2) (9,17) (18,20) (8,12) (17,7) (21,17) (18,2) (3,18) (18,11) (19,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1054", "image": "data/cycle/graph_visual/medium/graph1054.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,1) (10,11) (2,7) (4,2) (9,0) (3,6) (8,7) (5,10) (12,5) (2,11) (1,11) (0,3) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1130", "image": "data/cycle/graph_visual/medium/graph1130.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,13) (6,8) (4,13) (0,2) (0,3) (0,4) (1,13) (2,3) (3,10) (1,0) (11,8) (8,4) (12,13) (3,13) (5,8) (7,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph634", "image": "data/cycle/graph_visual/medium/graph634.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (17,12) (0,20) (12,1) (14,2) (13,20) (4,2) (19,11) (20,12) (19,16) (0,10) (19,9) (6,15) (4,18) (9,5) (3,17) (16,7) (6,8) (0,14) (7,0) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1404", "image": "data/cycle/graph_visual/medium/graph1404.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,8) (13,12) (7,0) (12,1) (0,9) (17,16) (15,14) (4,0) (9,10) (2,0) (6,11) (1,0) (16,7) (2,4) (0,14) (3,17) (6,8) (3,0) (18,5) (0,5) (12,4) (5,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph437", "image": "data/cycle/graph_visual/medium/graph437.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (5,16) (3,14) (6,8) (15,14) (12,1) (6,5) (0,3) (2,4) (14,13) (9,4) (5,17) (5,10) (0,16) (0,9) (11,6) (7,5) (12,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph891", "image": "data/cycle/graph_visual/medium/graph891.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,21) (19,2) (6,3) (8,4) (16,13) (6,14) (23,16) (12,22) (5,19) (5,23) (8,23) (23,11) (18,0) (14,17) (15,11) (0,1) (23,14) (20,11) (1,22) (7,16) (5,1) (22,9) (1,24) (15,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph475", "image": "data/cycle/graph_visual/medium/graph475.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,2) (4,6) (11,8) (7,5) (15,7) (15,17) (11,12) (16,7) (15,0) (8,2) (9,2) (9,3) (1,8) (12,5) (17,13) (8,10) (10,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph52", "image": "data/cycle/graph_visual/medium/graph52.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,0) (2,3) (7,5) (3,7) (0,7) (9,1) (6,7) (8,5) (9,8) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph484", "image": "data/cycle/graph_visual/medium/graph484.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,2) (10,11) (10,8) (17,3) (17,6) (1,12) (16,14) (14,7) (15,12) (1,13) (3,0) (0,13) (18,8) (0,8) (9,18) (11,4) (16,12) (2,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph607", "image": "data/cycle/graph_visual/medium/graph607.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (15,5) (0,2) (9,1) (17,3) (9,8) (19,16) (5,13) (13,6) (7,14) (11,2) (13,14) (9,12) (15,3) (20,14) (14,18) (5,11) (10,7) (17,8) (16,4) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1539", "image": "data/cycle/graph_visual/medium/graph1539.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (12,0) (1,0) (8,14) (4,2) (11,7) (15,18) (12,8) (19,20) (19,9) (19,13) (19,2) (6,13) (4,7) (3,0) (5,10) (0,2) (1,12) (16,12) (17,2) (15,6) (0,4) (3,6) (16,17) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1663", "image": "data/cycle/graph_visual/medium/graph1663.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (5,12) (9,18) (20,2) (16,9) (9,7) (10,17) (6,9) (0,1) (15,7) (22,0) (10,7) (17,1) (12,13) (15,14) (8,6) (1,11) (2,10) (0,2) (3,11) (9,21) (7,13) (4,14) (19,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1446", "image": "data/cycle/graph_visual/medium/graph1446.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (3,8) (13,0) (10,15) (4,3) (16,13) (19,6) (0,5) (11,18) (14,18) (6,13) (12,5) (4,1) (4,10) (9,10) (2,3) (0,1) (2,17) (8,7) (0,2) (15,18) (13,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1310", "image": "data/cycle/graph_visual/medium/graph1310.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (9,6) (16,7) (0,2) (5,0) (10,9) (15,13) (4,9) (0,3) (8,5) (2,15) (15,3) (1,0) (16,4) (1,5) (1,13) (4,0) (6,3) (12,5) (14,8) (5,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph120", "image": "data/cycle/graph_visual/medium/graph120.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,3) (9,0) (1,2) (10,12) (10,5) (7,10) (8,2) (4,3) (7,4) (8,11) (2,10) (8,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph337", "image": "data/cycle/graph_visual/medium/graph337.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,14) (11,12) (5,0) (2,1) (8,9) (7,15) (12,10) (4,7) (0,13) (5,11) (1,11) (9,13) (3,0) (12,15) (10,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph177", "image": "data/cycle/graph_visual/medium/graph177.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,2) (3,8) (10,5) (0,5) (0,12) (8,6) (7,6) (11,4) (1,4) (9,5) (6,5) (11,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph613", "image": "data/cycle/graph_visual/medium/graph613.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (13,20) (15,10) (7,16) (0,18) (12,17) (19,4) (19,16) (12,11) (1,11) (0,6) (18,3) (13,9) (10,14) (12,20) (16,5) (2,1) (0,5) (7,8) (15,9) (19,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph538", "image": "data/cycle/graph_visual/medium/graph538.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (16,12) (3,11) (13,14) (1,0) (14,0) (3,13) (15,3) (9,12) (17,6) (4,17) (8,2) (7,0) (6,16) (5,10) (0,18) (9,10) (2,16) (6,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph614", "image": "data/cycle/graph_visual/medium/graph614.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,0) (10,7) (19,6) (5,12) (13,11) (13,16) (14,2) (14,9) (12,11) (3,16) (10,6) (1,8) (18,17) (20,7) (5,15) (3,2) (14,8) (4,14) (3,17) (20,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph579", "image": "data/cycle/graph_visual/medium/graph579.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,10) (8,2) (3,17) (2,13) (13,5) (10,12) (15,6) (8,4) (14,15) (19,2) (8,7) (16,9) (1,19) (9,3) (9,1) (0,3) (0,15) (9,11) (18,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1554", "image": "data/cycle/graph_visual/medium/graph1554.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,3) (4,0) (15,18) (20,8) (0,3) (9,3) (19,2) (14,13) (6,13) (1,0) (4,10) (6,20) (0,2) (0,13) (18,14) (16,5) (15,10) (12,18) (0,5) (7,8) (2,3) (17,13) (1,4) (11,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph817", "image": "data/cycle/graph_visual/medium/graph817.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (12,2) (8,12) (7,3) (23,22) (6,17) (13,10) (19,22) (19,16) (3,11) (10,20) (0,11) (21,3) (4,23) (0,8) (9,8) (10,22) (16,15) (6,5) (1,4) (17,18) (15,2) (14,20) (22,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1604", "image": "data/cycle/graph_visual/medium/graph1604.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (4,9) (1,0) (7,0) (20,10) (21,14) (12,21) (8,13) (20,12) (17,5) (3,17) (16,10) (11,6) (16,8) (13,18) (5,9) (15,8) (7,12) (2,13) (19,21) (0,3) (1,16) (9,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1566", "image": "data/cycle/graph_visual/medium/graph1566.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,0) (4,12) (8,20) (0,3) (12,0) (4,10) (14,16) (19,20) (16,5) (13,11) (21,19) (1,15) (19,14) (11,9) (0,21) (0,17) (18,7) (1,0) (7,17) (11,15) (8,15) (21,6) (8,2) (4,0) (3,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1688", "image": "data/cycle/graph_visual/medium/graph1688.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (17,19) (2,0) (23,0) (22,23) (13,21) (1,14) (6,13) (23,7) (19,9) (3,21) (4,15) (8,6) (1,0) (16,18) (20,5) (22,13) (0,3) (10,17) (12,4) (1,11) (4,0) (23,1) (15,21) (20,7) (19,13) (5,16) (6,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1144", "image": "data/cycle/graph_visual/medium/graph1144.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (6,2) (1,14) (6,3) (0,2) (0,1) (6,5) (4,13) (0,4) (11,8) (3,1) (1,11) (12,2) (7,8) (3,0) (9,8) (10,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1791", "image": "data/cycle/graph_visual/medium/graph1791.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (9,11) (11,15) (14,4) (7,17) (17,0) (11,16) (19,21) (21,6) (21,3) (21,0) (22,19) (15,1) (1,0) (8,15) (8,2) (7,23) (16,5) (0,12) (12,13) (24,14) (19,4) (10,4) (20,8) (22,20) (14,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph287", "image": "data/cycle/graph_visual/medium/graph287.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,0) (2,12) (10,9) (3,5) (4,11) (9,14) (13,4) (1,14) (8,7) (6,10) (1,3) (2,13) (0,11) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph222", "image": "data/cycle/graph_visual/medium/graph222.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,7) (1,12) (8,2) (11,12) (11,10) (1,7) (11,4) (7,2) (5,9) (10,5) (12,6) (3,0) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1282", "image": "data/cycle/graph_visual/medium/graph1282.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,15) (2,11) (13,5) (16,12) (1,5) (11,14) (3,0) (8,6) (9,10) (4,2) (0,1) (14,16) (2,0) (13,12) (8,9) (2,3) (6,1) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1227", "image": "data/cycle/graph_visual/medium/graph1227.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,14) (14,4) (13,11) (9,5) (5,12) (1,6) (2,0) (1,8) (14,7) (12,3) (8,14) (6,15) (11,10) (0,4) (2,3) (3,13) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph56", "image": "data/cycle/graph_visual/medium/graph56.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,6) (3,4) (1,2) (10,2) (1,0) (2,7) (9,10) (4,7) (8,5) (5,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1253", "image": "data/cycle/graph_visual/medium/graph1253.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,0) (0,1) (3,9) (11,6) (13,0) (0,5) (10,4) (6,14) (8,12) (15,11) (10,3) (0,6) (9,2) (13,3) (14,12) (2,0) (7,2) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1232", "image": "data/cycle/graph_visual/medium/graph1232.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,0) (3,0) (15,2) (1,13) (11,5) (3,14) (4,9) (5,8) (15,4) (9,7) (5,10) (6,9) (2,0) (12,8) (15,13) (6,3) (5,1) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1362", "image": "data/cycle/graph_visual/medium/graph1362.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,2) (11,0) (0,17) (13,9) (0,3) (17,9) (7,13) (15,2) (1,8) (11,3) (5,11) (15,10) (12,1) (15,6) (12,6) (0,1) (14,2) (1,4) (1,11) (0,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph683", "image": "data/cycle/graph_visual/medium/graph683.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,10) (17,6) (5,14) (1,2) (8,12) (7,21) (18,2) (10,13) (19,0) (9,21) (6,9) (13,4) (11,2) (14,19) (0,7) (5,18) (15,11) (19,3) (10,20) (8,4) (16,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1512", "image": "data/cycle/graph_visual/medium/graph1512.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (10,16) (20,9) (16,11) (5,20) (3,7) (8,4) (5,1) (17,16) (16,15) (2,0) (19,20) (15,6) (14,15) (9,14) (2,20) (18,0) (20,7) (5,12) (19,13) (17,8) (0,1) (10,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1708", "image": "data/cycle/graph_visual/medium/graph1708.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (11,23) (0,2) (10,7) (1,0) (14,16) (22,4) (9,8) (4,0) (6,13) (7,14) (9,12) (18,15) (11,21) (0,3) (22,2) (5,0) (14,19) (4,16) (5,13) (3,17) (2,20) (8,17) (5,22) (23,3) (13,23) (9,1) (15,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph542", "image": "data/cycle/graph_visual/medium/graph542.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,19) (7,1) (6,16) (2,9) (3,14) (7,4) (14,12) (2,17) (15,8) (18,1) (5,9) (9,19) (2,12) (6,9) (13,2) (15,2) (11,8) (0,14) (4,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph866", "image": "data/cycle/graph_visual/medium/graph866.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (15,18) (15,6) (24,19) (2,5) (16,18) (21,4) (23,6) (10,11) (7,24) (0,22) (17,24) (1,0) (0,8) (12,1) (8,15) (15,2) (24,10) (23,20) (17,13) (13,23) (18,3) (21,11) (14,4) (8,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1224", "image": "data/cycle/graph_visual/medium/graph1224.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,5) (3,14) (1,12) (14,12) (9,4) (0,3) (0,4) (13,14) (0,1) (6,11) (5,6) (2,4) (0,2) (6,8) (0,15) (5,2) (0,9) (10,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1720", "image": "data/cycle/graph_visual/medium/graph1720.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (16,22) (20,10) (0,16) (19,11) (23,22) (9,10) (18,15) (12,14) (2,12) (20,0) (0,1) (5,3) (2,11) (6,7) (1,15) (9,8) (10,14) (22,13) (5,21) (10,6) (17,0) (10,5) (17,4) (11,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph587", "image": "data/cycle/graph_visual/medium/graph587.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (12,16) (13,19) (14,9) (10,16) (16,8) (13,9) (10,17) (17,7) (2,18) (5,19) (2,9) (1,5) (14,15) (5,11) (6,15) (18,0) (7,3) (15,16) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1325", "image": "data/cycle/graph_visual/medium/graph1325.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (10,3) (5,13) (3,0) (1,0) (11,2) (11,1) (16,15) (17,1) (6,3) (9,17) (17,7) (16,10) (4,14) (16,7) (13,8) (12,1) (0,2) (4,8) (14,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1793", "image": "data/cycle/graph_visual/medium/graph1793.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (2,1) (2,0) (19,0) (24,3) (2,11) (21,22) (7,24) (1,0) (6,23) (0,4) (9,22) (0,3) (18,2) (5,18) (13,4) (22,15) (5,14) (11,17) (10,2) (19,14) (7,0) (9,6) (13,10) (10,21) (12,19) (8,16) (20,4) (8,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1268", "image": "data/cycle/graph_visual/medium/graph1268.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (3,9) (16,15) (4,7) (3,0) (10,2) (8,1) (15,9) (15,0) (0,8) (14,8) (11,6) (2,0) (0,1) (7,12) (10,7) (4,16) (3,6) (13,0) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph321", "image": "data/cycle/graph_visual/medium/graph321.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (6,13) (1,8) (15,14) (5,2) (10,2) (10,12) (2,8) (3,4) (11,7) (14,5) (4,13) (2,0) (4,11) (6,9) (10,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1088", "image": "data/cycle/graph_visual/medium/graph1088.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (10,3) (6,0) (1,2) (9,7) (4,7) (3,12) (13,3) (1,7) (0,11) (6,2) (0,1) (13,8) (10,0) (5,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1767", "image": "data/cycle/graph_visual/medium/graph1767.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (8,23) (13,5) (11,5) (11,15) (3,8) (16,13) (20,0) (1,0) (12,14) (18,1) (10,15) (17,1) (2,7) (1,6) (21,13) (23,1) (19,4) (24,2) (22,20) (0,14) (14,11) (12,17) (9,16) (7,0) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1245", "image": "data/cycle/graph_visual/medium/graph1245.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,8) (7,15) (9,15) (3,15) (3,5) (0,4) (4,1) (13,12) (2,0) (3,0) (0,12) (15,13) (2,8) (1,0) (2,4) (0,14) (10,12) (11,6) (3,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1637", "image": "data/cycle/graph_visual/medium/graph1637.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (9,1) (0,16) (8,21) (14,15) (13,22) (17,19) (19,15) (4,6) (14,4) (1,2) (18,21) (20,0) (0,1) (22,5) (10,3) (19,11) (13,17) (9,22) (19,12) (13,16) (11,7) (11,18) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph137", "image": "data/cycle/graph_visual/medium/graph137.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,6) (6,5) (8,4) (7,2) (5,1) (4,12) (0,9) (0,6) (11,12) (7,3) (4,3) (4,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1288", "image": "data/cycle/graph_visual/medium/graph1288.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (2,16) (0,4) (7,0) (9,3) (16,14) (10,12) (5,0) (1,0) (15,7) (4,11) (2,4) (0,3) (13,0) (6,8) (14,12) (0,2) (1,12) (8,1) (9,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph678", "image": "data/cycle/graph_visual/medium/graph678.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,17) (1,8) (6,20) (21,7) (10,12) (15,10) (4,11) (11,5) (10,7) (15,9) (14,17) (2,4) (7,8) (0,15) (3,11) (10,11) (21,18) (13,2) (16,7) (19,17) (3,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph864", "image": "data/cycle/graph_visual/medium/graph864.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (11,8) (16,4) (0,7) (19,0) (0,14) (4,23) (9,13) (20,2) (12,17) (7,15) (9,10) (24,4) (18,16) (11,5) (12,11) (18,21) (2,13) (0,24) (10,3) (6,18) (16,1) (22,3) (19,11) (8,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph910", "image": "data/cycle/graph_visual/medium/graph910.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,7) (0,4) (5,2) (8,6) (0,9) (5,4) (1,0) (2,0) (3,6) (0,5) (0,10) (0,3) (3,1) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph651", "image": "data/cycle/graph_visual/medium/graph651.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (2,13) (15,8) (9,18) (14,3) (19,1) (7,4) (17,2) (2,15) (14,0) (6,9) (6,16) (19,9) (10,20) (8,11) (2,12) (10,4) (12,14) (5,9) (1,7) (2,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph294", "image": "data/cycle/graph_visual/medium/graph294.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,5) (1,0) (12,6) (12,7) (9,11) (10,7) (14,6) (11,1) (3,13) (2,3) (4,2) (10,2) (2,11) (8,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph586", "image": "data/cycle/graph_visual/medium/graph586.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (13,2) (7,18) (14,3) (0,3) (5,16) (8,5) (0,16) (2,4) (6,10) (9,4) (9,0) (14,17) (15,19) (14,18) (6,12) (1,12) (15,5) (11,5) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph498", "image": "data/cycle/graph_visual/medium/graph498.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,11) (8,15) (16,1) (10,5) (10,4) (0,18) (9,13) (2,17) (12,8) (11,3) (3,17) (7,10) (18,13) (6,4) (0,11) (14,1) (18,16) (4,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1142", "image": "data/cycle/graph_visual/medium/graph1142.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,9) (0,14) (0,2) (10,4) (14,12) (11,10) (7,14) (14,8) (13,10) (13,14) (3,10) (0,1) (12,6) (4,2) (0,4) (3,0) (5,12) (11,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph213", "image": "data/cycle/graph_visual/medium/graph213.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,13) (13,2) (8,1) (2,0) (9,5) (13,3) (6,7) (4,7) (8,10) (6,8) (11,0) (2,12) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph775", "image": "data/cycle/graph_visual/medium/graph775.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (19,22) (18,4) (2,17) (2,15) (11,3) (13,15) (11,0) (10,1) (14,9) (8,13) (22,12) (6,15) (5,1) (6,12) (12,0) (7,11) (18,1) (16,17) (0,21) (20,1) (21,9) (11,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph669", "image": "data/cycle/graph_visual/medium/graph669.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (7,11) (16,1) (2,11) (3,17) (5,4) (11,19) (12,21) (8,3) (20,19) (5,18) (18,6) (2,9) (17,18) (0,15) (12,13) (11,12) (1,19) (4,10) (15,5) (21,3) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph708", "image": "data/cycle/graph_visual/medium/graph708.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (8,5) (21,4) (9,17) (14,2) (16,15) (10,0) (1,19) (0,3) (1,20) (6,13) (4,2) (3,9) (9,12) (7,15) (2,19) (10,13) (15,0) (11,8) (3,18) (20,9) (8,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph654", "image": "data/cycle/graph_visual/medium/graph654.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,12) (1,11) (19,14) (17,0) (3,7) (10,6) (15,18) (15,12) (4,2) (8,12) (6,13) (14,12) (4,9) (16,7) (2,1) (20,16) (14,0) (20,15) (4,7) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1438", "image": "data/cycle/graph_visual/medium/graph1438.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,5) (6,16) (18,2) (10,13) (11,2) (11,12) (18,7) (9,6) (14,0) (0,7) (15,4) (10,9) (4,8) (0,1) (2,10) (5,14) (4,13) (2,1) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1039", "image": "data/cycle/graph_visual/medium/graph1039.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,10) (0,3) (0,7) (9,5) (4,0) (6,0) (10,8) (4,7) (2,0) (1,5) (6,5) (8,12) (0,1) (2,9) (4,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph488", "image": "data/cycle/graph_visual/medium/graph488.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (12,6) (7,3) (17,15) (4,9) (14,15) (2,1) (16,0) (18,12) (13,6) (4,7) (7,16) (14,0) (4,2) (11,1) (12,14) (6,10) (12,8) (5,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1235", "image": "data/cycle/graph_visual/medium/graph1235.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (15,6) (9,15) (10,0) (14,1) (0,1) (0,13) (14,11) (3,12) (5,12) (10,2) (9,7) (8,0) (11,7) (9,10) (4,14) (5,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1046", "image": "data/cycle/graph_visual/medium/graph1046.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,12) (1,4) (0,3) (0,1) (11,4) (8,7) (2,0) (0,6) (6,5) (12,11) (8,9) (10,2) (7,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph989", "image": "data/cycle/graph_visual/medium/graph989.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,2) (0,2) (11,5) (0,10) (0,1) (0,3) (10,1) (3,9) (4,7) (11,8) (4,1) (4,6) (4,8) (1,3) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph856", "image": "data/cycle/graph_visual/medium/graph856.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (2,19) (10,7) (11,15) (19,18) (20,4) (0,24) (17,21) (7,12) (22,23) (11,5) (20,0) (17,13) (4,19) (22,10) (3,23) (11,9) (14,19) (22,8) (22,16) (9,23) (1,2) (5,6) (12,4) (22,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph426", "image": "data/cycle/graph_visual/medium/graph426.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,1) (9,11) (2,8) (15,8) (8,17) (11,16) (15,11) (14,15) (8,13) (14,0) (12,3) (4,13) (7,15) (3,10) (14,5) (2,10) (1,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph610", "image": "data/cycle/graph_visual/medium/graph610.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (7,4) (11,6) (9,3) (12,17) (14,7) (10,2) (6,3) (17,20) (15,9) (8,19) (5,6) (0,8) (17,4) (20,15) (16,0) (13,19) (18,16) (1,8) (10,7) (15,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph49", "image": "data/cycle/graph_visual/medium/graph49.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,9) (4,2) (7,8) (7,6) (8,4) (3,5) (0,6) (3,7) (4,1) (10,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph134", "image": "data/cycle/graph_visual/medium/graph134.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,1) (1,0) (3,4) (2,1) (3,5) (10,7) (7,2) (6,9) (11,8) (12,6) (4,1) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1055", "image": "data/cycle/graph_visual/medium/graph1055.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,9) (7,3) (1,0) (0,5) (9,8) (12,8) (8,10) (3,0) (0,9) (0,2) (9,6) (4,1) (6,1) (2,11) (3,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph144", "image": "data/cycle/graph_visual/medium/graph144.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,8) (12,2) (0,9) (0,1) (9,4) (6,11) (12,3) (1,10) (7,4) (5,2) (4,6) (6,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph727", "image": "data/cycle/graph_visual/medium/graph727.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (11,15) (16,7) (5,1) (17,8) (13,12) (16,6) (2,13) (16,4) (21,22) (14,15) (8,19) (12,9) (22,17) (9,4) (8,1) (4,3) (18,6) (15,10) (3,19) (9,20) (11,18) (0,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph822", "image": "data/cycle/graph_visual/medium/graph822.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,4) (13,1) (12,14) (6,23) (21,15) (9,4) (4,7) (14,22) (2,1) (10,6) (19,20) (15,18) (7,3) (11,22) (11,5) (7,16) (0,14) (12,15) (20,0) (16,6) (8,12) (12,17) (18,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph15", "image": "data/cycle/graph_visual/medium/graph15.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,2) (4,8) (7,8) (0,8) (3,8) (5,2) (6,3) (9,4) (6,10) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1338", "image": "data/cycle/graph_visual/medium/graph1338.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,2) (11,4) (13,5) (15,4) (7,17) (6,3) (14,5) (9,17) (13,6) (1,10) (7,15) (8,13) (16,1) (6,0) (1,12) (7,0) (16,13) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph135", "image": "data/cycle/graph_visual/medium/graph135.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,12) (5,1) (4,5) (2,4) (7,10) (8,1) (5,11) (12,8) (0,7) (11,3) (10,6) (3,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph550", "image": "data/cycle/graph_visual/medium/graph550.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,10) (5,4) (9,3) (10,1) (17,15) (18,2) (7,8) (6,9) (7,1) (14,15) (16,8) (13,0) (7,0) (1,12) (9,18) (13,19) (4,12) (11,4) (5,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph395", "image": "data/cycle/graph_visual/medium/graph395.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,15) (16,14) (10,9) (2,5) (6,9) (4,0) (2,1) (8,4) (0,14) (7,14) (13,7) (5,11) (12,4) (3,11) (12,11) (10,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1229", "image": "data/cycle/graph_visual/medium/graph1229.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (15,7) (11,0) (6,14) (4,13) (2,10) (5,8) (14,10) (0,2) (15,1) (7,2) (15,9) (0,1) (12,15) (1,3) (13,8) (0,6) (5,1) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1025", "image": "data/cycle/graph_visual/medium/graph1025.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,12) (1,0) (8,9) (1,3) (9,1) (6,7) (8,5) (0,2) (10,2) (2,7) (4,0) (4,9) (4,11) (1,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1393", "image": "data/cycle/graph_visual/medium/graph1393.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,16) (7,14) (0,15) (3,0) (4,9) (1,7) (15,6) (13,8) (4,11) (17,15) (10,15) (8,17) (17,18) (2,0) (5,17) (7,6) (0,1) (18,11) (3,18) (2,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1148", "image": "data/cycle/graph_visual/medium/graph1148.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (14,7) (9,6) (2,14) (5,3) (12,11) (9,14) (0,2) (6,10) (13,8) (4,14) (5,1) (2,3) (4,0) (4,8) (0,3) (0,6) (11,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1607", "image": "data/cycle/graph_visual/medium/graph1607.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (20,17) (0,8) (9,15) (0,15) (19,16) (1,8) (8,20) (5,6) (4,17) (0,1) (12,17) (18,21) (0,2) (10,2) (21,15) (3,9) (16,0) (3,6) (4,7) (7,10) (19,13) (6,11) (7,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1765", "image": "data/cycle/graph_visual/medium/graph1765.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (7,8) (20,21) (2,9) (16,0) (6,9) (13,15) (16,5) (18,13) (13,20) (7,5) (19,23) (14,20) (0,3) (11,17) (0,1) (10,3) (12,24) (2,17) (0,2) (0,10) (1,4) (8,23) (22,11) (12,15) (8,17) (2,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph93", "image": "data/cycle/graph_visual/medium/graph93.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,3) (7,5) (2,6) (2,3) (10,0) (2,1) (5,6) (0,1) (9,11) (3,11) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1741", "image": "data/cycle/graph_visual/medium/graph1741.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (15,12) (6,14) (0,7) (17,9) (22,11) (23,5) (5,22) (18,23) (8,4) (21,10) (19,16) (7,1) (15,0) (9,24) (19,0) (0,4) (17,15) (21,14) (2,3) (0,1) (9,4) (0,3) (24,21) (18,10) (12,20) (0,2) (0,13) (20,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph893", "image": "data/cycle/graph_visual/medium/graph893.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (9,5) (6,17) (6,19) (5,21) (2,7) (2,1) (24,22) (4,8) (15,6) (13,1) (17,9) (0,15) (20,22) (12,10) (20,15) (14,1) (14,3) (20,16) (11,4) (12,1) (13,4) (18,6) (9,11) (23,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1159", "image": "data/cycle/graph_visual/medium/graph1159.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,8) (0,5) (14,9) (4,10) (2,11) (2,0) (14,5) (10,12) (3,0) (4,1) (14,2) (10,2) (13,3) (10,6) (0,4) (3,10) (0,1) (12,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1372", "image": "data/cycle/graph_visual/medium/graph1372.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (14,17) (14,8) (7,5) (13,7) (16,14) (3,9) (10,13) (14,11) (10,15) (13,0) (9,16) (4,16) (14,6) (1,9) (12,17) (1,0) (7,2) (17,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1331", "image": "data/cycle/graph_visual/medium/graph1331.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,5) (6,16) (7,9) (4,11) (0,14) (8,2) (14,7) (17,7) (10,1) (1,0) (0,8) (13,11) (7,3) (3,16) (3,5) (11,15) (12,15) (17,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph33", "image": "data/cycle/graph_visual/medium/graph33.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,8) (9,6) (4,9) (2,5) (0,1) (5,7) (0,3) (0,9) (10,7) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1125", "image": "data/cycle/graph_visual/medium/graph1125.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (3,1) (9,4) (6,7) (13,6) (8,7) (4,12) (1,0) (1,7) (1,9) (7,2) (2,0) (5,0) (4,0) (5,8) (11,2) (9,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph552", "image": "data/cycle/graph_visual/medium/graph552.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,5) (15,11) (10,17) (18,0) (3,13) (7,8) (10,3) (7,15) (9,0) (10,1) (16,15) (16,14) (1,12) (19,0) (16,1) (4,9) (2,6) (4,6) (19,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph898", "image": "data/cycle/graph_visual/medium/graph898.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (18,10) (19,2) (22,6) (15,17) (5,9) (17,2) (10,16) (14,19) (6,1) (24,17) (23,21) (7,13) (14,3) (15,1) (23,18) (8,15) (23,14) (7,14) (4,0) (20,12) (4,17) (15,9) (12,6) (12,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1522", "image": "data/cycle/graph_visual/medium/graph1522.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (4,11) (18,6) (11,9) (3,14) (2,7) (1,12) (12,10) (1,0) (16,6) (15,20) (2,1) (5,6) (0,15) (19,2) (13,4) (9,17) (8,4) (1,13) (14,1) (20,17) (9,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph212", "image": "data/cycle/graph_visual/medium/graph212.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (2,10) (0,1) (12,11) (0,8) (2,3) (7,0) (9,12) (5,0) (13,3) (5,6) (4,1) (8,10) (12,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph884", "image": "data/cycle/graph_visual/medium/graph884.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,2) (9,10) (2,4) (19,16) (17,3) (11,0) (16,24) (9,19) (12,20) (5,2) (20,15) (7,0) (19,13) (18,12) (4,20) (22,16) (1,12) (19,5) (8,1) (21,14) (6,17) (7,23) (6,8) (14,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1097", "image": "data/cycle/graph_visual/medium/graph1097.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,3) (2,6) (3,8) (5,7) (0,2) (0,1) (6,11) (3,0) (9,12) (5,0) (1,8) (10,0) (1,2) (7,1) (4,0) (12,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph507", "image": "data/cycle/graph_visual/medium/graph507.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,16) (11,1) (0,14) (3,7) (12,8) (12,18) (11,5) (4,7) (2,4) (14,12) (4,9) (10,6) (1,2) (15,14) (6,13) (12,6) (17,15) (7,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph653", "image": "data/cycle/graph_visual/medium/graph653.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (8,10) (16,17) (19,0) (19,14) (11,3) (3,7) (6,13) (16,8) (1,16) (5,10) (9,5) (4,10) (14,5) (14,15) (8,18) (20,16) (12,9) (3,14) (6,11) (2,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph557", "image": "data/cycle/graph_visual/medium/graph557.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,1) (14,11) (17,1) (13,16) (12,17) (5,4) (1,0) (19,14) (14,12) (2,8) (16,6) (15,4) (13,5) (9,13) (5,11) (11,8) (1,3) (15,7) (18,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1635", "image": "data/cycle/graph_visual/medium/graph1635.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,18) (5,1) (14,15) (16,15) (12,15) (21,16) (13,22) (18,17) (6,0) (10,2) (0,2) (13,9) (7,11) (5,20) (15,10) (14,6) (7,2) (11,1) (8,19) (18,3) (4,1) (8,20) (0,1) (13,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph485", "image": "data/cycle/graph_visual/medium/graph485.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,15) (3,9) (9,1) (13,10) (14,9) (16,4) (17,14) (7,13) (7,5) (8,18) (8,14) (2,17) (11,16) (14,6) (2,7) (10,16) (13,0) (14,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph520", "image": "data/cycle/graph_visual/medium/graph520.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,1) (6,5) (9,18) (9,5) (1,12) (13,4) (13,1) (3,14) (4,8) (12,10) (9,11) (15,0) (7,2) (4,11) (17,2) (16,6) (6,15) (2,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph876", "image": "data/cycle/graph_visual/medium/graph876.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (18,16) (5,13) (16,22) (1,5) (20,5) (2,9) (21,23) (16,15) (21,20) (12,16) (3,20) (4,7) (6,8) (7,15) (19,17) (19,10) (2,20) (8,20) (11,17) (0,18) (14,15) (10,21) (9,14) (9,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph330", "image": "data/cycle/graph_visual/medium/graph330.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,8) (6,14) (2,9) (1,11) (5,6) (15,13) (6,12) (13,1) (12,4) (7,2) (5,9) (2,1) (3,14) (0,15) (10,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1259", "image": "data/cycle/graph_visual/medium/graph1259.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (15,10) (1,0) (9,2) (11,5) (6,14) (0,4) (2,15) (12,1) (12,6) (1,4) (11,0) (7,13) (3,11) (11,1) (0,2) (3,0) (15,0) (8,1) (13,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph183", "image": "data/cycle/graph_visual/medium/graph183.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,2) (13,5) (5,4) (12,8) (9,0) (0,8) (7,12) (3,12) (0,10) (9,11) (13,6) (13,12) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph915", "image": "data/cycle/graph_visual/medium/graph915.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,9) (3,1) (0,10) (0,4) (0,3) (1,0) (7,2) (5,8) (0,8) (2,0) (2,3) (6,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1111", "image": "data/cycle/graph_visual/medium/graph1111.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,2) (8,7) (11,13) (13,4) (1,13) (0,1) (8,10) (4,0) (12,3) (7,6) (12,6) (9,0) (6,5) (4,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph816", "image": "data/cycle/graph_visual/medium/graph816.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (10,2) (1,17) (20,10) (20,12) (22,0) (19,11) (17,9) (19,2) (18,6) (3,7) (15,5) (14,16) (6,21) (8,18) (9,15) (16,13) (7,17) (23,6) (3,11) (4,0) (13,22) (8,20) (18,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1501", "image": "data/cycle/graph_visual/medium/graph1501.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (8,11) (17,8) (14,6) (9,19) (0,13) (11,2) (0,11) (5,0) (4,0) (3,20) (18,5) (4,8) (10,12) (1,6) (0,15) (6,7) (12,7) (2,0) (3,0) (12,18) (9,2) (0,1) (20,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1686", "image": "data/cycle/graph_visual/medium/graph1686.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,1) (0,1) (5,11) (16,6) (6,18) (20,0) (16,7) (17,12) (9,4) (2,4) (2,0) (18,15) (12,15) (11,22) (14,22) (21,15) (6,10) (13,1) (4,7) (3,7) (6,23) (3,0) (14,12) (12,8) (0,14) (20,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1482", "image": "data/cycle/graph_visual/medium/graph1482.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,5) (4,2) (5,16) (17,14) (8,5) (6,12) (1,0) (14,18) (2,13) (16,0) (4,9) (6,5) (3,14) (5,15) (0,3) (6,10) (12,1) (19,15) (18,7) (0,2) (9,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph734", "image": "data/cycle/graph_visual/medium/graph734.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (21,8) (20,17) (6,12) (13,17) (9,15) (18,7) (8,1) (6,10) (21,19) (3,6) (5,15) (0,15) (16,20) (4,17) (22,5) (7,4) (19,14) (9,3) (7,11) (0,16) (0,8) (10,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1407", "image": "data/cycle/graph_visual/medium/graph1407.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (18,9) (13,10) (16,11) (12,11) (9,14) (8,18) (3,8) (0,4) (6,7) (15,4) (5,16) (3,2) (3,16) (8,4) (1,16) (13,17) (5,0) (8,10) (3,0) (2,0) (12,6) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph518", "image": "data/cycle/graph_visual/medium/graph518.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,11) (12,15) (3,1) (10,8) (13,8) (14,0) (9,7) (13,7) (17,18) (17,14) (6,18) (11,15) (5,17) (16,3) (10,14) (3,4) (2,16) (1,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph897", "image": "data/cycle/graph_visual/medium/graph897.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (8,22) (22,3) (2,21) (5,0) (16,10) (23,24) (15,13) (20,17) (6,7) (20,6) (11,10) (21,24) (3,1) (8,14) (19,5) (15,18) (10,3) (8,6) (5,15) (7,12) (9,14) (4,14) (21,16) (9,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph366", "image": "data/cycle/graph_visual/medium/graph366.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,14) (16,12) (2,11) (2,5) (4,13) (14,11) (13,7) (13,9) (1,0) (10,6) (1,3) (5,3) (16,13) (8,14) (10,15) (10,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1156", "image": "data/cycle/graph_visual/medium/graph1156.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,4) (9,13) (0,2) (7,2) (3,13) (1,13) (2,3) (12,13) (14,13) (10,3) (3,0) (8,11) (5,8) (8,6) (0,1) (8,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph210", "image": "data/cycle/graph_visual/medium/graph210.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (2,8) (12,4) (3,11) (8,0) (8,7) (8,3) (8,10) (11,6) (1,5) (13,12) (11,12) (5,2) (4,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph450", "image": "data/cycle/graph_visual/medium/graph450.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (14,17) (2,15) (0,10) (14,5) (12,5) (8,4) (16,1) (9,0) (1,12) (14,3) (8,7) (11,16) (6,11) (5,4) (2,10) (13,14) (10,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph45", "image": "data/cycle/graph_visual/medium/graph45.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,6) (1,10) (2,6) (7,3) (4,7) (5,9) (5,6) (8,1) (2,0) (2,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1340", "image": "data/cycle/graph_visual/medium/graph1340.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (5,1) (3,13) (9,16) (10,8) (14,17) (3,2) (15,5) (1,0) (8,6) (1,6) (13,11) (13,8) (4,14) (0,2) (7,13) (15,12) (14,5) (1,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph671", "image": "data/cycle/graph_visual/medium/graph671.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (10,20) (12,2) (5,10) (13,0) (20,0) (4,17) (14,10) (5,19) (11,15) (5,3) (10,6) (2,11) (6,7) (17,15) (18,11) (9,8) (12,14) (21,16) (15,1) (16,0) (10,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph235", "image": "data/cycle/graph_visual/medium/graph235.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,6) (6,8) (9,0) (7,4) (10,13) (13,2) (1,0) (3,12) (5,8) (6,4) (9,4) (2,5) (1,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1164", "image": "data/cycle/graph_visual/medium/graph1164.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,0) (1,4) (12,5) (7,10) (3,4) (6,4) (11,7) (5,14) (14,0) (0,2) (8,9) (2,4) (0,1) (7,14) (9,2) (3,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1180", "image": "data/cycle/graph_visual/medium/graph1180.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,3) (14,8) (14,3) (8,12) (13,1) (9,8) (6,11) (6,13) (8,2) (0,1) (0,5) (0,7) (10,4) (2,0) (3,0) (10,7) (12,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1729", "image": "data/cycle/graph_visual/medium/graph1729.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,6) (0,5) (4,0) (17,1) (6,23) (6,16) (6,1) (18,3) (18,9) (19,14) (6,4) (19,13) (6,5) (9,13) (8,22) (23,7) (8,14) (0,15) (0,1) (2,0) (3,0) (11,9) (18,2) (12,11) (20,14) (21,12) (20,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph716", "image": "data/cycle/graph_visual/medium/graph716.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (5,19) (2,21) (6,9) (4,5) (18,2) (13,0) (1,7) (14,15) (10,14) (12,4) (4,11) (8,16) (20,7) (3,9) (7,8) (15,17) (18,9) (12,1) (21,13) (20,0) (10,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph394", "image": "data/cycle/graph_visual/medium/graph394.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,1) (15,3) (9,0) (15,14) (10,3) (0,11) (10,16) (2,0) (6,4) (6,11) (13,5) (7,1) (11,8) (0,1) (8,13) (14,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1221", "image": "data/cycle/graph_visual/medium/graph1221.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,11) (3,4) (6,13) (10,12) (3,0) (15,14) (4,13) (5,2) (0,2) (10,2) (7,11) (0,4) (1,8) (14,5) (2,8) (5,0) (1,0) (9,10) (9,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1258", "image": "data/cycle/graph_visual/medium/graph1258.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,13) (2,1) (1,0) (6,10) (11,1) (9,8) (10,12) (0,3) (11,5) (13,0) (12,11) (14,12) (12,15) (0,5) (7,4) (15,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph799", "image": "data/cycle/graph_visual/medium/graph799.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (20,10) (8,15) (13,21) (2,8) (23,15) (22,23) (14,6) (18,4) (5,13) (21,17) (21,8) (21,12) (22,3) (3,11) (9,16) (22,18) (14,0) (7,1) (1,23) (21,16) (15,14) (2,10) (11,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph132", "image": "data/cycle/graph_visual/medium/graph132.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,5) (4,2) (7,12) (6,11) (11,3) (9,1) (0,7) (11,10) (8,10) (0,8) (5,4) (11,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1497", "image": "data/cycle/graph_visual/medium/graph1497.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (6,13) (4,1) (2,17) (11,13) (19,3) (4,5) (15,4) (6,19) (1,0) (6,17) (8,5) (10,14) (0,3) (6,18) (6,14) (4,19) (12,5) (16,12) (7,4) (9,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph792", "image": "data/cycle/graph_visual/medium/graph792.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (6,18) (13,14) (10,2) (0,14) (0,1) (8,0) (10,5) (9,23) (3,16) (15,23) (7,23) (11,16) (12,3) (23,6) (6,22) (21,16) (13,3) (20,17) (17,4) (19,9) (12,20) (18,0) (22,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1519", "image": "data/cycle/graph_visual/medium/graph1519.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,11) (12,8) (20,16) (20,15) (14,12) (16,7) (7,3) (0,1) (12,6) (15,18) (10,6) (2,4) (0,2) (14,0) (17,0) (7,4) (14,19) (6,13) (1,2) (15,12) (9,4) (5,11) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph640", "image": "data/cycle/graph_visual/medium/graph640.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (5,15) (2,3) (0,6) (11,13) (15,8) (20,1) (8,9) (2,11) (17,2) (10,9) (18,14) (14,16) (4,1) (7,18) (6,18) (19,15) (20,12) (9,18) (4,17) (8,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph196", "image": "data/cycle/graph_visual/medium/graph196.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,12) (10,6) (12,3) (11,2) (3,10) (9,13) (4,7) (2,0) (11,7) (4,8) (6,1) (12,13) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph20", "image": "data/cycle/graph_visual/medium/graph20.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,3) (5,6) (7,2) (8,4) (6,3) (0,9) (7,3) (6,0) (1,5) (10,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph303", "image": "data/cycle/graph_visual/medium/graph303.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,2) (12,14) (0,15) (9,11) (6,4) (7,10) (15,10) (1,15) (8,0) (10,14) (11,13) (3,5) (6,9) (5,10) (11,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1064", "image": "data/cycle/graph_visual/medium/graph1064.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,11) (0,3) (6,1) (2,0) (2,11) (6,10) (7,10) (6,5) (12,3) (3,9) (4,8) (7,12) (0,1) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1356", "image": "data/cycle/graph_visual/medium/graph1356.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,5) (16,10) (16,17) (11,6) (2,0) (3,14) (4,9) (2,17) (3,5) (12,16) (6,5) (9,14) (13,15) (3,0) (0,14) (14,8) (14,7) (1,0) (1,17) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1646", "image": "data/cycle/graph_visual/medium/graph1646.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,10) (6,1) (20,15) (20,9) (11,2) (6,7) (14,0) (3,8) (0,4) (0,1) (8,21) (18,22) (19,5) (11,17) (9,21) (0,2) (0,11) (22,0) (12,18) (3,0) (13,6) (2,21) (12,7) (5,0) (4,12) (8,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph833", "image": "data/cycle/graph_visual/medium/graph833.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (16,11) (8,4) (6,3) (11,2) (13,21) (0,2) (14,4) (23,14) (8,21) (19,7) (22,1) (20,1) (9,23) (1,15) (19,9) (1,12) (3,10) (10,17) (16,7) (20,17) (18,23) (17,16) (5,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph392", "image": "data/cycle/graph_visual/medium/graph392.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,1) (4,13) (16,9) (14,9) (3,15) (2,15) (0,3) (0,10) (10,11) (7,2) (9,8) (6,8) (5,15) (2,12) (9,3) (13,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph735", "image": "data/cycle/graph_visual/medium/graph735.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,19) (6,2) (21,15) (12,0) (3,10) (18,16) (7,9) (6,4) (1,16) (4,9) (10,1) (11,19) (15,11) (1,13) (22,17) (15,7) (0,17) (10,20) (16,22) (22,8) (3,14) (5,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph442", "image": "data/cycle/graph_visual/medium/graph442.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (4,7) (9,1) (4,10) (17,3) (8,4) (15,1) (15,0) (17,7) (5,3) (2,0) (12,7) (14,4) (12,6) (13,4) (3,11) (16,1) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1654", "image": "data/cycle/graph_visual/medium/graph1654.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (2,12) (18,9) (2,0) (15,13) (0,4) (22,10) (3,20) (14,8) (1,9) (16,6) (21,6) (3,18) (3,13) (6,0) (8,1) (21,18) (16,19) (0,1) (11,15) (18,17) (10,19) (7,20) (9,5) (1,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph370", "image": "data/cycle/graph_visual/medium/graph370.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,3) (12,5) (7,4) (2,7) (5,13) (4,6) (9,0) (8,7) (5,10) (1,16) (1,8) (1,13) (11,2) (10,15) (3,11) (14,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1059", "image": "data/cycle/graph_visual/medium/graph1059.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,10) (8,7) (1,11) (0,3) (5,12) (10,5) (0,4) (9,0) (2,4) (7,2) (6,3) (2,0) (2,11) (9,1) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1385", "image": "data/cycle/graph_visual/medium/graph1385.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,9) (16,2) (13,15) (18,0) (9,17) (3,11) (18,4) (0,11) (1,12) (12,6) (5,1) (10,1) (15,2) (17,0) (11,1) (2,0) (11,7) (15,6) (8,13) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph244", "image": "data/cycle/graph_visual/medium/graph244.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (5,8) (1,9) (5,9) (11,13) (4,0) (12,13) (14,12) (1,2) (7,2) (1,0) (14,10) (10,3) (14,5) (6,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1320", "image": "data/cycle/graph_visual/medium/graph1320.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (11,4) (12,15) (8,0) (0,3) (12,1) (0,2) (8,10) (2,13) (8,17) (17,6) (16,11) (3,16) (4,0) (0,1) (13,1) (12,14) (10,9) (0,13) (5,2) (14,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph242", "image": "data/cycle/graph_visual/medium/graph242.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,6) (11,3) (2,1) (3,8) (1,7) (9,12) (10,0) (0,4) (5,7) (1,8) (14,11) (2,6) (2,0) (13,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1337", "image": "data/cycle/graph_visual/medium/graph1337.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,5) (4,13) (1,0) (2,9) (15,6) (13,1) (2,0) (12,10) (0,15) (12,1) (2,7) (5,6) (1,14) (1,2) (8,4) (11,4) (17,11) (3,14) (6,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1113", "image": "data/cycle/graph_visual/medium/graph1113.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,1) (13,3) (6,9) (5,1) (13,8) (1,12) (2,0) (2,13) (11,4) (2,4) (12,3) (0,13) (0,3) (5,10) (9,1) (7,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1411", "image": "data/cycle/graph_visual/medium/graph1411.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,5) (15,12) (1,9) (10,8) (5,18) (13,8) (0,4) (13,11) (3,0) (5,15) (5,1) (13,7) (1,0) (2,0) (9,16) (13,3) (6,1) (6,8) (14,17) (2,3) (4,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph380", "image": "data/cycle/graph_visual/medium/graph380.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,11) (2,8) (7,11) (9,6) (2,4) (12,13) (3,14) (14,7) (0,1) (2,11) (11,5) (3,1) (0,13) (16,9) (12,15) (2,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1627", "image": "data/cycle/graph_visual/medium/graph1627.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,21) (1,21) (16,10) (4,7) (10,4) (20,13) (21,2) (0,5) (1,0) (3,2) (11,20) (18,17) (22,6) (5,19) (13,6) (18,15) (10,15) (8,9) (14,18) (13,14) (13,0) (3,4) (3,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1185", "image": "data/cycle/graph_visual/medium/graph1185.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,3) (8,9) (13,1) (6,11) (2,8) (0,2) (10,4) (13,6) (0,1) (5,0) (14,8) (4,12) (3,0) (3,11) (10,7) (8,12) (7,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph84", "image": "data/cycle/graph_visual/medium/graph84.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,11) (11,0) (6,3) (3,9) (9,1) (7,8) (6,11) (7,2) (1,8) (11,4) (9,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1540", "image": "data/cycle/graph_visual/medium/graph1540.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,19) (6,13) (14,15) (5,10) (5,14) (12,9) (11,6) (1,16) (16,8) (3,2) (4,10) (1,0) (11,3) (19,0) (17,16) (7,3) (10,8) (18,8) (20,16) (5,9) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1580", "image": "data/cycle/graph_visual/medium/graph1580.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (7,16) (4,18) (11,15) (3,15) (10,11) (2,11) (6,0) (5,13) (2,4) (12,19) (5,9) (0,3) (5,14) (8,14) (0,4) (7,17) (7,15) (4,1) (11,21) (15,13) (2,0) (3,6) (0,19) (9,20) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph707", "image": "data/cycle/graph_visual/medium/graph707.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (8,12) (21,19) (13,3) (1,9) (6,16) (18,3) (1,11) (13,14) (16,19) (4,0) (3,17) (9,18) (15,18) (9,5) (7,20) (18,21) (8,1) (6,20) (15,10) (12,2) (6,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1671", "image": "data/cycle/graph_visual/medium/graph1671.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (10,20) (21,22) (9,5) (13,12) (0,7) (14,22) (10,16) (16,8) (2,0) (2,13) (20,21) (18,8) (17,15) (12,7) (21,17) (5,22) (9,4) (4,0) (6,11) (3,19) (0,1) (3,0) (11,9) (5,0) (13,8) (1,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1677", "image": "data/cycle/graph_visual/medium/graph1677.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (19,5) (2,4) (5,6) (13,16) (6,12) (17,22) (14,0) (2,0) (17,1) (2,17) (16,15) (3,0) (16,10) (21,20) (14,8) (14,9) (20,15) (11,18) (4,9) (1,0) (7,14) (22,20) (5,3) (18,19) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph258", "image": "data/cycle/graph_visual/medium/graph258.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,11) (0,2) (10,9) (7,1) (12,3) (2,10) (14,7) (9,7) (5,9) (0,4) (4,12) (1,8) (0,13) (13,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph581", "image": "data/cycle/graph_visual/medium/graph581.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,0) (12,7) (12,18) (12,10) (6,14) (2,11) (13,0) (4,8) (9,18) (6,1) (7,6) (0,3) (16,8) (15,0) (2,9) (11,8) (3,19) (0,5) (17,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph339", "image": "data/cycle/graph_visual/medium/graph339.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,4) (6,5) (15,9) (10,2) (0,4) (12,7) (10,7) (0,15) (8,1) (6,3) (6,11) (8,0) (3,9) (15,14) (8,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph236", "image": "data/cycle/graph_visual/medium/graph236.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,7) (5,6) (6,8) (2,7) (2,11) (10,11) (7,1) (0,2) (12,4) (12,13) (11,5) (12,8) (9,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1596", "image": "data/cycle/graph_visual/medium/graph1596.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,0) (14,3) (5,9) (0,15) (14,1) (6,17) (9,17) (5,19) (11,4) (4,8) (16,6) (15,20) (0,3) (9,11) (2,0) (13,1) (6,21) (6,18) (20,2) (7,2) (1,12) (1,2) (13,4) (10,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1577", "image": "data/cycle/graph_visual/medium/graph1577.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,16) (0,3) (2,0) (21,19) (3,17) (18,13) (0,4) (7,12) (2,13) (11,9) (6,11) (0,1) (8,16) (16,10) (9,5) (0,7) (12,21) (10,20) (8,15) (13,8) (14,21) (12,20) (9,4) (17,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph427", "image": "data/cycle/graph_visual/medium/graph427.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (12,5) (9,3) (1,8) (15,0) (6,2) (7,5) (2,9) (6,4) (10,8) (7,16) (8,2) (17,13) (17,15) (8,11) (11,12) (14,10) (7,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1469", "image": "data/cycle/graph_visual/medium/graph1469.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (17,19) (14,8) (10,16) (17,2) (1,0) (0,2) (2,4) (5,18) (3,5) (14,7) (15,16) (3,0) (9,4) (15,19) (0,14) (9,14) (14,3) (13,16) (12,6) (11,18) (17,1) (5,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph945", "image": "data/cycle/graph_visual/medium/graph945.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,2) (3,0) (5,0) (1,2) (2,3) (8,4) (9,7) (5,9) (0,4) (6,2) (10,2) (10,7) (3,8) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1262", "image": "data/cycle/graph_visual/medium/graph1262.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,15) (6,1) (7,3) (16,1) (0,1) (10,2) (8,6) (13,7) (0,2) (5,15) (2,11) (6,0) (12,16) (9,14) (10,8) (0,4) (13,9) (3,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph645", "image": "data/cycle/graph_visual/medium/graph645.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (11,12) (3,4) (2,5) (0,19) (9,13) (18,13) (13,11) (10,15) (6,13) (8,17) (14,9) (11,20) (9,5) (15,19) (0,17) (13,0) (17,1) (3,8) (7,0) (16,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph417", "image": "data/cycle/graph_visual/medium/graph417.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (2,7) (8,5) (15,10) (12,15) (16,7) (15,14) (10,2) (3,1) (1,16) (13,4) (1,5) (9,15) (6,14) (0,11) (13,8) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph270", "image": "data/cycle/graph_visual/medium/graph270.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,2) (0,1) (11,8) (5,14) (2,13) (12,3) (1,12) (10,5) (4,9) (7,9) (13,11) (13,6) (2,4) (5,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph545", "image": "data/cycle/graph_visual/medium/graph545.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,18) (17,9) (10,12) (2,1) (15,0) (17,19) (15,6) (1,13) (5,6) (11,9) (1,14) (5,9) (13,4) (3,14) (11,4) (7,2) (12,1) (16,6) (8,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1798", "image": "data/cycle/graph_visual/medium/graph1798.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (2,24) (19,7) (1,6) (11,8) (21,0) (13,4) (5,2) (17,10) (0,3) (17,23) (12,13) (18,14) (22,16) (18,21) (11,17) (15,13) (17,14) (3,5) (0,1) (4,14) (2,0) (9,10) (13,20) (16,10) (14,19) (3,1) (2,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1313", "image": "data/cycle/graph_visual/medium/graph1313.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,1) (10,11) (14,9) (8,6) (2,16) (3,4) (1,6) (11,7) (12,7) (14,7) (5,10) (0,2) (7,6) (0,3) (14,13) (3,13) (15,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph247", "image": "data/cycle/graph_visual/medium/graph247.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,10) (6,12) (12,7) (11,1) (11,2) (6,14) (3,2) (1,0) (3,13) (4,2) (2,10) (9,11) (5,8) (8,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1077", "image": "data/cycle/graph_visual/medium/graph1077.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,2) (2,12) (1,0) (2,8) (4,7) (1,3) (0,3) (7,3) (0,2) (4,0) (0,9) (11,8) (2,6) (9,1) (5,10) (10,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1756", "image": "data/cycle/graph_visual/medium/graph1756.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,24) (20,15) (19,8) (13,5) (0,1) (8,1) (7,1) (18,6) (4,9) (18,11) (8,17) (15,13) (10,16) (24,2) (3,19) (17,22) (12,0) (16,4) (9,21) (11,15) (23,3) (16,6) (24,22) (12,9) (12,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1553", "image": "data/cycle/graph_visual/medium/graph1553.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (15,12) (11,8) (2,8) (12,13) (6,13) (20,16) (11,14) (12,3) (17,7) (5,7) (12,1) (12,7) (17,4) (1,19) (1,0) (19,18) (0,11) (17,10) (9,11) (5,16) (0,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1195", "image": "data/cycle/graph_visual/medium/graph1195.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,11) (7,13) (14,7) (8,9) (4,7) (14,10) (2,0) (3,0) (2,9) (8,10) (3,6) (6,12) (1,7) (4,0) (0,1) (12,10) (5,0) (11,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph907", "image": "data/cycle/graph_visual/medium/graph907.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,7) (9,2) (7,3) (5,9) (3,6) (4,1) (2,0) (5,1) (0,1) (3,8) (0,3) (10,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph765", "image": "data/cycle/graph_visual/medium/graph765.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (19,12) (3,6) (14,15) (13,10) (7,2) (9,2) (17,13) (1,22) (15,17) (6,4) (20,17) (2,11) (21,16) (16,12) (11,21) (5,9) (4,9) (12,18) (8,5) (0,2) (20,1) (10,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1448", "image": "data/cycle/graph_visual/medium/graph1448.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,0) (15,11) (17,2) (0,5) (0,1) (5,7) (2,18) (10,3) (17,11) (2,9) (0,4) (16,8) (13,14) (13,18) (8,7) (19,13) (4,1) (3,0) (2,0) (9,6) (5,12) (17,8) (16,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph490", "image": "data/cycle/graph_visual/medium/graph490.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,5) (9,4) (13,15) (10,12) (4,16) (14,11) (16,6) (8,15) (9,17) (6,15) (11,18) (9,12) (16,7) (0,12) (3,18) (3,4) (1,8) (2,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1659", "image": "data/cycle/graph_visual/medium/graph1659.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (22,3) (13,9) (12,18) (5,0) (19,16) (15,9) (11,19) (12,21) (19,6) (5,16) (11,12) (0,20) (4,18) (7,14) (10,15) (0,8) (10,17) (1,0) (0,3) (1,2) (13,20) (1,11) (3,12) (2,0) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1276", "image": "data/cycle/graph_visual/medium/graph1276.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,2) (7,12) (3,4) (9,14) (13,14) (7,14) (6,8) (0,3) (13,3) (10,11) (7,11) (15,12) (1,6) (6,7) (10,5) (1,0) (16,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph18", "image": "data/cycle/graph_visual/medium/graph18.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,2) (8,7) (10,8) (5,10) (0,2) (9,3) (7,3) (4,7) (6,4) (6,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1309", "image": "data/cycle/graph_visual/medium/graph1309.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,7) (0,3) (9,13) (6,8) (14,9) (12,14) (8,7) (10,9) (2,11) (5,8) (16,1) (8,3) (3,12) (15,12) (2,14) (0,1) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1377", "image": "data/cycle/graph_visual/medium/graph1377.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (7,15) (1,9) (0,4) (6,4) (12,13) (14,8) (16,2) (10,17) (4,3) (12,7) (9,4) (14,3) (0,2) (0,3) (10,11) (12,2) (6,13) (10,16) (0,1) (5,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph416", "image": "data/cycle/graph_visual/medium/graph416.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,13) (7,5) (2,8) (5,16) (1,12) (10,11) (16,15) (9,12) (8,11) (14,1) (7,13) (12,3) (12,7) (6,11) (12,0) (0,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph509", "image": "data/cycle/graph_visual/medium/graph509.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,17) (4,7) (7,18) (14,5) (12,10) (17,12) (0,6) (18,13) (15,7) (13,14) (9,7) (14,17) (18,16) (1,3) (18,8) (6,3) (2,10) (11,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph470", "image": "data/cycle/graph_visual/medium/graph470.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,12) (3,14) (9,4) (6,11) (5,17) (14,15) (5,7) (14,13) (5,16) (1,12) (8,6) (5,6) (2,4) (10,5) (0,9) (16,0) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1014", "image": "data/cycle/graph_visual/medium/graph1014.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,0) (8,1) (3,9) (3,2) (0,1) (2,7) (8,6) (5,8) (3,0) (4,0) (8,3) (4,10) (8,11) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph914", "image": "data/cycle/graph_visual/medium/graph914.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (7,3) (4,6) (2,7) (0,3) (0,2) (7,5) (10,6) (4,8) (1,0) (0,4) (1,5) (7,0) (9,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1223", "image": "data/cycle/graph_visual/medium/graph1223.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,0) (11,3) (15,0) (0,1) (0,4) (0,3) (5,2) (1,2) (12,4) (7,13) (9,6) (10,7) (0,14) (11,12) (10,9) (4,8) (11,5) (7,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph675", "image": "data/cycle/graph_visual/medium/graph675.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (14,15) (12,1) (16,8) (20,0) (21,2) (10,1) (7,8) (9,3) (7,20) (7,1) (4,12) (21,13) (5,19) (11,4) (18,9) (5,4) (18,2) (6,9) (17,15) (14,10) (13,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1314", "image": "data/cycle/graph_visual/medium/graph1314.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (15,13) (16,2) (11,3) (3,10) (0,1) (10,9) (14,16) (6,8) (8,12) (8,0) (11,0) (15,2) (12,2) (5,3) (4,1) (10,7) (2,0) (6,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph174", "image": "data/cycle/graph_visual/medium/graph174.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,1) (3,11) (10,5) (8,6) (4,12) (6,11) (7,8) (0,7) (2,0) (8,10) (9,4) (3,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph9", "image": "data/cycle/graph_visual/medium/graph9.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,1) (9,7) (7,6) (0,5) (10,8) (8,3) (4,5) (8,4) (5,9) (1,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph692", "image": "data/cycle/graph_visual/medium/graph692.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (15,16) (20,0) (8,13) (4,2) (21,4) (5,1) (6,15) (13,2) (11,0) (12,9) (6,14) (11,18) (5,16) (13,3) (16,19) (0,7) (15,9) (20,10) (16,7) (5,17) (13,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1170", "image": "data/cycle/graph_visual/medium/graph1170.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,0) (1,11) (2,0) (12,13) (0,4) (4,9) (4,7) (3,10) (7,2) (0,3) (4,5) (8,5) (3,1) (10,0) (1,4) (11,6) (4,14) (8,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1408", "image": "data/cycle/graph_visual/medium/graph1408.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,16) (7,1) (2,0) (13,5) (9,18) (3,15) (2,14) (14,15) (10,18) (3,10) (4,6) (1,0) (8,11) (17,8) (6,11) (13,17) (11,0) (3,0) (12,0) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1710", "image": "data/cycle/graph_visual/medium/graph1710.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,2) (2,20) (12,23) (16,21) (4,9) (19,22) (23,9) (19,1) (3,14) (20,9) (7,21) (7,1) (21,23) (6,17) (8,15) (5,8) (0,1) (11,2) (9,6) (2,18) (14,0) (21,10) (14,2) (12,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph712", "image": "data/cycle/graph_visual/medium/graph712.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (19,15) (8,6) (7,13) (13,15) (8,10) (3,13) (1,5) (6,20) (9,1) (14,4) (20,9) (19,5) (2,3) (18,21) (19,11) (13,12) (0,2) (8,16) (21,14) (17,1) (14,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1332", "image": "data/cycle/graph_visual/medium/graph1332.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,17) (11,0) (7,13) (6,12) (3,11) (1,8) (15,10) (3,0) (5,11) (0,16) (12,1) (14,2) (15,2) (4,1) (11,1) (6,15) (1,0) (0,4) (0,2) (9,13) (0,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph230", "image": "data/cycle/graph_visual/medium/graph230.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,5) (8,0) (6,0) (0,7) (11,13) (6,5) (13,10) (12,10) (13,3) (5,1) (4,7) (2,9) (4,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph77", "image": "data/cycle/graph_visual/medium/graph77.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,2) (9,3) (1,10) (11,5) (4,2) (5,6) (1,0) (6,2) (11,7) (9,5) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1104", "image": "data/cycle/graph_visual/medium/graph1104.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,11) (0,1) (2,8) (1,12) (5,10) (6,12) (4,0) (0,3) (12,11) (7,2) (5,9) (7,1) (7,13) (11,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1087", "image": "data/cycle/graph_visual/medium/graph1087.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,3) (7,0) (10,1) (4,3) (10,5) (11,2) (6,1) (0,2) (13,11) (0,11) (11,10) (0,1) (2,3) (8,4) (1,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph921", "image": "data/cycle/graph_visual/medium/graph921.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,9) (6,7) (7,4) (2,0) (9,1) (0,3) (6,3) (0,1) (0,7) (0,4) (3,9) (4,10) (1,5) (2,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1471", "image": "data/cycle/graph_visual/medium/graph1471.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,14) (4,0) (2,0) (10,5) (0,1) (18,6) (4,17) (6,11) (0,18) (12,9) (9,10) (16,3) (12,3) (3,0) (14,13) (6,17) (16,2) (15,16) (2,8) (0,7) (11,19) (13,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1670", "image": "data/cycle/graph_visual/medium/graph1670.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (9,5) (0,4) (2,16) (11,6) (6,15) (0,2) (0,3) (19,1) (4,3) (18,16) (16,19) (20,8) (14,5) (3,14) (11,3) (0,22) (13,9) (14,17) (21,14) (3,12) (10,5) (7,10) (19,0) (10,8) (1,0) (16,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1045", "image": "data/cycle/graph_visual/medium/graph1045.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,11) (10,6) (4,7) (0,3) (7,12) (12,11) (0,2) (1,0) (12,3) (6,1) (7,10) (5,6) (8,4) (9,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1231", "image": "data/cycle/graph_visual/medium/graph1231.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,8) (8,10) (0,5) (1,0) (11,4) (5,9) (5,8) (2,0) (9,6) (9,2) (10,12) (14,13) (3,0) (15,12) (7,0) (1,13) (11,3) (0,4) (12,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph412", "image": "data/cycle/graph_visual/medium/graph412.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,9) (2,11) (15,0) (10,12) (16,3) (5,4) (8,2) (1,5) (3,13) (6,11) (7,3) (15,11) (3,12) (1,3) (14,5) (12,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1783", "image": "data/cycle/graph_visual/medium/graph1783.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (16,15) (20,16) (21,3) (14,4) (21,0) (19,5) (2,0) (11,18) (8,23) (24,4) (14,11) (17,1) (12,23) (16,3) (14,21) (9,12) (13,23) (2,19) (2,6) (0,1) (14,13) (10,20) (22,19) (19,9) (1,20) (7,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph431", "image": "data/cycle/graph_visual/medium/graph431.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (5,17) (17,16) (14,0) (1,17) (13,7) (11,5) (8,12) (11,14) (10,8) (13,17) (3,4) (15,9) (16,2) (1,3) (3,15) (6,7) (14,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph21", "image": "data/cycle/graph_visual/medium/graph21.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,5) (8,4) (6,5) (10,4) (7,2) (3,4) (6,0) (0,9) (6,3) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1168", "image": "data/cycle/graph_visual/medium/graph1168.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,10) (1,0) (11,4) (14,0) (7,14) (11,6) (13,10) (3,5) (13,0) (11,9) (3,1) (6,14) (1,4) (4,12) (13,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1202", "image": "data/cycle/graph_visual/medium/graph1202.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,9) (6,5) (14,7) (1,8) (2,7) (9,11) (2,15) (13,15) (3,0) (12,4) (7,10) (3,14) (0,2) (9,6) (0,1) (12,9) (11,0) (13,1) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1197", "image": "data/cycle/graph_visual/medium/graph1197.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,8) (7,8) (6,5) (4,14) (11,9) (4,1) (14,2) (0,6) (2,12) (0,1) (11,5) (7,13) (14,0) (0,3) (2,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1132", "image": "data/cycle/graph_visual/medium/graph1132.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,12) (9,13) (0,2) (0,8) (11,10) (0,3) (1,0) (9,1) (2,10) (1,4) (10,5) (10,13) (0,10) (7,11) (9,3) (4,0) (13,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1311", "image": "data/cycle/graph_visual/medium/graph1311.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,5) (9,6) (9,2) (0,3) (8,11) (16,13) (0,10) (3,10) (13,2) (2,0) (7,8) (15,11) (14,13) (5,7) (0,16) (0,1) (8,2) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph354", "image": "data/cycle/graph_visual/medium/graph354.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,11) (10,12) (14,12) (15,10) (9,4) (7,5) (3,4) (5,9) (1,6) (12,13) (8,2) (0,2) (12,11) (9,15) (6,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph385", "image": "data/cycle/graph_visual/medium/graph385.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (15,13) (1,5) (9,10) (11,5) (2,15) (5,8) (12,5) (8,14) (4,9) (6,9) (16,7) (13,1) (16,4) (3,15) (0,4) (3,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph722", "image": "data/cycle/graph_visual/medium/graph722.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,2) (19,1) (17,0) (22,6) (22,18) (0,11) (16,18) (1,12) (8,13) (17,12) (11,10) (9,11) (4,17) (13,17) (20,7) (7,5) (16,5) (7,12) (11,15) (21,19) (14,12) (3,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1409", "image": "data/cycle/graph_visual/medium/graph1409.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,17) (18,11) (14,3) (1,8) (1,5) (11,15) (7,15) (0,1) (6,2) (4,16) (13,0) (14,12) (1,11) (10,11) (6,16) (16,9) (14,5) (4,8) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph971", "image": "data/cycle/graph_visual/medium/graph971.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,8) (0,1) (1,2) (0,3) (6,2) (4,3) (11,0) (9,8) (2,0) (6,5) (10,1) (3,6) (8,11) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1508", "image": "data/cycle/graph_visual/medium/graph1508.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (14,4) (8,0) (13,6) (11,18) (15,16) (3,17) (0,10) (11,10) (8,9) (12,1) (0,3) (7,2) (17,19) (3,20) (13,17) (15,6) (8,15) (18,5) (18,4) (1,0) (15,2) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1243", "image": "data/cycle/graph_visual/medium/graph1243.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,13) (5,3) (5,10) (14,10) (15,1) (12,2) (8,0) (0,2) (6,4) (0,15) (1,0) (3,0) (6,9) (7,10) (4,0) (14,12) (15,10) (11,2) (9,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph193", "image": "data/cycle/graph_visual/medium/graph193.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,7) (10,12) (13,12) (5,3) (1,8) (3,9) (4,9) (11,13) (7,12) (13,6) (11,2) (1,5) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph325", "image": "data/cycle/graph_visual/medium/graph325.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,3) (3,6) (8,11) (2,0) (6,13) (6,1) (10,4) (8,2) (8,12) (5,4) (12,15) (9,0) (0,4) (14,1) (15,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph404", "image": "data/cycle/graph_visual/medium/graph404.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (6,14) (0,6) (16,12) (0,2) (6,9) (4,11) (10,8) (7,0) (4,2) (6,8) (14,13) (1,15) (13,15) (5,3) (3,12) (12,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1649", "image": "data/cycle/graph_visual/medium/graph1649.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (13,22) (15,22) (0,16) (4,18) (6,2) (5,14) (0,11) (16,12) (1,0) (19,4) (20,9) (12,1) (6,10) (19,5) (17,14) (3,22) (21,4) (20,7) (7,3) (10,21) (10,0) (0,2) (8,5) (14,13) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph116", "image": "data/cycle/graph_visual/medium/graph116.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (8,0) (0,7) (8,4) (8,5) (10,3) (10,2) (6,3) (1,8) (4,11) (6,5) (1,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph807", "image": "data/cycle/graph_visual/medium/graph807.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (17,20) (8,0) (2,22) (23,9) (17,4) (6,18) (16,3) (12,20) (12,3) (22,6) (2,10) (13,14) (23,7) (9,19) (18,0) (11,16) (23,15) (23,6) (16,21) (10,5) (3,13) (0,1) (14,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph175", "image": "data/cycle/graph_visual/medium/graph175.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,0) (6,11) (9,7) (7,6) (9,12) (6,3) (8,6) (5,7) (10,4) (12,1) (1,2) (9,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph126", "image": "data/cycle/graph_visual/medium/graph126.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,5) (11,0) (2,8) (12,3) (10,11) (1,7) (5,4) (3,7) (5,8) (4,9) (0,12) (6,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph553", "image": "data/cycle/graph_visual/medium/graph553.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (12,16) (6,15) (0,12) (2,4) (1,12) (7,5) (17,16) (17,2) (15,18) (7,4) (2,19) (7,11) (8,14) (13,19) (12,8) (5,10) (19,9) (3,6) (13,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph881", "image": "data/cycle/graph_visual/medium/graph881.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (24,6) (11,1) (17,7) (23,20) (1,21) (14,7) (3,13) (4,7) (4,9) (16,24) (21,23) (12,8) (0,2) (12,4) (22,15) (19,4) (10,21) (18,4) (4,1) (3,17) (15,0) (5,3) (24,17) (22,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph567", "image": "data/cycle/graph_visual/medium/graph567.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,14) (12,19) (10,14) (8,7) (14,13) (8,14) (5,2) (0,2) (6,18) (15,11) (1,18) (17,11) (14,9) (6,7) (5,3) (4,12) (6,15) (12,6) (16,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph443", "image": "data/cycle/graph_visual/medium/graph443.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,10) (10,3) (8,17) (5,16) (10,0) (11,7) (6,17) (16,1) (14,4) (15,12) (7,17) (12,13) (0,15) (9,11) (2,14) (0,14) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1124", "image": "data/cycle/graph_visual/medium/graph1124.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,10) (7,6) (0,3) (4,13) (4,5) (12,0) (0,1) (6,5) (1,9) (11,9) (3,7) (0,4) (10,11) (3,2) (3,8) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph561", "image": "data/cycle/graph_visual/medium/graph561.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,7) (8,0) (4,13) (16,6) (10,5) (0,9) (5,4) (13,17) (9,3) (1,8) (0,18) (2,15) (7,11) (12,4) (14,7) (8,19) (9,6) (17,2) (4,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph279", "image": "data/cycle/graph_visual/medium/graph279.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,6) (14,5) (11,12) (2,4) (7,11) (13,9) (1,4) (13,14) (2,3) (4,8) (5,1) (10,1) (2,11) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1764", "image": "data/cycle/graph_visual/medium/graph1764.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (23,12) (9,5) (24,21) (20,10) (2,13) (10,16) (13,23) (16,1) (16,8) (24,5) (8,19) (20,21) (8,13) (17,18) (4,9) (0,1) (7,0) (3,0) (22,15) (3,22) (11,6) (17,21) (7,12) (22,14) (9,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph379", "image": "data/cycle/graph_visual/medium/graph379.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,16) (3,1) (8,11) (15,7) (0,14) (1,0) (9,13) (8,2) (5,13) (11,5) (11,14) (13,15) (12,4) (5,4) (6,16) (10,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph187", "image": "data/cycle/graph_visual/medium/graph187.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,13) (3,11) (6,11) (1,5) (11,12) (8,2) (2,5) (12,4) (8,10) (8,3) (9,4) (8,7) (0,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph920", "image": "data/cycle/graph_visual/medium/graph920.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,1) (5,6) (7,2) (8,6) (0,2) (1,8) (0,3) (7,3) (9,5) (2,6) (7,4) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph83", "image": "data/cycle/graph_visual/medium/graph83.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,5) (11,2) (7,6) (9,8) (7,3) (7,0) (2,0) (1,8) (10,2) (6,8) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1699", "image": "data/cycle/graph_visual/medium/graph1699.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (21,4) (14,12) (6,13) (7,0) (1,0) (13,15) (17,8) (3,15) (10,9) (8,7) (10,21) (16,22) (7,11) (7,19) (22,23) (11,1) (4,23) (9,0) (2,15) (9,5) (13,21) (20,18) (0,14) (20,9) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1441", "image": "data/cycle/graph_visual/medium/graph1441.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,0) (0,18) (1,0) (15,8) (0,13) (4,3) (11,9) (3,8) (5,2) (13,19) (11,12) (8,17) (17,1) (14,19) (17,13) (16,0) (9,13) (13,6) (15,10) (9,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1563", "image": "data/cycle/graph_visual/medium/graph1563.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (5,12) (4,9) (1,15) (0,2) (2,13) (14,8) (7,15) (0,20) (10,8) (0,1) (20,2) (0,3) (2,6) (17,10) (11,12) (18,21) (20,18) (6,9) (4,0) (7,5) (16,17) (15,2) (3,8) (8,11) (7,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1608", "image": "data/cycle/graph_visual/medium/graph1608.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (17,2) (3,11) (0,2) (17,9) (19,8) (14,16) (13,7) (6,20) (21,18) (2,10) (4,0) (18,8) (9,15) (12,20) (10,20) (0,18) (16,13) (0,1) (15,5) (7,3) (19,11) (1,17) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph524", "image": "data/cycle/graph_visual/medium/graph524.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,15) (3,16) (1,16) (0,1) (8,18) (8,3) (2,3) (11,16) (6,7) (12,6) (10,13) (8,10) (16,5) (4,8) (11,12) (9,14) (18,9) (13,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph233", "image": "data/cycle/graph_visual/medium/graph233.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,0) (12,0) (9,3) (5,8) (11,0) (12,10) (3,0) (2,13) (1,3) (6,11) (2,8) (10,2) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1757", "image": "data/cycle/graph_visual/medium/graph1757.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,5) (1,9) (2,20) (12,9) (14,19) (21,11) (22,5) (3,23) (17,3) (11,23) (24,23) (8,17) (4,0) (22,2) (9,8) (1,0) (2,0) (15,5) (6,13) (14,16) (23,13) (10,7) (18,15) (7,14) (13,5) (16,4) (22,4) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph329", "image": "data/cycle/graph_visual/medium/graph329.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,13) (0,10) (9,3) (15,2) (3,11) (13,12) (4,12) (2,1) (8,2) (5,4) (6,1) (13,14) (1,7) (11,6) (10,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1567", "image": "data/cycle/graph_visual/medium/graph1567.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (3,18) (0,4) (9,18) (16,6) (5,9) (21,19) (6,0) (17,3) (16,19) (20,7) (11,1) (1,9) (15,18) (14,13) (2,12) (20,6) (3,13) (0,2) (8,1) (1,0) (8,12) (10,15) (18,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph753", "image": "data/cycle/graph_visual/medium/graph753.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,1) (12,14) (11,2) (4,6) (4,7) (9,0) (18,11) (7,2) (5,19) (20,13) (22,21) (13,22) (10,19) (16,3) (19,0) (22,15) (8,7) (1,10) (14,5) (17,21) (3,20) (5,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph301", "image": "data/cycle/graph_visual/medium/graph301.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,1) (4,0) (10,7) (7,14) (14,0) (4,8) (0,15) (9,6) (11,12) (10,9) (11,3) (2,5) (5,11) (4,12) (13,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph986", "image": "data/cycle/graph_visual/medium/graph986.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,7) (2,11) (1,6) (10,8) (3,4) (4,5) (8,9) (10,11) (2,0) (1,0) (5,6) (2,4) (8,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1101", "image": "data/cycle/graph_visual/medium/graph1101.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,2) (11,1) (13,10) (12,5) (7,12) (5,13) (12,6) (2,8) (1,13) (0,3) (11,0) (10,4) (1,0) (2,0) (3,10) (9,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1434", "image": "data/cycle/graph_visual/medium/graph1434.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (5,0) (10,16) (6,11) (0,4) (15,2) (12,13) (0,2) (0,3) (18,15) (14,7) (13,0) (9,8) (1,3) (7,11) (2,11) (0,1) (12,17) (14,3) (17,4) (11,16) (5,2) (2,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph241", "image": "data/cycle/graph_visual/medium/graph241.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,14) (9,5) (9,3) (11,13) (10,4) (1,8) (14,12) (4,2) (7,13) (8,6) (1,12) (5,1) (0,13) (13,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1775", "image": "data/cycle/graph_visual/medium/graph1775.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (23,10) (20,22) (15,7) (0,14) (11,23) (7,21) (20,13) (14,24) (7,12) (1,20) (0,16) (5,1) (17,3) (17,12) (8,11) (18,24) (15,11) (16,19) (18,3) (2,0) (0,1) (6,23) (3,5) (8,4) (9,22) (19,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph894", "image": "data/cycle/graph_visual/medium/graph894.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (22,0) (10,13) (4,24) (16,20) (17,6) (20,12) (5,16) (15,16) (3,13) (13,18) (8,22) (4,2) (18,11) (5,1) (0,21) (19,5) (7,23) (15,9) (16,7) (0,11) (2,13) (9,14) (7,24) (6,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph596", "image": "data/cycle/graph_visual/medium/graph596.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,3) (13,16) (17,1) (11,8) (6,16) (2,8) (18,0) (10,1) (15,7) (1,0) (13,5) (9,13) (19,14) (11,14) (14,12) (4,5) (4,15) (11,5) (12,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph327", "image": "data/cycle/graph_visual/medium/graph327.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,2) (3,10) (14,11) (2,13) (7,5) (13,12) (8,2) (1,0) (9,6) (7,8) (13,15) (1,4) (10,0) (8,11) (5,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph147", "image": "data/cycle/graph_visual/medium/graph147.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,6) (2,12) (7,9) (1,4) (3,11) (12,8) (4,0) (1,12) (10,2) (0,9) (5,8) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph316", "image": "data/cycle/graph_visual/medium/graph316.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (6,1) (14,6) (0,6) (2,6) (5,1) (9,13) (8,12) (10,11) (8,14) (9,3) (7,12) (13,14) (3,15) (6,4) (11,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph346", "image": "data/cycle/graph_visual/medium/graph346.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,9) (4,5) (12,3) (1,14) (13,0) (15,9) (4,14) (7,11) (6,15) (10,2) (9,10) (12,5) (11,14) (10,0) (0,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph35", "image": "data/cycle/graph_visual/medium/graph35.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,3) (1,3) (3,2) (7,2) (9,10) (6,0) (4,0) (8,0) (8,5) (0,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1773", "image": "data/cycle/graph_visual/medium/graph1773.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (10,9) (3,8) (0,7) (0,19) (24,4) (7,15) (23,4) (0,14) (2,20) (1,16) (11,12) (11,8) (13,2) (16,4) (11,5) (9,13) (1,0) (0,24) (6,18) (18,21) (3,10) (17,12) (19,11) (16,18) (3,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph351", "image": "data/cycle/graph_visual/medium/graph351.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,0) (15,9) (0,9) (8,13) (7,8) (6,7) (4,9) (3,15) (12,13) (7,14) (2,15) (11,1) (13,5) (10,14) (0,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph114", "image": "data/cycle/graph_visual/medium/graph114.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,5) (5,9) (8,7) (9,0) (3,1) (11,0) (8,0) (4,0) (10,11) (6,2) (6,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph827", "image": "data/cycle/graph_visual/medium/graph827.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (8,6) (17,1) (2,20) (23,20) (4,10) (0,12) (14,2) (18,23) (19,0) (4,13) (9,17) (16,21) (1,18) (15,8) (11,15) (16,5) (17,3) (6,20) (19,6) (23,7) (16,19) (22,20) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1772", "image": "data/cycle/graph_visual/medium/graph1772.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (19,1) (21,19) (18,6) (11,12) (3,0) (18,5) (3,12) (7,23) (4,13) (5,4) (11,8) (15,3) (10,2) (18,1) (20,3) (19,11) (12,14) (17,22) (23,21) (20,24) (3,9) (3,17) (11,2) (15,0) (1,0) (0,2) (16,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1183", "image": "data/cycle/graph_visual/medium/graph1183.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (4,8) (9,12) (9,2) (3,8) (12,10) (5,8) (14,11) (2,0) (4,12) (9,7) (0,6) (1,0) (6,12) (10,13) (14,12) (1,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1269", "image": "data/cycle/graph_visual/medium/graph1269.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,13) (11,7) (2,4) (9,16) (5,11) (3,1) (3,0) (8,2) (16,2) (9,6) (3,14) (2,0) (12,15) (10,11) (0,4) (0,1) (14,7) (13,0) (2,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1128", "image": "data/cycle/graph_visual/medium/graph1128.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,13) (10,13) (0,1) (5,6) (6,2) (0,4) (1,2) (8,9) (3,6) (4,12) (1,11) (7,8) (3,0) (11,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph151", "image": "data/cycle/graph_visual/medium/graph151.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,10) (4,2) (8,2) (10,9) (7,0) (11,4) (7,6) (1,10) (3,5) (9,12) (11,0) (1,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1717", "image": "data/cycle/graph_visual/medium/graph1717.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (14,13) (7,0) (12,18) (17,0) (6,2) (23,22) (1,13) (21,15) (23,7) (3,9) (5,3) (19,21) (20,4) (10,23) (9,21) (8,11) (1,20) (16,4) (12,17) (0,1) (20,6) (15,12) (6,22) (23,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1752", "image": "data/cycle/graph_visual/medium/graph1752.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (8,24) (24,12) (21,14) (2,21) (12,21) (20,6) (13,23) (16,10) (0,3) (18,2) (1,19) (20,9) (24,5) (14,19) (17,23) (8,3) (1,0) (4,22) (8,15) (23,3) (9,14) (9,16) (22,12) (8,7) (7,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph983", "image": "data/cycle/graph_visual/medium/graph983.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,0) (4,9) (3,8) (1,0) (5,7) (1,2) (0,2) (2,8) (1,4) (11,5) (7,10) (3,0) (0,6) (4,0) (6,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph492", "image": "data/cycle/graph_visual/medium/graph492.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,11) (3,15) (15,14) (13,17) (14,2) (10,3) (0,12) (17,8) (10,18) (7,1) (0,11) (18,9) (1,16) (4,6) (13,5) (6,11) (0,1) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph679", "image": "data/cycle/graph_visual/medium/graph679.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,0) (6,3) (17,10) (9,19) (2,11) (8,18) (12,1) (14,4) (4,8) (21,9) (1,14) (16,7) (3,10) (17,16) (15,1) (20,17) (11,16) (7,19) (1,20) (5,13) (13,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1647", "image": "data/cycle/graph_visual/medium/graph1647.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (0,1) (21,19) (8,7) (17,20) (3,11) (15,0) (3,21) (17,2) (22,9) (10,11) (0,2) (7,10) (10,13) (1,8) (11,4) (17,15) (16,10) (2,14) (7,22) (5,11) (20,6) (15,12) (4,2) (18,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph637", "image": "data/cycle/graph_visual/medium/graph637.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (1,14) (11,17) (18,19) (4,9) (2,17) (8,20) (10,5) (0,16) (8,15) (16,20) (18,3) (6,4) (11,3) (16,1) (9,13) (8,12) (10,7) (10,4) (0,11) (18,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph455", "image": "data/cycle/graph_visual/medium/graph455.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,6) (8,0) (5,2) (13,2) (3,16) (9,10) (11,4) (1,12) (8,17) (15,12) (10,8) (3,0) (14,7) (0,13) (16,11) (1,13) (12,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph885", "image": "data/cycle/graph_visual/medium/graph885.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (19,2) (15,10) (23,14) (22,12) (23,5) (22,9) (16,23) (0,1) (4,8) (4,21) (16,13) (17,14) (16,7) (5,19) (5,1) (11,23) (24,1) (18,0) (11,20) (15,11) (14,6) (1,22) (23,8) (3,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1514", "image": "data/cycle/graph_visual/medium/graph1514.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (7,11) (16,5) (18,4) (15,14) (16,12) (3,6) (5,1) (16,9) (1,8) (4,8) (2,19) (0,14) (20,7) (17,11) (0,1) (19,5) (6,14) (10,15) (0,3) (11,13) (2,0) (1,11) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1477", "image": "data/cycle/graph_visual/medium/graph1477.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (13,17) (0,16) (0,1) (19,10) (14,3) (4,14) (18,15) (11,16) (19,8) (4,5) (14,13) (11,6) (9,1) (7,3) (0,12) (18,17) (2,1) (13,19) (11,19) (9,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1160", "image": "data/cycle/graph_visual/medium/graph1160.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,1) (5,3) (10,11) (1,8) (5,11) (13,6) (7,12) (9,4) (4,2) (0,2) (0,9) (6,4) (8,2) (2,12) (5,13) (14,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1535", "image": "data/cycle/graph_visual/medium/graph1535.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (0,16) (16,9) (1,13) (19,12) (5,7) (2,0) (0,6) (8,12) (5,15) (4,1) (14,10) (3,10) (14,11) (18,8) (0,1) (2,6) (11,20) (4,11) (7,3) (11,8) (17,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1470", "image": "data/cycle/graph_visual/medium/graph1470.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (8,5) (5,4) (17,2) (19,3) (19,4) (7,4) (15,4) (6,19) (4,1) (6,13) (0,1) (17,6) (14,6) (14,10) (11,13) (5,12) (3,0) (18,6) (9,7) (16,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1694", "image": "data/cycle/graph_visual/medium/graph1694.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (2,15) (16,15) (8,0) (12,2) (23,22) (4,1) (21,3) (10,13) (6,17) (16,19) (6,5) (9,8) (12,8) (3,7) (11,3) (18,17) (22,19) (11,0) (23,4) (1,0) (10,22) (10,20) (20,14) (17,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1485", "image": "data/cycle/graph_visual/medium/graph1485.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,12) (8,15) (10,2) (1,16) (13,3) (14,8) (15,18) (14,6) (8,2) (19,11) (18,4) (14,0) (16,15) (15,9) (19,8) (11,17) (1,7) (3,10) (13,5) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph693", "image": "data/cycle/graph_visual/medium/graph693.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (12,0) (5,2) (4,6) (7,9) (11,19) (16,15) (19,0) (10,3) (15,11) (3,14) (2,6) (1,16) (15,7) (10,1) (16,18) (21,4) (1,13) (9,8) (10,20) (17,0) (17,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph508", "image": "data/cycle/graph_visual/medium/graph508.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (15,10) (7,16) (4,0) (3,18) (11,12) (0,5) (11,1) (10,8) (6,7) (12,13) (18,12) (11,16) (9,13) (5,16) (0,15) (12,17) (1,2) (14,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph94", "image": "data/cycle/graph_visual/medium/graph94.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,7) (6,7) (9,11) (1,6) (5,6) (1,2) (4,9) (4,8) (0,1) (7,3) (6,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1570", "image": "data/cycle/graph_visual/medium/graph1570.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (2,17) (15,10) (2,4) (0,2) (11,4) (11,3) (8,7) (3,0) (15,9) (2,13) (20,3) (0,1) (18,21) (7,21) (14,17) (5,11) (8,1) (11,10) (0,15) (20,6) (10,7) (12,10) (19,17) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1003", "image": "data/cycle/graph_visual/medium/graph1003.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,8) (2,11) (11,0) (1,0) (0,2) (0,7) (3,9) (11,1) (3,2) (0,3) (3,4) (10,5) (4,0) (6,1) (1,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1068", "image": "data/cycle/graph_visual/medium/graph1068.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,5) (8,10) (0,9) (7,2) (8,3) (11,4) (0,2) (7,6) (9,11) (1,3) (1,0) (7,12) (5,11) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph691", "image": "data/cycle/graph_visual/medium/graph691.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (11,12) (17,3) (5,15) (17,18) (19,20) (12,13) (8,3) (5,4) (9,2) (14,3) (16,1) (19,11) (15,0) (21,3) (2,11) (21,12) (6,18) (10,4) (5,18) (1,19) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1461", "image": "data/cycle/graph_visual/medium/graph1461.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,11) (13,7) (4,0) (11,16) (17,19) (13,15) (3,0) (8,15) (5,17) (2,0) (10,8) (12,7) (10,14) (1,17) (14,0) (1,0) (6,19) (14,17) (1,3) (2,16) (18,3) (4,3) (18,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph540", "image": "data/cycle/graph_visual/medium/graph540.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,18) (14,19) (10,3) (6,14) (3,2) (18,14) (11,8) (15,7) (10,7) (12,11) (0,6) (19,16) (19,1) (7,5) (17,13) (18,17) (4,6) (18,7) (12,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1774", "image": "data/cycle/graph_visual/medium/graph1774.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (5,11) (0,14) (1,0) (0,21) (6,5) (0,2) (18,7) (2,22) (12,3) (1,22) (20,23) (15,2) (6,12) (24,19) (10,6) (22,14) (23,14) (21,5) (13,21) (4,22) (24,16) (24,20) (9,23) (5,8) (9,18) (17,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph127", "image": "data/cycle/graph_visual/medium/graph127.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,8) (7,10) (7,3) (4,8) (0,2) (7,4) (9,12) (9,5) (6,3) (6,11) (7,1) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1547", "image": "data/cycle/graph_visual/medium/graph1547.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,9) (0,3) (0,4) (17,8) (16,0) (19,8) (11,17) (0,10) (12,20) (20,18) (7,5) (1,4) (2,18) (10,3) (2,17) (8,7) (0,2) (15,20) (16,13) (2,9) (0,1) (11,13) (14,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1207", "image": "data/cycle/graph_visual/medium/graph1207.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,14) (3,12) (11,13) (15,11) (2,0) (9,14) (5,2) (5,14) (5,1) (1,0) (15,6) (8,12) (8,7) (6,14) (10,14) (6,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph967", "image": "data/cycle/graph_visual/medium/graph967.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,0) (3,0) (3,6) (2,8) (0,9) (10,7) (10,8) (1,2) (7,4) (4,3) (8,9) (5,10) (11,2) (0,4) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph709", "image": "data/cycle/graph_visual/medium/graph709.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (16,19) (12,15) (16,12) (11,15) (20,17) (9,21) (0,2) (13,10) (2,6) (7,5) (10,12) (4,3) (9,5) (8,2) (12,18) (9,4) (2,11) (1,6) (17,13) (21,20) (14,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1042", "image": "data/cycle/graph_visual/medium/graph1042.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,4) (4,1) (4,0) (11,12) (11,8) (1,0) (10,8) (3,0) (3,8) (9,5) (2,11) (3,6) (0,2) (1,7) (5,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph963", "image": "data/cycle/graph_visual/medium/graph963.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,6) (5,0) (4,0) (11,7) (3,2) (5,10) (4,10) (8,2) (2,0) (10,7) (1,0) (6,7) (0,3) (1,9) (11,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1052", "image": "data/cycle/graph_visual/medium/graph1052.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,10) (7,3) (0,2) (0,8) (10,12) (3,0) (0,1) (1,11) (3,6) (9,6) (3,4) (9,8) (12,11) (12,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph559", "image": "data/cycle/graph_visual/medium/graph559.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (18,12) (2,11) (3,1) (7,14) (19,10) (13,12) (2,5) (2,9) (16,11) (15,9) (1,0) (6,11) (17,16) (14,3) (0,13) (2,19) (17,4) (19,8) (7,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph425", "image": "data/cycle/graph_visual/medium/graph425.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,14) (8,0) (9,4) (12,15) (17,14) (6,0) (3,2) (10,16) (9,5) (5,10) (13,12) (7,1) (7,4) (15,9) (0,11) (5,17) (0,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1016", "image": "data/cycle/graph_visual/medium/graph1016.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,0) (0,2) (8,11) (9,2) (0,10) (2,4) (5,6) (2,10) (7,1) (0,5) (8,5) (1,0) (9,3) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1112", "image": "data/cycle/graph_visual/medium/graph1112.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,3) (0,11) (13,7) (5,9) (12,5) (2,8) (12,3) (1,0) (7,1) (4,5) (7,0) (11,12) (0,3) (0,2) (2,6) (4,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1255", "image": "data/cycle/graph_visual/medium/graph1255.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,1) (2,14) (9,12) (0,2) (4,2) (4,13) (5,7) (0,12) (15,10) (7,11) (0,1) (1,9) (0,3) (9,6) (3,12) (15,11) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1061", "image": "data/cycle/graph_visual/medium/graph1061.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,6) (0,1) (0,2) (12,2) (8,10) (3,4) (7,0) (10,12) (4,11) (1,6) (5,0) (9,7) (0,12) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1033", "image": "data/cycle/graph_visual/medium/graph1033.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (10,0) (1,5) (7,2) (3,4) (8,6) (7,9) (4,11) (0,1) (10,1) (0,3) (9,6) (8,10) (11,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph547", "image": "data/cycle/graph_visual/medium/graph547.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,17) (4,1) (19,6) (5,16) (1,10) (12,7) (11,8) (9,6) (16,4) (18,14) (2,14) (14,8) (19,14) (11,15) (3,18) (4,13) (7,9) (1,6) (16,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1475", "image": "data/cycle/graph_visual/medium/graph1475.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,15) (14,4) (1,15) (0,2) (9,12) (18,4) (16,7) (0,3) (15,19) (4,6) (19,14) (8,14) (0,1) (13,8) (7,17) (5,11) (19,0) (2,8) (0,10) (16,3) (11,12) (0,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1334", "image": "data/cycle/graph_visual/medium/graph1334.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (4,15) (1,0) (15,2) (8,5) (1,7) (3,0) (14,6) (11,10) (13,17) (6,13) (0,10) (0,5) (15,8) (0,4) (8,0) (11,12) (4,9) (17,15) (0,2) (16,17) (2,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph795", "image": "data/cycle/graph_visual/medium/graph795.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (8,20) (13,8) (10,5) (18,22) (13,9) (6,4) (23,1) (16,0) (22,21) (9,4) (11,3) (20,11) (16,17) (16,23) (17,2) (18,3) (10,12) (8,19) (15,1) (7,23) (18,14) (10,4) (0,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1657", "image": "data/cycle/graph_visual/medium/graph1657.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (11,14) (0,1) (2,5) (11,13) (13,0) (3,8) (9,13) (11,15) (19,8) (17,1) (3,0) (21,10) (20,13) (12,15) (17,0) (13,6) (5,9) (7,0) (3,4) (0,2) (9,16) (21,0) (22,14) (8,17) (19,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1728", "image": "data/cycle/graph_visual/medium/graph1728.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (18,16) (1,19) (3,12) (7,12) (17,12) (12,14) (15,11) (16,5) (1,0) (11,0) (6,22) (17,13) (18,0) (2,8) (12,1) (11,9) (10,11) (7,5) (2,0) (21,7) (22,19) (17,4) (0,3) (8,13) (17,20) (0,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph254", "image": "data/cycle/graph_visual/medium/graph254.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,7) (9,2) (2,0) (3,11) (3,10) (14,5) (2,1) (6,5) (12,3) (1,5) (7,2) (4,7) (8,9) (11,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph541", "image": "data/cycle/graph_visual/medium/graph541.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (12,11) (13,16) (3,2) (7,10) (7,19) (1,8) (18,17) (2,14) (5,15) (4,14) (12,5) (3,16) (6,10) (1,6) (0,4) (9,14) (8,14) (11,13) (17,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph781", "image": "data/cycle/graph_visual/medium/graph781.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,5) (21,20) (15,0) (10,1) (14,22) (6,12) (4,15) (1,4) (9,21) (8,4) (1,21) (17,3) (17,7) (12,3) (2,0) (19,1) (22,23) (17,23) (4,11) (23,18) (7,13) (16,4) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1397", "image": "data/cycle/graph_visual/medium/graph1397.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (3,14) (2,9) (0,14) (2,15) (2,17) (7,4) (4,10) (9,6) (1,0) (10,18) (12,2) (13,2) (16,6) (7,1) (14,12) (11,8) (9,5) (15,8) (9,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1304", "image": "data/cycle/graph_visual/medium/graph1304.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,1) (3,12) (0,2) (8,5) (10,9) (16,7) (0,5) (7,4) (3,8) (0,1) (14,9) (4,0) (8,7) (12,14) (11,2) (6,8) (9,13) (2,14) (3,0) (15,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1089", "image": "data/cycle/graph_visual/medium/graph1089.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,0) (5,4) (10,1) (11,1) (1,12) (10,13) (1,8) (10,7) (4,3) (1,0) (7,2) (4,7) (6,9) (6,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph72", "image": "data/cycle/graph_visual/medium/graph72.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,7) (11,9) (2,3) (7,10) (11,7) (2,0) (5,9) (5,4) (3,11) (2,6) (8,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1266", "image": "data/cycle/graph_visual/medium/graph1266.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,13) (2,3) (12,6) (1,16) (16,5) (8,3) (6,7) (12,11) (0,2) (14,9) (8,4) (9,4) (1,0) (15,3) (10,16) (16,11) (13,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1693", "image": "data/cycle/graph_visual/medium/graph1693.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (19,7) (10,18) (17,21) (21,20) (11,10) (0,1) (15,13) (0,2) (22,3) (16,17) (6,23) (20,8) (11,5) (22,12) (3,0) (14,10) (15,2) (10,7) (6,7) (0,15) (4,0) (2,4) (9,7) (8,1) (11,4) (17,2) (3,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph673", "image": "data/cycle/graph_visual/medium/graph673.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (9,17) (11,6) (11,1) (8,0) (16,19) (12,9) (4,0) (6,18) (0,18) (20,15) (2,16) (5,17) (14,0) (10,2) (13,3) (14,13) (20,6) (16,3) (21,1) (12,3) (10,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1081", "image": "data/cycle/graph_visual/medium/graph1081.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,1) (6,5) (9,7) (12,3) (0,3) (13,4) (1,13) (0,2) (10,4) (12,11) (8,12) (4,7) (8,1) (4,2) (3,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph274", "image": "data/cycle/graph_visual/medium/graph274.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,0) (3,12) (6,13) (10,9) (11,9) (3,4) (9,7) (6,0) (2,12) (8,1) (13,10) (4,0) (6,14) (5,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph382", "image": "data/cycle/graph_visual/medium/graph382.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,16) (16,6) (4,15) (9,6) (9,2) (1,4) (10,13) (13,7) (5,11) (3,12) (0,10) (4,5) (16,8) (6,7) (3,15) (16,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1078", "image": "data/cycle/graph_visual/medium/graph1078.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,6) (2,10) (10,5) (3,12) (8,10) (10,4) (2,3) (4,1) (4,0) (2,7) (10,11) (3,9) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1342", "image": "data/cycle/graph_visual/medium/graph1342.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,4) (0,12) (9,10) (13,2) (13,9) (6,0) (0,7) (5,11) (17,8) (11,12) (15,16) (0,1) (3,4) (16,1) (2,11) (3,10) (14,7) (8,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph190", "image": "data/cycle/graph_visual/medium/graph190.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,0) (7,0) (4,9) (6,5) (5,8) (1,11) (8,1) (6,3) (9,13) (12,3) (8,10) (10,2) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph452", "image": "data/cycle/graph_visual/medium/graph452.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,15) (12,15) (11,0) (4,7) (17,5) (7,1) (0,6) (2,3) (9,5) (10,16) (14,2) (9,4) (0,8) (13,12) (15,0) (10,5) (14,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph249", "image": "data/cycle/graph_visual/medium/graph249.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,9) (8,0) (13,8) (0,10) (10,6) (3,9) (1,4) (9,5) (12,10) (2,10) (7,13) (14,10) (1,14) (13,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1598", "image": "data/cycle/graph_visual/medium/graph1598.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (13,20) (20,6) (9,21) (1,10) (8,14) (0,2) (14,0) (0,16) (18,3) (11,8) (17,6) (9,7) (21,6) (11,19) (0,3) (21,15) (5,16) (7,12) (2,14) (4,18) (16,4) (1,20) (1,4) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph353", "image": "data/cycle/graph_visual/medium/graph353.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,12) (2,4) (12,2) (6,3) (11,8) (5,7) (15,2) (6,13) (1,12) (15,13) (14,6) (7,4) (10,7) (9,5) (12,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph777", "image": "data/cycle/graph_visual/medium/graph777.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (21,13) (13,15) (0,7) (0,9) (20,9) (10,21) (4,21) (6,13) (3,15) (18,20) (1,11) (5,9) (14,12) (15,2) (19,7) (14,0) (16,22) (7,11) (22,4) (9,10) (8,7) (8,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph599", "image": "data/cycle/graph_visual/medium/graph599.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (13,2) (7,0) (4,19) (16,10) (4,12) (14,11) (9,5) (11,9) (5,17) (1,16) (6,9) (10,12) (12,7) (13,8) (16,8) (15,8) (13,18) (0,3) (17,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1611", "image": "data/cycle/graph_visual/medium/graph1611.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (0,15) (1,8) (8,20) (15,21) (17,20) (0,3) (19,16) (2,10) (0,1) (8,0) (9,15) (17,4) (7,10) (12,17) (21,18) (3,6) (7,14) (3,9) (6,11) (13,19) (16,0) (6,5) (2,0) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1552", "image": "data/cycle/graph_visual/medium/graph1552.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (6,7) (4,2) (18,2) (0,12) (5,8) (3,0) (1,9) (20,5) (13,3) (4,15) (3,12) (12,17) (1,7) (8,11) (17,11) (9,10) (16,7) (16,17) (9,19) (0,1) (0,2) (14,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph780", "image": "data/cycle/graph_visual/medium/graph780.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (3,11) (15,9) (16,13) (12,20) (2,10) (3,7) (18,8) (18,6) (23,6) (0,22) (18,0) (21,6) (1,17) (10,20) (5,15) (16,14) (8,20) (7,17) (13,22) (9,17) (4,0) (2,19) (19,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph740", "image": "data/cycle/graph_visual/medium/graph740.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (15,7) (11,3) (16,9) (9,7) (7,10) (7,13) (1,0) (9,6) (10,2) (0,22) (9,18) (8,6) (2,20) (14,19) (21,9) (14,15) (12,5) (17,10) (13,12) (1,11) (4,14) (17,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph950", "image": "data/cycle/graph_visual/medium/graph950.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,0) (7,4) (5,3) (10,9) (10,1) (3,7) (7,10) (0,1) (2,1) (3,8) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1158", "image": "data/cycle/graph_visual/medium/graph1158.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,9) (7,10) (10,14) (1,0) (0,2) (1,2) (2,10) (4,7) (14,11) (0,4) (12,8) (3,13) (9,4) (5,3) (0,3) (13,14) (8,14) (6,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1157", "image": "data/cycle/graph_visual/medium/graph1157.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,7) (2,0) (4,1) (13,12) (11,3) (3,9) (14,3) (0,12) (10,3) (4,2) (6,5) (1,13) (7,4) (3,5) (9,8) (0,3) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph801", "image": "data/cycle/graph_visual/medium/graph801.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,6) (6,5) (19,13) (18,2) (17,1) (8,14) (3,18) (6,23) (0,3) (1,6) (12,21) (18,9) (4,6) (13,9) (8,22) (20,14) (12,11) (14,19) (7,23) (11,9) (16,6) (15,0) (10,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph800", "image": "data/cycle/graph_visual/medium/graph800.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (16,20) (18,11) (13,3) (15,6) (21,0) (9,14) (1,5) (10,13) (13,2) (5,19) (9,15) (11,0) (22,0) (2,4) (8,22) (7,23) (18,13) (12,20) (16,15) (17,6) (5,16) (7,4) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1192", "image": "data/cycle/graph_visual/medium/graph1192.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,4) (0,8) (6,1) (14,4) (10,8) (0,1) (8,11) (11,12) (5,7) (4,6) (12,3) (2,12) (11,13) (0,3) (10,4) (9,2) (2,0) (5,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph578", "image": "data/cycle/graph_visual/medium/graph578.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,6) (10,1) (8,16) (17,15) (0,13) (12,4) (18,2) (7,8) (5,4) (14,15) (11,4) (14,10) (12,1) (9,18) (3,9) (0,7) (13,19) (1,7) (5,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph810", "image": "data/cycle/graph_visual/medium/graph810.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (14,17) (5,14) (2,16) (11,3) (11,6) (22,0) (8,16) (1,19) (10,5) (4,3) (0,19) (5,9) (18,16) (13,9) (8,20) (22,23) (3,12) (14,21) (6,15) (10,8) (10,7) (14,3) (19,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph715", "image": "data/cycle/graph_visual/medium/graph715.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (20,10) (19,14) (11,15) (6,9) (0,7) (2,11) (2,1) (4,13) (3,19) (10,13) (2,18) (14,5) (6,17) (5,18) (19,0) (12,8) (2,10) (8,4) (9,21) (21,7) (16,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1306", "image": "data/cycle/graph_visual/medium/graph1306.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,1) (8,11) (6,9) (0,3) (7,10) (6,16) (4,12) (14,0) (9,7) (11,13) (0,1) (16,3) (0,2) (14,8) (2,14) (4,1) (4,15) (16,0) (6,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph318", "image": "data/cycle/graph_visual/medium/graph318.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,11) (3,0) (6,8) (2,5) (3,15) (12,11) (12,0) (12,7) (12,8) (10,13) (7,5) (7,4) (14,8) (7,1) (9,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1697", "image": "data/cycle/graph_visual/medium/graph1697.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (5,0) (17,21) (23,6) (14,18) (11,19) (3,18) (12,4) (20,13) (15,6) (1,0) (2,15) (21,4) (17,22) (23,21) (5,2) (23,18) (0,10) (8,7) (10,11) (8,0) (0,4) (15,8) (1,9) (15,16) (0,3) (2,0) (13,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1267", "image": "data/cycle/graph_visual/medium/graph1267.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,6) (7,3) (12,8) (16,15) (2,0) (12,0) (14,15) (11,1) (14,0) (6,13) (7,16) (7,4) (9,4) (4,2) (2,1) (0,1) (6,12) (5,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph435", "image": "data/cycle/graph_visual/medium/graph435.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,4) (6,9) (16,7) (0,12) (1,7) (12,17) (7,5) (2,0) (8,3) (2,13) (17,16) (9,14) (4,11) (9,1) (15,10) (12,3) (15,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph756", "image": "data/cycle/graph_visual/medium/graph756.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (5,16) (0,17) (7,5) (10,11) (12,7) (6,22) (4,17) (13,8) (12,17) (13,17) (11,15) (16,18) (18,22) (12,3) (1,19) (9,11) (21,19) (2,8) (12,14) (0,11) (7,20) (12,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph873", "image": "data/cycle/graph_visual/medium/graph873.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (4,17) (11,9) (22,7) (2,8) (6,22) (16,5) (15,11) (10,11) (17,13) (11,0) (8,13) (14,12) (1,19) (5,7) (0,24) (12,1) (17,20) (7,12) (23,19) (18,16) (17,24) (21,12) (12,3) (0,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1619", "image": "data/cycle/graph_visual/medium/graph1619.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (13,20) (7,19) (12,9) (11,21) (14,6) (13,14) (4,19) (18,20) (16,8) (6,17) (5,3) (0,5) (15,1) (0,4) (6,0) (1,0) (0,12) (10,17) (3,0) (21,2) (2,0) (20,8) (2,4) (20,3) (6,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1094", "image": "data/cycle/graph_visual/medium/graph1094.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (5,12) (3,1) (5,9) (2,5) (10,0) (0,1) (11,0) (13,1) (0,2) (10,7) (6,8) (11,12) (3,6) (0,13) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph434", "image": "data/cycle/graph_visual/medium/graph434.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,13) (12,4) (7,2) (0,11) (6,9) (3,14) (1,13) (12,9) (10,2) (6,5) (17,9) (10,9) (14,16) (15,14) (7,15) (11,7) (1,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph887", "image": "data/cycle/graph_visual/medium/graph887.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (23,5) (0,20) (9,8) (1,15) (11,15) (16,0) (19,11) (2,22) (2,24) (17,4) (10,14) (10,6) (10,9) (10,5) (21,12) (22,16) (7,6) (14,12) (10,20) (18,15) (11,2) (13,22) (0,17) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph573", "image": "data/cycle/graph_visual/medium/graph573.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,15) (1,8) (15,7) (7,5) (16,10) (17,14) (9,2) (2,6) (12,11) (13,8) (4,6) (8,11) (17,7) (9,3) (12,5) (8,10) (0,15) (19,18) (2,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph778", "image": "data/cycle/graph_visual/medium/graph778.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (17,22) (16,10) (12,6) (4,17) (2,17) (9,5) (18,10) (14,19) (9,15) (18,12) (6,1) (2,19) (4,0) (12,11) (1,15) (17,15) (7,14) (6,20) (7,13) (21,14) (3,14) (15,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph65", "image": "data/cycle/graph_visual/medium/graph65.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,11) (7,10) (9,2) (2,0) (5,4) (4,1) (7,1) (1,3) (6,10) (8,7) (7,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph951", "image": "data/cycle/graph_visual/medium/graph951.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,0) (1,0) (3,0) (5,6) (9,6) (2,1) (7,10) (2,0) (8,4) (4,0) (9,4) (6,1) (7,3) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph108", "image": "data/cycle/graph_visual/medium/graph108.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,10) (8,0) (3,8) (8,2) (8,4) (4,9) (2,5) (7,8) (1,5) (11,6) (3,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1294", "image": "data/cycle/graph_visual/medium/graph1294.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,13) (1,5) (10,14) (6,14) (16,6) (15,11) (3,12) (14,5) (15,6) (8,12) (7,8) (2,5) (3,0) (2,0) (1,0) (9,14) (4,14) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph879", "image": "data/cycle/graph_visual/medium/graph879.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (17,21) (14,8) (4,21) (13,21) (3,15) (24,10) (10,14) (4,3) (23,7) (20,12) (2,16) (5,22) (21,22) (13,12) (19,6) (6,22) (3,0) (9,14) (19,18) (11,4) (16,10) (7,12) (1,9) (2,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph41", "image": "data/cycle/graph_visual/medium/graph41.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,10) (3,9) (4,10) (9,7) (8,4) (6,0) (8,6) (1,9) (8,2) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1218", "image": "data/cycle/graph_visual/medium/graph1218.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (6,0) (6,10) (6,3) (1,8) (9,1) (15,10) (9,13) (1,11) (1,0) (12,2) (0,4) (5,9) (7,15) (13,3) (14,3) (12,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1480", "image": "data/cycle/graph_visual/medium/graph1480.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,0) (1,10) (13,0) (7,1) (4,5) (9,18) (2,5) (15,17) (1,0) (0,2) (9,6) (12,1) (18,2) (14,10) (16,8) (14,15) (13,19) (12,4) (4,11) (3,9) (8,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1599", "image": "data/cycle/graph_visual/medium/graph1599.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (12,17) (6,14) (18,2) (18,9) (6,5) (6,4) (20,8) (12,11) (1,0) (11,9) (9,13) (8,14) (0,15) (6,10) (7,20) (18,3) (15,21) (1,6) (14,19) (1,16) (3,0) (19,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph665", "image": "data/cycle/graph_visual/medium/graph665.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (3,17) (9,4) (6,8) (19,0) (17,16) (20,19) (10,15) (7,17) (13,2) (1,18) (16,19) (14,8) (12,4) (1,15) (2,20) (6,18) (16,5) (0,11) (6,20) (0,4) (20,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1001", "image": "data/cycle/graph_visual/medium/graph1001.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,9) (0,7) (10,0) (0,2) (1,0) (11,4) (3,8) (2,4) (1,5) (0,4) (6,2) (0,11) (0,3) (7,3) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph85", "image": "data/cycle/graph_visual/medium/graph85.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,2) (4,7) (7,1) (3,9) (0,6) (0,10) (5,7) (10,3) (0,8) (2,6) (11,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1787", "image": "data/cycle/graph_visual/medium/graph1787.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (23,21) (21,13) (23,14) (4,0) (1,20) (14,4) (20,17) (6,3) (18,24) (5,13) (8,22) (2,0) (24,9) (3,0) (11,16) (24,19) (1,0) (1,12) (15,1) (16,17) (2,11) (8,4) (3,10) (1,23) (17,10) (7,19) (7,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph200", "image": "data/cycle/graph_visual/medium/graph200.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (11,5) (8,12) (5,0) (8,6) (5,6) (5,10) (2,6) (7,13) (0,13) (11,4) (1,4) (8,3) (9,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1483", "image": "data/cycle/graph_visual/medium/graph1483.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,18) (13,1) (11,10) (15,9) (13,4) (14,5) (0,2) (10,19) (18,9) (10,8) (14,7) (2,3) (13,0) (1,19) (11,12) (16,11) (0,1) (8,17) (6,3) (15,19) (11,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph611", "image": "data/cycle/graph_visual/medium/graph611.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,0) (6,2) (4,5) (7,2) (0,3) (20,8) (5,18) (13,5) (16,12) (9,10) (8,17) (0,15) (18,1) (5,11) (14,5) (3,5) (20,15) (7,14) (19,15) (11,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1707", "image": "data/cycle/graph_visual/medium/graph1707.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (0,1) (15,3) (1,4) (6,18) (18,4) (13,19) (17,12) (2,8) (0,19) (15,0) (23,8) (8,14) (23,22) (11,15) (10,14) (5,2) (7,3) (0,22) (9,15) (12,13) (20,16) (6,3) (21,14) (20,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph696", "image": "data/cycle/graph_visual/medium/graph696.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (10,17) (12,5) (21,18) (8,10) (6,2) (15,2) (2,20) (20,0) (8,14) (15,7) (5,7) (16,17) (8,11) (3,8) (1,15) (12,11) (18,20) (9,6) (13,2) (9,4) (7,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph700", "image": "data/cycle/graph_visual/medium/graph700.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (7,0) (9,5) (15,9) (21,10) (19,16) (14,11) (13,0) (6,13) (17,8) (17,1) (9,13) (5,2) (3,8) (13,19) (21,11) (0,20) (18,8) (4,3) (17,0) (11,13) (15,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph194", "image": "data/cycle/graph_visual/medium/graph194.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,4) (3,10) (13,8) (1,2) (6,2) (7,1) (5,13) (10,0) (12,3) (0,6) (13,3) (9,7) (11,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1374", "image": "data/cycle/graph_visual/medium/graph1374.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,0) (17,15) (3,12) (1,0) (1,7) (0,5) (1,9) (4,0) (17,12) (8,3) (14,9) (12,0) (7,16) (13,2) (11,4) (15,10) (7,5) (17,16) (6,9) (0,3) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1283", "image": "data/cycle/graph_visual/medium/graph1283.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (3,0) (16,12) (2,11) (8,14) (1,0) (5,2) (3,1) (6,10) (0,2) (10,15) (9,13) (16,13) (4,14) (14,11) (3,5) (13,7) (14,10) (13,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph449", "image": "data/cycle/graph_visual/medium/graph449.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,0) (12,17) (9,6) (9,2) (4,11) (14,17) (17,4) (11,13) (16,8) (0,5) (14,16) (14,6) (1,15) (1,3) (10,15) (10,7) (8,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph797", "image": "data/cycle/graph_visual/medium/graph797.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (8,2) (12,1) (0,18) (12,7) (0,11) (10,11) (4,17) (12,14) (17,20) (7,5) (17,12) (11,9) (22,6) (23,0) (1,19) (18,16) (15,11) (13,17) (22,19) (12,3) (8,13) (21,7) (5,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph461", "image": "data/cycle/graph_visual/medium/graph461.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (3,2) (6,7) (5,6) (17,0) (13,14) (3,13) (3,0) (15,17) (14,8) (10,4) (12,17) (1,6) (7,10) (9,11) (11,12) (7,16) (14,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph870", "image": "data/cycle/graph_visual/medium/graph870.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (14,24) (2,6) (13,24) (6,8) (1,23) (17,15) (16,5) (4,24) (17,10) (13,6) (20,13) (7,23) (16,19) (15,1) (21,19) (23,13) (22,7) (0,23) (3,21) (9,19) (11,1) (20,5) (12,4) (18,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph650", "image": "data/cycle/graph_visual/medium/graph650.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (5,17) (7,4) (5,14) (13,1) (1,20) (18,10) (15,3) (19,5) (19,0) (17,13) (1,8) (3,20) (4,6) (14,12) (9,0) (7,2) (11,16) (19,10) (2,11) (8,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1240", "image": "data/cycle/graph_visual/medium/graph1240.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,10) (2,0) (13,0) (2,11) (2,15) (9,6) (2,8) (12,13) (4,2) (3,1) (11,9) (7,14) (11,5) (1,0) (14,3) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1762", "image": "data/cycle/graph_visual/medium/graph1762.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (6,9) (9,13) (0,2) (10,17) (20,0) (21,7) (3,0) (11,8) (23,2) (4,8) (1,0) (22,20) (23,18) (19,17) (2,6) (1,15) (11,12) (8,10) (7,5) (20,24) (8,16) (22,3) (2,15) (14,2) (7,15) (12,5) (20,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph465", "image": "data/cycle/graph_visual/medium/graph465.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,12) (1,9) (11,4) (0,2) (13,9) (6,8) (7,16) (4,6) (2,3) (8,14) (5,9) (13,11) (0,14) (15,0) (7,14) (0,17) (10,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1400", "image": "data/cycle/graph_visual/medium/graph1400.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,6) (1,6) (2,14) (3,0) (1,0) (4,13) (3,18) (10,1) (11,8) (16,4) (9,6) (11,15) (7,12) (14,18) (0,16) (5,16) (8,14) (9,7) (4,1) (0,2) (17,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1095", "image": "data/cycle/graph_visual/medium/graph1095.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,6) (0,5) (6,8) (11,5) (1,0) (8,4) (9,7) (6,9) (8,3) (0,2) (6,1) (3,0) (5,4) (10,7) (0,4) (2,1) (13,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1495", "image": "data/cycle/graph_visual/medium/graph1495.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,16) (12,14) (17,15) (18,10) (0,8) (1,0) (13,0) (0,15) (7,1) (4,7) (0,2) (19,5) (0,6) (11,19) (15,12) (4,9) (5,9) (2,14) (10,5) (2,3) (17,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1491", "image": "data/cycle/graph_visual/medium/graph1491.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,16) (5,15) (1,0) (5,18) (4,17) (2,0) (3,6) (16,7) (13,14) (16,10) (19,2) (15,9) (6,14) (1,11) (5,1) (11,12) (14,0) (8,1) (19,11) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph927", "image": "data/cycle/graph_visual/medium/graph927.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,6) (0,9) (1,4) (7,3) (6,1) (8,2) (10,2) (3,10) (1,0) (0,5) (9,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph642", "image": "data/cycle/graph_visual/medium/graph642.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (16,12) (6,17) (0,13) (2,13) (18,9) (3,0) (1,18) (11,4) (15,8) (5,2) (14,7) (13,1) (11,10) (8,0) (14,16) (12,19) (3,19) (15,20) (17,12) (8,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1021", "image": "data/cycle/graph_visual/medium/graph1021.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,2) (10,2) (4,7) (10,12) (5,10) (7,10) (3,4) (9,8) (2,1) (11,8) (3,6) (0,9) (3,0) (0,2) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1740", "image": "data/cycle/graph_visual/medium/graph1740.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (0,17) (22,13) (3,21) (1,0) (24,6) (21,4) (3,0) (16,23) (1,10) (24,17) (12,9) (13,5) (10,22) (7,20) (15,20) (5,4) (9,16) (15,3) (0,2) (18,22) (11,17) (6,7) (6,14) (8,17) (16,17) (4,2) (0,4) (19,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph204", "image": "data/cycle/graph_visual/medium/graph204.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,13) (3,6) (4,0) (11,8) (1,11) (1,2) (12,4) (6,5) (3,0) (2,6) (8,9) (13,10) (8,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph895", "image": "data/cycle/graph_visual/medium/graph895.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (5,15) (11,10) (21,24) (3,1) (17,20) (13,15) (10,16) (18,15) (19,5) (6,20) (9,14) (0,5) (14,8) (8,22) (7,6) (12,7) (9,15) (2,21) (23,24) (10,3) (16,21) (8,6) (4,14) (3,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1239", "image": "data/cycle/graph_visual/medium/graph1239.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,9) (9,15) (9,2) (15,14) (5,10) (3,8) (1,7) (15,4) (11,2) (6,5) (13,12) (7,15) (9,13) (8,14) (5,0) (0,1) (3,0) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1141", "image": "data/cycle/graph_visual/medium/graph1141.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,0) (12,2) (13,4) (4,10) (13,12) (5,14) (7,10) (6,13) (6,1) (13,8) (0,14) (3,14) (0,9) (2,0) (1,0) (11,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph632", "image": "data/cycle/graph_visual/medium/graph632.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (5,14) (0,10) (14,15) (16,13) (19,6) (8,4) (14,3) (16,19) (4,5) (10,2) (12,5) (1,19) (14,20) (10,17) (12,1) (18,2) (7,11) (0,11) (19,17) (8,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph562", "image": "data/cycle/graph_visual/medium/graph562.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,17) (11,12) (0,14) (19,8) (10,2) (15,9) (19,11) (7,1) (18,4) (8,14) (3,10) (5,13) (16,1) (6,14) (8,15) (18,15) (8,2) (13,3) (16,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1630", "image": "data/cycle/graph_visual/medium/graph1630.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (1,15) (8,21) (13,6) (14,16) (9,2) (15,17) (18,15) (0,5) (10,22) (16,0) (12,10) (22,17) (19,11) (3,1) (8,16) (21,7) (4,17) (19,4) (1,0) (10,9) (14,6) (14,12) (0,2) (11,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph211", "image": "data/cycle/graph_visual/medium/graph211.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,1) (1,11) (2,11) (13,12) (10,5) (9,0) (0,3) (2,7) (2,4) (10,11) (5,12) (6,3) (8,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph793", "image": "data/cycle/graph_visual/medium/graph793.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (11,8) (23,6) (4,9) (5,0) (3,4) (14,18) (6,13) (21,7) (15,10) (1,23) (18,15) (18,19) (17,10) (16,3) (5,20) (10,4) (3,2) (20,12) (2,22) (8,21) (14,13) (0,13) (21,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1532", "image": "data/cycle/graph_visual/medium/graph1532.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 20, and the edges are: (12,9) (1,0) (9,6) (13,1) (7,15) (14,15) (12,4) (2,0) (10,7) (5,6) (3,14) (1,8) (17,10) (9,7) (9,19) (14,16) (2,10) (9,13) (20,17) (11,0) (7,11) (18,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1782", "image": "data/cycle/graph_visual/medium/graph1782.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 24, and the edges are: (1,0) (8,17) (6,13) (5,13) (13,23) (23,3) (17,3) (14,7) (2,0) (2,22) (5,15) (8,9) (14,19) (16,14) (23,24) (21,11) (9,1) (11,23) (22,4) (15,18) (16,4) (7,10) (20,2) (9,12) (5,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1056", "image": "data/cycle/graph_visual/medium/graph1056.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,7) (5,12) (1,0) (7,8) (2,4) (7,3) (1,4) (10,8) (6,3) (9,7) (0,6) (8,5) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1105", "image": "data/cycle/graph_visual/medium/graph1105.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,2) (0,2) (7,10) (6,4) (3,4) (2,9) (0,1) (11,7) (5,0) (8,9) (0,12) (3,12) (7,5) (12,13) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph336", "image": "data/cycle/graph_visual/medium/graph336.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,13) (2,1) (11,6) (13,12) (10,0) (2,8) (3,11) (10,1) (2,15) (5,4) (1,7) (1,6) (3,9) (4,12) (14,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph32", "image": "data/cycle/graph_visual/medium/graph32.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,6) (10,1) (10,7) (7,0) (4,7) (4,3) (2,7) (5,4) (6,1) (1,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1674", "image": "data/cycle/graph_visual/medium/graph1674.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (4,21) (14,15) (20,7) (7,8) (1,12) (0,1) (13,0) (21,2) (5,13) (9,18) (20,0) (0,2) (18,2) (4,11) (4,12) (5,19) (17,15) (10,14) (3,0) (3,9) (1,10) (8,16) (6,9) (7,1) (5,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph22", "image": "data/cycle/graph_visual/medium/graph22.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,8) (0,6) (8,5) (3,9) (1,10) (10,4) (9,1) (4,8) (8,2) (9,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1030", "image": "data/cycle/graph_visual/medium/graph1030.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,3) (0,2) (2,12) (8,12) (7,0) (8,11) (8,7) (0,1) (10,9) (6,7) (7,5) (1,8) (2,3) (4,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph240", "image": "data/cycle/graph_visual/medium/graph240.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (5,2) (14,6) (0,8) (1,5) (7,11) (8,13) (8,2) (3,11) (11,12) (4,10) (3,8) (12,4) (9,8) (6,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph760", "image": "data/cycle/graph_visual/medium/graph760.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (20,13) (1,19) (11,17) (5,7) (15,6) (8,19) (2,3) (21,10) (18,21) (20,12) (6,19) (9,14) (22,17) (5,21) (16,12) (18,1) (0,1) (13,5) (2,11) (16,11) (2,4) (9,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph677", "image": "data/cycle/graph_visual/medium/graph677.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (1,18) (12,11) (5,14) (18,8) (20,8) (15,20) (5,11) (13,16) (2,6) (9,21) (17,0) (9,10) (5,16) (0,15) (7,14) (21,15) (7,2) (5,3) (5,4) (5,19) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph349", "image": "data/cycle/graph_visual/medium/graph349.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,11) (6,14) (12,1) (4,1) (13,9) (11,1) (15,2) (11,5) (6,12) (1,8) (10,15) (9,2) (13,7) (0,11) (15,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph208", "image": "data/cycle/graph_visual/medium/graph208.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,10) (7,13) (8,5) (3,7) (1,4) (11,10) (2,12) (7,10) (6,7) (7,2) (5,3) (9,3) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1353", "image": "data/cycle/graph_visual/medium/graph1353.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (13,11) (8,6) (14,7) (0,15) (1,9) (3,2) (0,1) (0,3) (8,14) (16,12) (12,10) (0,2) (13,9) (9,5) (0,14) (17,0) (6,4) (7,16) (4,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph95", "image": "data/cycle/graph_visual/medium/graph95.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,3) (5,7) (6,0) (1,2) (9,3) (1,7) (0,8) (4,7) (10,0) (6,2) (11,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1363", "image": "data/cycle/graph_visual/medium/graph1363.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,14) (12,9) (0,1) (2,10) (12,4) (9,6) (13,1) (0,11) (14,3) (7,15) (11,7) (13,9) (17,9) (8,1) (7,2) (5,6) (9,10) (16,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1675", "image": "data/cycle/graph_visual/medium/graph1675.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (6,10) (2,0) (11,5) (1,13) (0,1) (4,7) (20,15) (4,9) (2,4) (17,20) (12,15) (14,12) (15,18) (7,3) (7,16) (12,8) (14,21) (18,22) (6,16) (12,6) (22,11) (0,19) (2,1) (14,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1639", "image": "data/cycle/graph_visual/medium/graph1639.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (3,2) (6,15) (5,13) (21,10) (19,8) (11,2) (2,4) (5,21) (21,18) (18,1) (20,13) (12,20) (4,0) (16,12) (17,22) (1,0) (0,2) (11,17) (6,19) (3,0) (0,5) (1,19) (11,16) (9,8) (14,9) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1", "image": "data/cycle/graph_visual/medium/graph1.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,8) (8,4) (5,10) (3,10) (4,9) (0,7) (0,2) (3,6) (7,8) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph785", "image": "data/cycle/graph_visual/medium/graph785.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (19,12) (19,15) (4,2) (14,5) (7,23) (22,18) (10,11) (8,14) (23,3) (22,15) (5,13) (22,9) (3,6) (2,11) (21,15) (9,5) (17,7) (11,0) (23,13) (4,20) (16,7) (4,1) (6,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph29", "image": "data/cycle/graph_visual/medium/graph29.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,1) (10,3) (0,9) (2,3) (5,6) (6,2) (3,4) (0,1) (5,7) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph757", "image": "data/cycle/graph_visual/medium/graph757.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 22, and the edges are: (8,20) (8,12) (19,22) (4,10) (0,22) (10,7) (16,1) (9,4) (11,17) (18,3) (0,16) (8,15) (18,20) (2,17) (10,5) (1,14) (6,4) (13,18) (13,9) (11,0) (21,16) (3,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph164", "image": "data/cycle/graph_visual/medium/graph164.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,8) (11,4) (2,4) (1,7) (12,1) (3,2) (9,0) (9,1) (5,3) (5,1) (12,10) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph453", "image": "data/cycle/graph_visual/medium/graph453.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (8,6) (9,8) (15,11) (16,12) (11,17) (2,3) (1,5) (2,11) (16,14) (6,1) (10,9) (13,5) (12,13) (14,17) (5,7) (0,1) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1592", "image": "data/cycle/graph_visual/medium/graph1592.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 21, and the edges are: (8,17) (3,0) (9,5) (7,0) (11,13) (2,0) (13,19) (5,2) (13,9) (6,13) (13,0) (20,0) (15,9) (10,21) (21,11) (12,15) (17,1) (3,8) (0,17) (16,19) (11,14) (3,4) (18,8) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1373", "image": "data/cycle/graph_visual/medium/graph1373.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (4,11) (9,12) (5,13) (0,1) (2,8) (2,15) (10,16) (3,10) (12,6) (10,11) (3,6) (8,17) (14,1) (10,7) (5,0) (13,10) (0,2) (0,3) (8,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph64", "image": "data/cycle/graph_visual/medium/graph64.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,6) (2,0) (7,8) (2,11) (10,6) (10,3) (11,8) (7,4) (3,7) (5,6) (4,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1725", "image": "data/cycle/graph_visual/medium/graph1725.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 23, and the edges are: (15,9) (22,12) (3,12) (16,5) (13,9) (19,11) (18,4) (2,0) (18,12) (10,15) (20,13) (1,0) (7,14) (2,1) (6,19) (0,8) (11,12) (20,0) (19,16) (21,5) (1,11) (3,23) (16,7) (0,23) (17,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph253", "image": "data/cycle/graph_visual/medium/graph253.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,3) (10,3) (7,2) (14,4) (10,0) (1,11) (8,5) (12,13) (4,9) (11,6) (4,7) (13,8) (1,4) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1493", "image": "data/cycle/graph_visual/medium/graph1493.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (13,4) (5,15) (9,17) (1,18) (16,14) (3,0) (1,0) (1,10) (18,3) (0,4) (12,18) (16,15) (0,2) (7,18) (8,3) (10,17) (2,5) (13,8) (2,18) (16,6) (19,0) (11,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph13", "image": "data/cycle/graph_visual/hard/graph13.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (25,16) (9,7) (25,19) (6,0) (23,6) (23,21) (1,9) (15,11) (19,24) (0,5) (1,8) (6,16) (22,3) (24,14) (8,15) (13,17) (18,9) (18,20) (4,24) (2,12) (21,18) (12,1) (20,10) (13,3) (3,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1374", "image": "data/cycle/graph_visual/hard/graph1374.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,9) (13,10) (6,16) (25,19) (23,15) (12,2) (5,24) (4,24) (25,8) (9,22) (8,28) (11,15) (12,25) (8,1) (24,3) (1,0) (26,6) (18,11) (16,4) (19,3) (18,28) (27,0) (7,28) (13,1) (21,26) (16,14) (2,0) (12,20) (15,17) (9,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph726", "image": "data/cycle/graph_visual/hard/graph726.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,7) (29,27) (0,20) (23,0) (2,13) (4,29) (4,18) (12,8) (0,32) (1,11) (0,12) (17,4) (5,24) (1,18) (6,25) (22,27) (3,16) (19,31) (24,6) (22,14) (21,23) (19,17) (26,27) (25,10) (22,28) (27,16) (9,14) (16,13) (25,32) (20,16) (15,11) (30,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1229", "image": "data/cycle/graph_visual/hard/graph1229.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,0) (9,19) (26,19) (5,26) (6,8) (18,26) (2,0) (17,20) (2,4) (16,7) (0,1) (19,27) (2,5) (23,14) (12,1) (12,22) (25,26) (17,3) (6,21) (0,13) (19,15) (9,11) (10,25) (16,24) (4,20) (20,12) (1,8) (14,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1548", "image": "data/cycle/graph_visual/hard/graph1548.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,2) (20,1) (26,24) (15,25) (10,24) (17,16) (18,9) (4,14) (9,19) (21,25) (19,28) (10,3) (2,11) (3,0) (7,16) (14,23) (20,17) (0,1) (11,3) (5,13) (16,13) (8,29) (23,24) (27,28) (7,27) (17,12) (23,1) (22,1) (18,30) (21,1) (6,29) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1903", "image": "data/cycle/graph_visual/hard/graph1903.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (21,6) (34,22) (32,5) (31,18) (8,14) (20,19) (1,15) (2,0) (21,10) (6,7) (29,9) (0,3) (0,1) (19,16) (17,24) (23,2) (16,33) (1,13) (28,23) (25,10) (19,5) (5,6) (4,5) (30,5) (27,7) (12,5) (33,11) (24,19) (8,19) (21,34) (20,29) (31,0) (26,11) (2,12) (14,3) (31,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1583", "image": "data/cycle/graph_visual/hard/graph1583.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,0) (23,30) (29,16) (30,27) (20,12) (12,7) (17,4) (21,11) (30,16) (26,7) (17,24) (22,8) (12,3) (19,28) (30,10) (19,1) (30,5) (26,22) (1,0) (9,27) (13,14) (12,1) (7,5) (13,11) (15,11) (17,18) (25,29) (0,11) (2,0) (24,12) (2,8) (28,6) (17,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1766", "image": "data/cycle/graph_visual/hard/graph1766.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (10,2) (2,0) (29,26) (17,28) (7,29) (17,9) (30,4) (9,23) (1,3) (14,27) (25,30) (5,20) (0,4) (22,30) (24,23) (28,31) (5,0) (14,11) (1,2) (0,1) (4,15) (13,2) (4,29) (20,16) (7,27) (18,8) (8,1) (21,32) (21,18) (0,3) (19,3) (6,25) (14,21) (5,25) (9,12) (9,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph996", "image": "data/cycle/graph_visual/hard/graph996.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (5,28) (11,27) (30,19) (19,24) (17,31) (16,13) (3,10) (21,11) (27,32) (12,23) (5,29) (12,15) (28,34) (2,34) (13,23) (25,4) (16,2) (26,5) (20,13) (25,24) (23,24) (6,29) (13,18) (31,22) (22,24) (8,29) (16,10) (9,29) (24,11) (7,28) (33,21) (0,5) (11,1) (15,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph703", "image": "data/cycle/graph_visual/hard/graph703.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (17,24) (1,14) (25,28) (10,7) (11,21) (32,3) (30,19) (16,32) (9,11) (8,0) (20,23) (2,12) (6,7) (11,27) (5,17) (9,26) (6,12) (31,13) (32,19) (23,6) (17,22) (11,25) (1,8) (23,30) (18,2) (21,29) (15,12) (5,0) (31,10) (8,4) (23,24) (16,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1016", "image": "data/cycle/graph_visual/hard/graph1016.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (19,6) (25,20) (10,12) (1,12) (2,0) (25,15) (11,4) (1,0) (6,18) (2,7) (1,2) (9,5) (0,15) (22,2) (24,20) (13,1) (9,11) (15,6) (17,25) (8,4) (17,9) (4,13) (1,14) (6,23) (3,0) (0,4) (5,21) (3,14) (20,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1980", "image": "data/cycle/graph_visual/hard/graph1980.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (26,3) (25,17) (7,11) (1,32) (25,23) (9,29) (34,26) (21,17) (18,23) (15,8) (3,25) (24,27) (4,34) (32,12) (1,15) (2,29) (28,9) (32,30) (7,20) (2,0) (20,22) (0,1) (13,4) (3,16) (6,27) (8,6) (5,22) (14,31) (26,10) (20,24) (0,4) (14,18) (2,19) (22,17) (33,13) (2,34)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1609", "image": "data/cycle/graph_visual/hard/graph1609.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,13) (1,0) (8,22) (22,23) (3,13) (18,7) (7,20) (12,22) (31,10) (9,12) (13,25) (17,29) (14,19) (9,11) (17,24) (6,25) (27,16) (28,21) (16,3) (30,11) (4,11) (27,15) (14,21) (29,2) (1,29) (26,23) (10,24) (29,25) (5,7) (0,9) (13,26) (29,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1080", "image": "data/cycle/graph_visual/hard/graph1080.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (16,22) (11,2) (24,11) (11,16) (8,19) (10,15) (6,11) (19,10) (17,25) (7,25) (0,1) (19,18) (1,3) (13,0) (9,2) (17,4) (7,20) (14,20) (13,12) (0,3) (21,9) (2,0) (2,15) (17,19) (12,23) (2,5) (3,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph213", "image": "data/cycle/graph_visual/hard/graph213.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (6,27) (13,18) (6,17) (16,19) (3,20) (1,13) (0,19) (22,17) (7,16) (7,26) (18,24) (3,21) (0,1) (4,23) (6,2) (7,14) (23,2) (0,10) (23,11) (9,3) (0,17) (7,8) (21,23) (2,25) (4,15) (8,12) (20,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph772", "image": "data/cycle/graph_visual/hard/graph772.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (8,11) (7,10) (31,17) (18,6) (16,10) (4,30) (20,17) (26,19) (13,1) (1,14) (18,2) (22,4) (28,21) (12,18) (20,25) (21,18) (7,14) (3,26) (9,24) (6,0) (32,23) (20,6) (32,2) (7,5) (4,6) (27,22) (32,7) (24,25) (29,10) (15,0) (24,19) (14,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph906", "image": "data/cycle/graph_visual/hard/graph906.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (29,22) (2,18) (32,4) (9,7) (7,32) (2,34) (17,33) (14,13) (12,11) (25,20) (26,3) (21,18) (21,30) (24,25) (0,23) (6,4) (32,27) (34,8) (19,24) (0,6) (20,17) (15,18) (10,7) (19,28) (20,6) (4,22) (10,31) (18,6) (10,26) (16,1) (1,14) (14,7) (11,24) (5,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph284", "image": "data/cycle/graph_visual/hard/graph284.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (25,17) (23,18) (21,27) (26,0) (9,11) (7,0) (19,0) (21,16) (15,12) (22,13) (18,10) (9,17) (24,9) (2,3) (25,15) (20,2) (14,6) (8,4) (7,1) (27,4) (14,0) (5,24) (19,20) (15,22) (10,21) (5,23) (12,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1698", "image": "data/cycle/graph_visual/hard/graph1698.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,17) (6,10) (25,22) (4,29) (7,23) (9,15) (18,28) (21,13) (8,7) (6,31) (0,31) (3,10) (9,11) (30,14) (1,22) (25,11) (18,27) (16,7) (3,4) (24,13) (19,2) (4,7) (2,7) (18,21) (23,20) (5,22) (10,26) (30,13) (0,2) (5,12) (25,14) (30,4) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph464", "image": "data/cycle/graph_visual/hard/graph464.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,14) (15,16) (15,27) (6,5) (18,11) (16,0) (2,10) (16,19) (17,21) (11,5) (20,8) (5,21) (3,26) (24,0) (14,9) (4,18) (15,28) (29,1) (22,5) (29,24) (23,0) (8,25) (5,20) (12,7) (28,9) (7,28) (3,0) (5,27) (26,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1607", "image": "data/cycle/graph_visual/hard/graph1607.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (21,31) (0,21) (12,15) (31,9) (7,27) (30,17) (18,29) (25,12) (20,7) (30,13) (16,19) (18,22) (10,15) (24,16) (1,11) (8,31) (28,3) (31,12) (11,15) (15,5) (20,11) (23,29) (14,11) (0,1) (16,0) (4,21) (19,13) (10,28) (16,26) (7,2) (12,23) (12,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1571", "image": "data/cycle/graph_visual/hard/graph1571.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,10) (11,9) (22,30) (16,12) (22,20) (5,27) (30,19) (8,14) (17,25) (15,25) (2,0) (27,7) (26,2) (1,0) (24,6) (2,28) (1,13) (4,13) (26,1) (12,1) (4,14) (21,20) (1,18) (0,15) (3,27) (15,6) (4,11) (17,9) (29,6) (9,5) (25,20) (23,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1735", "image": "data/cycle/graph_visual/hard/graph1735.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (3,32) (2,22) (10,8) (14,29) (23,24) (26,18) (10,30) (8,16) (0,27) (17,14) (15,0) (22,11) (20,28) (11,19) (2,13) (24,32) (12,26) (17,1) (31,26) (17,31) (7,26) (2,7) (10,4) (0,21) (30,31) (5,3) (28,25) (0,1) (10,28) (15,4) (9,23) (24,2) (6,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph236", "image": "data/cycle/graph_visual/hard/graph236.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,18) (21,8) (0,3) (14,7) (15,16) (20,8) (12,9) (22,3) (24,27) (2,6) (13,11) (0,19) (9,21) (5,11) (5,4) (15,25) (16,0) (14,16) (10,7) (15,23) (26,27) (20,5) (5,27) (18,5) (5,17) (2,26) (24,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph199", "image": "data/cycle/graph_visual/hard/graph199.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,9) (23,26) (7,26) (12,2) (18,21) (14,15) (8,19) (24,17) (0,10) (4,24) (3,13) (16,6) (0,6) (24,3) (6,25) (26,16) (26,5) (18,22) (21,23) (9,1) (18,9) (18,3) (1,15) (1,8) (20,12) (13,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1690", "image": "data/cycle/graph_visual/hard/graph1690.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,24) (10,3) (26,15) (17,20) (29,0) (10,12) (21,29) (17,16) (8,14) (13,22) (28,7) (12,0) (2,0) (17,15) (6,19) (9,28) (13,11) (4,20) (25,20) (22,17) (16,27) (7,19) (2,8) (7,5) (23,28) (26,9) (0,1) (18,11) (28,14) (30,2) (3,31) (1,7) (27,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1531", "image": "data/cycle/graph_visual/hard/graph1531.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,2) (27,2) (16,8) (28,6) (14,13) (18,25) (17,29) (23,30) (25,21) (21,12) (14,6) (9,12) (15,1) (24,26) (25,24) (4,20) (3,20) (22,26) (13,27) (6,23) (29,11) (20,19) (0,4) (3,0) (0,1) (22,29) (2,4) (8,22) (24,20) (19,7) (6,0) (3,5) (15,0) (10,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph92", "image": "data/cycle/graph_visual/hard/graph92.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (11,4) (18,9) (1,12) (5,21) (13,25) (1,7) (4,12) (7,8) (20,7) (15,18) (16,8) (14,15) (1,10) (2,22) (20,25) (13,0) (6,9) (17,25) (2,21) (0,23) (25,24) (14,10) (25,19) (5,4) (9,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph989", "image": "data/cycle/graph_visual/hard/graph989.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (28,3) (26,3) (0,22) (5,4) (16,20) (4,13) (16,17) (5,27) (31,4) (25,23) (10,12) (14,33) (30,1) (7,18) (28,22) (32,15) (0,30) (29,11) (21,8) (25,34) (4,12) (25,6) (24,23) (6,9) (11,15) (31,15) (30,16) (33,9) (16,8) (21,14) (21,19) (34,18) (17,2) (26,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1727", "image": "data/cycle/graph_visual/hard/graph1727.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,15) (10,2) (30,5) (3,27) (31,9) (24,22) (26,24) (29,16) (15,4) (27,8) (17,20) (17,12) (1,2) (14,31) (1,0) (8,29) (25,2) (6,0) (3,0) (0,2) (31,11) (28,32) (8,23) (29,7) (21,23) (4,20) (26,18) (11,19) (2,26) (16,18) (13,0) (29,15) (22,30) (23,19) (10,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph933", "image": "data/cycle/graph_visual/hard/graph933.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,1) (7,24) (28,26) (9,30) (1,30) (32,27) (2,7) (1,26) (3,16) (32,6) (31,4) (12,21) (17,0) (33,31) (3,11) (34,8) (26,22) (29,22) (25,17) (10,11) (14,19) (8,18) (4,15) (5,29) (27,31) (29,13) (5,12) (19,33) (20,32) (16,25) (22,18) (16,12) (11,27) (23,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph916", "image": "data/cycle/graph_visual/hard/graph916.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,12) (27,28) (9,11) (32,14) (25,5) (10,23) (6,17) (14,5) (27,5) (15,24) (19,30) (17,20) (29,17) (8,22) (2,30) (21,25) (31,21) (3,32) (24,0) (13,3) (3,1) (13,29) (12,4) (9,0) (16,0) (14,22) (7,33) (4,32) (23,26) (18,23) (28,9) (10,21) (1,33) (34,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1283", "image": "data/cycle/graph_visual/hard/graph1283.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (21,9) (11,8) (16,7) (15,4) (11,17) (25,24) (9,25) (3,13) (1,7) (12,0) (0,3) (20,2) (23,1) (10,9) (19,15) (17,16) (0,1) (26,3) (6,7) (4,2) (26,5) (2,0) (12,17) (5,24) (27,8) (24,22) (8,3) (23,14) (18,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1123", "image": "data/cycle/graph_visual/hard/graph1123.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,3) (13,26) (2,11) (2,15) (19,17) (16,11) (22,16) (1,3) (4,17) (8,19) (10,15) (23,12) (14,20) (1,0) (11,25) (11,6) (18,19) (7,20) (19,10) (2,0) (21,9) (5,2) (17,13) (25,7) (9,2) (12,13) (3,0) (24,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1630", "image": "data/cycle/graph_visual/hard/graph1630.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (21,11) (21,3) (19,13) (9,10) (12,10) (11,24) (22,18) (0,20) (28,14) (23,14) (8,26) (11,19) (19,25) (2,0) (6,30) (1,7) (27,1) (1,0) (31,18) (29,2) (28,15) (28,1) (3,0) (4,8) (4,13) (15,30) (17,18) (24,14) (24,5) (9,28) (27,22) (0,16) (21,29) (22,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph860", "image": "data/cycle/graph_visual/hard/graph860.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (3,16) (9,17) (19,8) (3,10) (24,16) (8,22) (23,27) (3,25) (13,29) (32,25) (20,31) (29,28) (2,1) (9,33) (8,30) (12,14) (13,0) (30,6) (10,2) (22,32) (21,3) (14,23) (22,18) (8,14) (4,29) (32,20) (11,23) (7,33) (1,15) (5,32) (26,10) (28,12) (21,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1143", "image": "data/cycle/graph_visual/hard/graph1143.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,20) (15,8) (1,0) (21,6) (0,21) (1,15) (0,2) (16,5) (0,17) (19,22) (26,11) (7,17) (16,11) (14,4) (23,14) (3,21) (12,0) (24,22) (10,4) (20,25) (19,4) (19,21) (13,12) (8,2) (9,11) (11,14) (25,7) (18,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph41", "image": "data/cycle/graph_visual/hard/graph41.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (24,10) (15,16) (7,2) (0,19) (9,21) (2,6) (0,16) (1,18) (15,22) (9,12) (4,5) (25,10) (5,20) (5,18) (14,16) (0,3) (11,5) (5,17) (21,8) (15,23) (14,7) (0,24) (20,8) (5,3) (11,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1928", "image": "data/cycle/graph_visual/hard/graph1928.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,14) (3,10) (25,11) (10,19) (11,9) (20,2) (21,31) (25,23) (10,27) (29,18) (26,14) (12,5) (28,18) (22,1) (8,7) (7,24) (17,7) (7,2) (7,4) (22,23) (0,1) (13,21) (10,6) (5,6) (9,16) (4,32) (0,31) (30,4) (5,33) (4,3) (30,13) (34,18) (13,25) (15,22) (5,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1850", "image": "data/cycle/graph_visual/hard/graph1850.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (26,5) (28,5) (31,27) (15,14) (9,29) (13,20) (23,13) (23,12) (24,22) (2,16) (1,0) (0,2) (19,28) (22,30) (24,23) (0,5) (21,32) (24,19) (3,0) (18,13) (24,25) (16,13) (4,25) (7,28) (27,11) (5,29) (24,11) (3,10) (10,16) (33,2) (21,11) (11,1) (31,17) (8,29) (29,6) (12,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph60", "image": "data/cycle/graph_visual/hard/graph60.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,11) (17,24) (24,20) (9,17) (3,7) (16,8) (21,0) (4,14) (14,0) (10,2) (15,9) (19,18) (0,18) (1,12) (22,7) (12,5) (21,7) (25,10) (13,22) (8,12) (24,4) (10,23) (23,4) (6,5) (12,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph918", "image": "data/cycle/graph_visual/hard/graph918.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (12,5) (17,1) (32,9) (2,16) (33,4) (7,5) (24,11) (12,27) (30,13) (32,28) (12,14) (30,32) (8,15) (19,7) (20,7) (0,25) (31,1) (11,21) (6,12) (24,29) (10,12) (15,9) (13,14) (26,11) (34,12) (21,20) (0,17) (5,4) (22,18) (23,15) (16,34) (3,20) (16,31) (18,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1532", "image": "data/cycle/graph_visual/hard/graph1532.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,27) (3,14) (12,22) (0,2) (20,5) (21,9) (0,5) (27,24) (13,29) (10,15) (17,15) (0,3) (19,18) (15,2) (18,2) (16,23) (1,8) (18,9) (13,15) (30,17) (14,6) (16,7) (16,12) (8,13) (13,0) (17,11) (6,16) (8,25) (24,26) (1,0) (3,4) (5,14) (11,28) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1638", "image": "data/cycle/graph_visual/hard/graph1638.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (4,25) (8,25) (29,1) (6,13) (18,25) (14,1) (3,0) (22,17) (1,27) (9,27) (24,10) (18,12) (31,2) (4,19) (20,13) (21,10) (11,5) (31,15) (28,21) (20,28) (29,22) (0,5) (26,0) (8,9) (20,31) (0,2) (21,18) (23,21) (11,21) (20,7) (1,0) (16,22) (30,18) (3,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1273", "image": "data/cycle/graph_visual/hard/graph1273.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (13,27) (3,0) (16,1) (6,25) (15,8) (3,25) (9,2) (21,4) (5,18) (10,24) (4,17) (2,0) (23,6) (24,0) (23,21) (11,22) (7,26) (27,23) (10,11) (15,18) (24,12) (18,19) (0,1) (14,8) (2,15) (25,15) (20,24) (13,26) (8,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph979", "image": "data/cycle/graph_visual/hard/graph979.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (22,34) (23,4) (7,32) (8,2) (32,23) (29,13) (20,9) (29,6) (24,16) (28,19) (12,33) (23,27) (18,23) (5,1) (33,2) (0,32) (17,27) (26,4) (18,24) (14,6) (4,21) (32,13) (10,23) (5,3) (18,15) (31,0) (0,33) (11,28) (26,30) (5,26) (28,2) (25,27) (4,34) (9,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph4", "image": "data/cycle/graph_visual/hard/graph4.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (13,22) (23,20) (2,25) (5,13) (16,9) (20,0) (5,4) (16,13) (15,10) (18,1) (12,14) (11,14) (19,4) (25,21) (0,14) (24,1) (17,12) (0,7) (17,1) (8,3) (23,8) (11,5) (15,11) (7,2) (1,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph205", "image": "data/cycle/graph_visual/hard/graph205.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,20) (22,3) (23,27) (2,12) (20,1) (15,0) (2,19) (18,9) (27,9) (1,19) (16,2) (15,17) (23,25) (23,24) (4,8) (13,6) (3,0) (8,25) (7,15) (8,11) (25,21) (2,4) (8,5) (10,0) (9,13) (9,3) (10,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph391", "image": "data/cycle/graph_visual/hard/graph391.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (26,5) (17,20) (7,0) (26,19) (17,3) (14,23) (9,11) (16,28) (22,12) (2,0) (19,15) (19,9) (20,4) (16,24) (20,12) (0,14) (7,25) (1,12) (19,16) (5,2) (2,4) (25,10) (26,27) (6,21) (1,8) (26,18) (13,0) (8,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1282", "image": "data/cycle/graph_visual/hard/graph1282.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,22) (0,6) (5,12) (19,6) (13,20) (18,14) (5,11) (23,2) (24,14) (3,4) (1,3) (24,12) (1,0) (20,17) (26,6) (4,23) (4,25) (13,7) (7,15) (22,6) (4,16) (8,17) (4,19) (26,5) (21,6) (27,7) (0,13) (19,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph388", "image": "data/cycle/graph_visual/hard/graph388.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,8) (19,6) (11,12) (12,22) (9,15) (28,27) (19,16) (3,12) (0,27) (11,19) (13,20) (21,28) (18,4) (13,9) (2,1) (25,23) (24,0) (23,5) (26,18) (10,15) (10,17) (5,16) (20,3) (1,11) (7,14) (16,7) (28,20) (26,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1410", "image": "data/cycle/graph_visual/hard/graph1410.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (11,26) (28,3) (2,11) (29,0) (11,13) (12,11) (25,5) (7,15) (14,28) (18,5) (0,2) (20,4) (1,18) (29,8) (15,3) (5,4) (25,24) (2,16) (19,21) (17,28) (1,0) (3,23) (27,17) (26,19) (29,12) (1,19) (23,10) (27,6) (12,22) (21,3) (18,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph402", "image": "data/cycle/graph_visual/hard/graph402.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,16) (24,0) (29,24) (9,28) (5,20) (26,2) (5,22) (27,5) (12,7) (19,16) (23,0) (5,6) (11,5) (0,3) (7,28) (18,11) (21,17) (21,5) (1,29) (14,9) (2,10) (27,15) (20,8) (16,0) (4,18) (28,15) (3,26) (14,13) (25,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph344", "image": "data/cycle/graph_visual/hard/graph344.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,16) (13,23) (17,19) (20,27) (9,5) (9,11) (26,16) (2,13) (0,7) (7,12) (21,17) (27,28) (18,22) (6,9) (25,16) (8,27) (12,26) (10,25) (15,22) (5,24) (24,23) (25,4) (0,3) (20,10) (11,14) (22,3) (8,21) (8,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1718", "image": "data/cycle/graph_visual/hard/graph1718.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,11) (2,1) (2,12) (0,1) (5,0) (0,3) (30,24) (10,11) (25,18) (6,10) (29,23) (13,9) (23,5) (10,27) (32,25) (15,31) (19,7) (17,26) (32,19) (0,4) (20,32) (28,23) (20,29) (4,5) (11,20) (17,2) (8,16) (13,10) (24,27) (22,28) (14,15) (14,1) (0,2) (3,5) (27,16) (23,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1736", "image": "data/cycle/graph_visual/hard/graph1736.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,10) (32,26) (15,19) (1,24) (18,24) (5,9) (14,4) (24,20) (19,18) (17,6) (4,27) (1,11) (22,0) (13,20) (6,28) (5,3) (10,19) (1,0) (9,0) (22,2) (13,31) (21,6) (0,2) (9,27) (17,22) (23,16) (23,12) (24,3) (25,21) (29,23) (3,16) (1,7) (32,13) (14,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph32", "image": "data/cycle/graph_visual/hard/graph32.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (2,9) (10,21) (21,20) (2,20) (18,0) (7,15) (15,14) (24,21) (9,13) (12,16) (19,18) (15,16) (16,19) (20,8) (13,25) (6,8) (3,20) (17,11) (5,20) (16,23) (5,17) (10,22) (1,5) (7,4) (9,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph713", "image": "data/cycle/graph_visual/hard/graph713.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (12,5) (13,9) (20,22) (30,12) (6,1) (3,32) (16,26) (18,20) (2,0) (16,9) (29,24) (7,29) (18,11) (12,23) (15,16) (6,4) (6,14) (32,25) (24,4) (25,27) (26,1) (20,19) (8,25) (7,12) (26,31) (1,19) (28,4) (2,7) (6,27) (10,22) (21,17) (6,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1173", "image": "data/cycle/graph_visual/hard/graph1173.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,17) (7,23) (26,15) (11,9) (14,25) (11,12) (6,1) (14,20) (8,14) (13,19) (12,21) (8,23) (5,6) (22,25) (0,2) (3,0) (15,6) (5,0) (4,0) (16,6) (9,18) (3,18) (15,0) (24,19) (6,4) (0,1) (13,9) (20,10) (18,2) (25,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph69", "image": "data/cycle/graph_visual/hard/graph69.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (21,22) (14,5) (2,11) (9,6) (3,24) (1,2) (0,7) (13,10) (23,13) (4,8) (15,22) (24,6) (2,18) (16,8) (25,4) (7,4) (18,5) (19,0) (12,19) (11,17) (22,9) (4,20) (2,10) (21,10) (14,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph118", "image": "data/cycle/graph_visual/hard/graph118.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (22,2) (8,10) (16,3) (16,17) (4,24) (17,6) (26,7) (1,25) (12,3) (15,2) (23,12) (13,25) (10,23) (20,19) (5,0) (14,26) (26,9) (0,11) (22,26) (0,24) (24,16) (3,26) (23,18) (13,14) (21,23) (20,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph101", "image": "data/cycle/graph_visual/hard/graph101.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,25) (26,11) (15,16) (23,13) (22,13) (18,9) (2,5) (8,5) (3,26) (11,15) (6,9) (13,9) (12,21) (19,20) (24,0) (13,7) (1,17) (10,0) (17,8) (21,8) (14,11) (19,26) (11,13) (17,0) (23,0) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph509", "image": "data/cycle/graph_visual/hard/graph509.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (8,28) (13,6) (22,8) (14,20) (24,29) (27,11) (19,23) (15,30) (17,22) (10,22) (5,18) (12,30) (18,24) (11,2) (23,9) (13,23) (11,14) (4,13) (1,25) (21,5) (16,3) (10,19) (26,21) (1,19) (20,0) (18,12) (3,2) (7,24) (11,10) (9,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph437", "image": "data/cycle/graph_visual/hard/graph437.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,2) (28,25) (23,5) (29,10) (25,15) (7,14) (22,14) (28,17) (26,15) (11,4) (18,23) (17,9) (24,9) (12,15) (22,26) (19,0) (13,9) (10,18) (1,7) (0,16) (0,29) (21,20) (8,0) (27,12) (20,6) (27,4) (24,5) (29,2) (19,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph384", "image": "data/cycle/graph_visual/hard/graph384.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (16,13) (9,4) (22,4) (7,17) (4,24) (6,24) (5,3) (3,15) (16,14) (8,12) (22,19) (1,4) (15,0) (10,21) (23,14) (26,1) (4,12) (20,24) (13,28) (3,17) (23,17) (23,25) (27,21) (7,18) (11,1) (21,1) (2,0) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1854", "image": "data/cycle/graph_visual/hard/graph1854.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,19) (8,12) (9,15) (2,33) (1,6) (22,20) (13,33) (7,29) (4,30) (18,6) (20,19) (11,22) (25,20) (26,32) (23,17) (29,24) (16,21) (2,0) (1,0) (10,25) (16,26) (6,17) (0,3) (7,3) (27,33) (7,12) (14,18) (12,28) (4,0) (6,27) (9,16) (4,24) (4,6) (1,26) (32,5) (12,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph594", "image": "data/cycle/graph_visual/hard/graph594.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,22) (26,24) (15,7) (18,30) (12,5) (17,10) (6,9) (7,28) (1,15) (17,22) (14,9) (29,27) (12,25) (15,26) (26,21) (8,10) (20,18) (11,8) (0,20) (5,7) (30,13) (29,23) (6,2) (19,8) (20,29) (26,11) (16,2) (23,2) (26,2) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1175", "image": "data/cycle/graph_visual/hard/graph1175.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,0) (5,11) (4,3) (9,19) (6,20) (5,26) (0,6) (4,24) (6,19) (19,4) (16,20) (5,12) (6,21) (24,14) (0,1) (7,4) (15,7) (17,14) (13,18) (2,23) (17,8) (22,10) (13,26) (3,1) (12,23) (6,25) (4,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1330", "image": "data/cycle/graph_visual/hard/graph1330.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,12) (6,25) (20,14) (13,5) (0,5) (20,2) (23,26) (21,15) (17,24) (26,3) (24,28) (7,11) (0,4) (10,26) (3,21) (26,9) (2,0) (14,15) (18,16) (23,25) (0,18) (11,0) (28,26) (8,11) (19,17) (6,0) (1,0) (3,0) (22,1) (1,13) (8,27) (6,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1174", "image": "data/cycle/graph_visual/hard/graph1174.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (17,19) (26,20) (17,10) (8,10) (6,9) (23,2) (12,5) (20,23) (15,26) (11,26) (25,2) (26,21) (2,6) (11,8) (14,2) (8,4) (16,8) (7,24) (15,1) (7,15) (9,13) (7,5) (20,0) (1,0) (18,26) (3,22) (12,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph874", "image": "data/cycle/graph_visual/hard/graph874.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (30,31) (1,4) (31,22) (29,27) (8,10) (7,32) (17,33) (6,20) (1,13) (0,20) (27,12) (13,28) (32,25) (32,21) (6,21) (8,4) (2,8) (12,11) (5,19) (13,14) (4,27) (14,23) (18,21) (6,15) (3,18) (3,8) (30,9) (10,31) (19,9) (16,10) (26,9) (24,32) (17,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1861", "image": "data/cycle/graph_visual/hard/graph1861.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (7,31) (33,18) (23,1) (16,15) (26,10) (2,4) (4,21) (20,30) (33,28) (29,13) (1,27) (23,4) (28,12) (32,29) (0,1) (29,25) (19,3) (18,14) (7,24) (15,9) (23,8) (19,8) (8,24) (13,0) (17,11) (13,20) (30,33) (10,22) (11,29) (26,32) (0,2) (6,16) (6,31) (27,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph718", "image": "data/cycle/graph_visual/hard/graph718.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,23) (23,15) (10,16) (30,17) (14,31) (10,29) (17,21) (9,19) (1,27) (17,7) (27,22) (11,3) (31,22) (22,13) (0,27) (4,17) (0,25) (29,26) (29,28) (2,13) (1,24) (7,6) (26,2) (4,23) (1,12) (19,18) (11,27) (8,5) (5,19) (27,20) (16,8) (30,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1203", "image": "data/cycle/graph_visual/hard/graph1203.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,0) (10,3) (16,11) (8,2) (0,10) (6,2) (24,27) (26,4) (0,4) (7,19) (6,17) (25,22) (5,16) (1,19) (24,15) (18,8) (6,16) (13,4) (20,16) (0,2) (23,0) (22,16) (24,14) (12,8) (1,21) (3,0) (9,25) (1,0) (6,19) (11,26) (26,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1667", "image": "data/cycle/graph_visual/hard/graph1667.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (24,23) (19,30) (14,5) (0,2) (9,1) (21,17) (28,9) (27,15) (12,29) (2,18) (26,25) (29,27) (22,10) (0,24) (20,17) (14,25) (26,3) (23,13) (23,1) (8,6) (6,16) (10,2) (4,11) (30,6) (22,20) (16,31) (23,4) (27,7) (21,19) (31,5) (30,9) (0,1) (0,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph419", "image": "data/cycle/graph_visual/hard/graph419.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,20) (12,24) (27,7) (27,21) (14,9) (15,23) (16,10) (5,24) (21,2) (26,3) (29,28) (9,17) (8,7) (6,20) (25,12) (23,12) (0,3) (19,1) (3,8) (7,11) (18,23) (16,8) (4,22) (29,24) (8,13) (14,21) (27,28) (22,9) (2,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph845", "image": "data/cycle/graph_visual/hard/graph845.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (3,4) (22,15) (18,21) (22,1) (31,0) (16,9) (4,7) (24,7) (31,4) (30,14) (10,27) (6,10) (25,13) (5,32) (7,2) (30,4) (20,2) (21,13) (7,17) (19,10) (7,8) (28,18) (10,3) (5,33) (23,22) (29,18) (5,6) (13,30) (25,11) (5,12) (25,23) (26,14) (9,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph94", "image": "data/cycle/graph_visual/hard/graph94.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,0) (15,18) (6,7) (22,3) (25,23) (22,8) (19,5) (15,9) (3,1) (13,15) (10,3) (20,17) (7,12) (16,10) (21,2) (16,21) (14,4) (20,6) (9,14) (10,11) (15,5) (8,6) (14,8) (21,24) (24,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph604", "image": "data/cycle/graph_visual/hard/graph604.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (14,7) (19,23) (3,26) (30,17) (14,1) (0,15) (20,25) (7,4) (22,31) (26,22) (20,17) (6,0) (10,29) (10,7) (4,27) (16,10) (19,24) (12,18) (22,2) (18,6) (18,21) (6,4) (11,8) (28,21) (25,24) (13,1) (7,5) (11,14) (2,18) (6,20) (9,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1108", "image": "data/cycle/graph_visual/hard/graph1108.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,17) (19,25) (20,21) (25,2) (16,15) (1,0) (26,10) (8,25) (10,20) (13,25) (4,18) (22,3) (11,18) (26,24) (5,15) (1,16) (9,25) (26,5) (3,18) (13,0) (14,21) (18,21) (12,8) (2,18) (17,7) (6,17) (16,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1089", "image": "data/cycle/graph_visual/hard/graph1089.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (17,15) (24,20) (2,23) (14,25) (1,7) (3,9) (13,10) (16,8) (23,11) (17,4) (16,14) (23,21) (16,0) (18,15) (12,21) (0,9) (24,17) (22,8) (6,10) (24,22) (6,14) (24,5) (11,19) (1,15) (4,19) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph544", "image": "data/cycle/graph_visual/hard/graph544.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (29,5) (20,12) (27,7) (19,16) (0,7) (17,3) (24,16) (21,6) (5,2) (20,17) (12,22) (9,11) (29,25) (8,1) (29,26) (8,6) (14,0) (14,23) (30,16) (25,10) (0,13) (18,26) (15,19) (4,2) (26,28) (9,19) (19,26) (12,1) (20,4) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph229", "image": "data/cycle/graph_visual/hard/graph229.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (21,24) (5,16) (0,16) (4,1) (9,21) (0,26) (23,4) (20,6) (22,27) (10,1) (13,20) (11,24) (11,8) (18,4) (18,3) (23,16) (8,23) (1,20) (12,7) (21,15) (19,22) (19,6) (9,7) (14,26) (6,17) (25,14) (2,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1074", "image": "data/cycle/graph_visual/hard/graph1074.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (12,3) (19,6) (9,15) (2,0) (25,23) (0,23) (0,1) (20,13) (12,24) (20,3) (21,0) (11,12) (5,22) (15,10) (4,18) (23,20) (7,16) (8,0) (1,11) (2,1) (16,19) (16,5) (18,12) (10,17) (9,13) (0,3) (14,7) (19,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph917", "image": "data/cycle/graph_visual/hard/graph917.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (26,17) (22,5) (8,31) (33,13) (12,1) (3,10) (13,0) (4,8) (23,7) (16,2) (10,34) (6,23) (26,27) (9,33) (30,28) (24,10) (18,7) (0,15) (25,13) (20,15) (11,24) (24,21) (8,0) (14,15) (22,34) (28,8) (19,30) (10,13) (29,1) (4,29) (17,11) (6,15) (3,16) (32,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph956", "image": "data/cycle/graph_visual/hard/graph956.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (16,2) (3,33) (26,2) (11,5) (7,19) (14,24) (32,30) (29,0) (19,10) (21,32) (32,27) (9,6) (16,28) (8,5) (30,15) (5,1) (27,12) (25,22) (5,32) (9,11) (19,24) (24,3) (0,31) (34,17) (14,2) (34,25) (29,14) (34,12) (20,23) (13,22) (12,4) (5,14) (27,20) (18,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1135", "image": "data/cycle/graph_visual/hard/graph1135.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (19,11) (20,8) (10,2) (5,0) (18,24) (6,23) (1,26) (13,17) (7,22) (9,24) (10,20) (20,14) (15,16) (0,1) (12,15) (0,24) (11,3) (17,4) (1,6) (18,6) (16,9) (19,2) (22,13) (3,7) (18,8) (25,0) (21,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1418", "image": "data/cycle/graph_visual/hard/graph1418.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (17,27) (29,16) (10,3) (27,28) (12,25) (18,11) (24,13) (24,7) (24,21) (10,14) (15,27) (18,21) (19,18) (24,14) (23,21) (17,7) (26,4) (0,2) (6,7) (1,0) (7,22) (0,3) (6,0) (11,20) (17,12) (8,28) (29,19) (1,22) (3,5) (6,9) (19,2) (26,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1535", "image": "data/cycle/graph_visual/hard/graph1535.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (5,26) (23,1) (28,7) (23,14) (6,14) (27,11) (8,28) (22,29) (25,29) (15,29) (16,18) (3,27) (19,2) (8,4) (23,19) (13,15) (5,30) (0,27) (0,21) (24,1) (2,0) (6,9) (14,20) (10,16) (4,29) (23,28) (22,12) (0,1) (23,11) (17,22) (11,16) (5,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph350", "image": "data/cycle/graph_visual/hard/graph350.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,13) (12,20) (18,1) (27,28) (5,14) (27,23) (21,5) (13,5) (19,6) (21,18) (2,11) (6,26) (19,1) (12,25) (27,0) (27,3) (21,17) (9,24) (23,15) (25,23) (2,7) (1,4) (16,25) (27,22) (19,8) (10,2) (26,11) (9,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1320", "image": "data/cycle/graph_visual/hard/graph1320.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (28,26) (1,8) (25,3) (13,16) (12,22) (7,10) (10,6) (14,23) (8,14) (0,4) (7,9) (2,0) (0,1) (19,5) (2,3) (5,22) (25,16) (2,23) (20,6) (9,26) (15,14) (24,11) (11,13) (1,21) (18,24) (17,27) (17,3) (0,3) (12,23) (4,14) (20,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph89", "image": "data/cycle/graph_visual/hard/graph89.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (2,0) (3,5) (11,17) (24,5) (18,12) (2,20) (23,14) (12,17) (24,8) (25,9) (22,24) (25,3) (10,9) (15,19) (7,16) (15,4) (1,23) (9,21) (3,13) (8,11) (7,6) (1,7) (2,4) (0,12) (17,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph302", "image": "data/cycle/graph_visual/hard/graph302.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (18,23) (22,2) (27,25) (3,12) (16,27) (9,26) (20,9) (23,12) (23,21) (17,6) (24,28) (11,0) (14,13) (3,26) (20,19) (3,16) (4,24) (24,0) (28,14) (25,1) (15,2) (5,0) (10,8) (22,26) (13,26) (17,16) (23,10) (7,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph529", "image": "data/cycle/graph_visual/hard/graph529.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (25,23) (25,17) (9,3) (29,24) (28,14) (0,13) (7,8) (25,20) (2,21) (27,5) (12,1) (8,16) (28,10) (7,1) (18,9) (21,27) (4,5) (9,6) (15,14) (28,0) (19,10) (7,20) (11,4) (28,25) (13,30) (2,29) (22,1) (4,12) (27,26) (18,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph347", "image": "data/cycle/graph_visual/hard/graph347.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,12) (1,9) (0,6) (23,7) (25,20) (4,28) (14,6) (3,18) (2,7) (25,5) (1,5) (23,11) (26,22) (16,26) (18,19) (24,8) (27,4) (15,21) (27,13) (16,15) (1,11) (2,10) (14,26) (13,1) (8,20) (17,15) (10,15) (18,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1030", "image": "data/cycle/graph_visual/hard/graph1030.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (13,14) (21,8) (25,9) (10,4) (13,0) (11,24) (10,15) (17,20) (6,25) (1,0) (2,3) (22,5) (21,7) (15,18) (6,13) (1,23) (18,14) (19,3) (3,4) (5,0) (12,4) (2,24) (23,13) (16,8) (21,18) (10,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1586", "image": "data/cycle/graph_visual/hard/graph1586.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (22,17) (11,9) (28,0) (11,15) (25,16) (12,7) (13,2) (3,24) (0,1) (7,0) (3,29) (13,23) (5,9) (18,22) (6,9) (23,26) (16,1) (8,21) (25,4) (12,26) (27,30) (29,16) (8,27) (10,25) (24,5) (21,17) (22,19) (2,0) (14,30) (20,27) (13,8) (10,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph142", "image": "data/cycle/graph_visual/hard/graph142.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,23) (9,1) (3,14) (24,13) (20,25) (10,22) (5,22) (11,8) (21,3) (11,18) (16,0) (11,19) (9,21) (19,15) (17,19) (4,14) (6,24) (18,25) (13,12) (26,12) (2,1) (13,16) (4,7) (14,19) (15,22) (17,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1556", "image": "data/cycle/graph_visual/hard/graph1556.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (29,12) (10,21) (27,23) (8,15) (18,19) (5,11) (15,13) (0,4) (17,20) (0,23) (30,3) (7,13) (2,0) (17,14) (4,22) (25,24) (1,0) (18,7) (21,27) (24,29) (23,8) (16,22) (14,10) (5,17) (25,3) (3,0) (28,11) (14,1) (3,16) (26,19) (30,2) (23,6) (20,24) (9,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph109", "image": "data/cycle/graph_visual/hard/graph109.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,9) (2,11) (0,19) (0,20) (22,2) (24,12) (25,5) (10,5) (12,14) (10,9) (6,7) (20,10) (11,15) (16,0) (6,25) (1,15) (25,17) (22,18) (5,3) (11,23) (17,4) (21,15) (10,14) (2,26) (8,10) (16,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph200", "image": "data/cycle/graph_visual/hard/graph200.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (23,13) (7,25) (21,19) (27,6) (3,21) (8,6) (5,20) (6,26) (14,4) (7,23) (0,23) (10,19) (24,17) (15,1) (1,12) (17,11) (16,19) (2,6) (22,13) (5,16) (13,9) (22,27) (23,1) (20,13) (24,21) (18,15) (24,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1494", "image": "data/cycle/graph_visual/hard/graph1494.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,27) (0,24) (11,14) (22,3) (9,11) (29,3) (0,7) (13,23) (1,16) (1,0) (16,28) (9,6) (13,8) (17,19) (22,15) (5,9) (25,16) (20,10) (27,20) (26,12) (7,12) (4,25) (21,17) (10,25) (2,13) (18,22) (27,29) (24,5) (26,23) (21,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph900", "image": "data/cycle/graph_visual/hard/graph900.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,33) (27,17) (11,28) (27,23) (13,32) (22,34) (24,16) (5,26) (2,33) (9,3) (34,4) (15,18) (4,26) (19,28) (8,2) (31,0) (6,14) (1,5) (10,23) (32,23) (0,32) (18,24) (21,4) (30,26) (23,18) (23,4) (29,6) (25,27) (2,28) (7,32) (13,29) (12,33) (3,5) (20,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph568", "image": "data/cycle/graph_visual/hard/graph568.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,17) (8,12) (0,1) (17,25) (7,14) (5,20) (28,2) (18,13) (3,24) (2,6) (1,13) (16,7) (7,8) (22,6) (18,27) (16,19) (29,7) (23,11) (9,3) (22,20) (4,15) (3,21) (20,30) (17,0) (26,2) (0,10) (23,28) (21,23) (19,0) (23,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1258", "image": "data/cycle/graph_visual/hard/graph1258.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (2,0) (17,21) (23,2) (20,23) (11,8) (22,3) (0,1) (0,20) (18,27) (12,24) (26,11) (2,26) (1,15) (5,12) (9,6) (17,10) (16,8) (2,14) (9,13) (7,15) (8,10) (26,15) (8,4) (3,0) (5,7) (26,19) (25,7) (6,2) (22,26) (18,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1779", "image": "data/cycle/graph_visual/hard/graph1779.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,9) (29,14) (1,0) (31,14) (14,32) (8,26) (13,14) (20,0) (4,21) (29,17) (10,0) (22,10) (9,24) (18,27) (23,30) (3,20) (1,12) (28,14) (27,4) (26,7) (14,6) (5,12) (30,8) (14,16) (27,30) (22,7) (2,0) (7,19) (28,25) (0,24) (2,6) (29,11) (24,15) (22,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1", "image": "data/cycle/graph_visual/hard/graph1.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,14) (9,11) (9,18) (17,1) (25,14) (8,14) (13,9) (2,18) (0,3) (6,5) (0,15) (25,6) (7,23) (23,8) (6,16) (6,4) (20,10) (24,19) (19,13) (11,12) (21,12) (6,1) (25,22) (15,6) (18,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph536", "image": "data/cycle/graph_visual/hard/graph536.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,1) (30,21) (29,6) (26,24) (15,14) (9,22) (21,0) (14,4) (27,9) (15,7) (0,1) (28,2) (19,7) (23,24) (1,16) (9,20) (8,12) (13,18) (5,30) (11,3) (6,11) (10,2) (10,25) (26,14) (7,10) (13,26) (17,25) (12,9) (9,7) (29,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1761", "image": "data/cycle/graph_visual/hard/graph1761.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (26,9) (2,0) (16,8) (1,19) (3,1) (20,7) (32,23) (2,23) (18,24) (27,23) (6,31) (9,27) (10,1) (29,32) (30,11) (32,15) (16,25) (14,15) (9,24) (11,27) (4,14) (22,6) (3,0) (8,28) (5,32) (13,18) (14,31) (23,10) (0,4) (24,8) (27,17) (25,21) (12,30) (20,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph951", "image": "data/cycle/graph_visual/hard/graph951.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (12,30) (23,32) (21,16) (30,34) (21,17) (3,18) (29,8) (33,14) (7,8) (7,31) (14,6) (29,4) (9,28) (5,32) (27,10) (12,24) (14,25) (10,33) (29,11) (1,18) (8,22) (25,28) (28,30) (22,23) (26,2) (20,4) (16,7) (28,15) (19,14) (27,18) (14,23) (0,26) (13,33) (2,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph469", "image": "data/cycle/graph_visual/hard/graph469.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (28,25) (18,3) (19,10) (28,20) (7,4) (12,0) (2,7) (21,17) (14,5) (25,11) (20,22) (23,29) (29,13) (23,21) (2,26) (24,11) (4,9) (22,16) (8,7) (14,15) (3,23) (5,19) (13,28) (0,19) (29,6) (29,5) (1,10) (1,8) (27,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1158", "image": "data/cycle/graph_visual/hard/graph1158.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,6) (22,2) (4,8) (17,25) (2,26) (14,3) (18,6) (10,12) (4,11) (7,2) (0,1) (9,5) (20,16) (1,12) (14,1) (25,15) (0,15) (2,0) (19,6) (3,0) (13,1) (6,15) (25,20) (1,23) (9,11) (26,20) (5,21) (13,4) (9,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1919", "image": "data/cycle/graph_visual/hard/graph1919.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (6,33) (34,12) (0,3) (2,12) (28,6) (0,23) (30,27) (27,22) (5,0) (15,16) (3,13) (14,0) (18,1) (16,20) (31,22) (5,16) (16,27) (14,10) (22,21) (1,0) (23,26) (27,29) (8,1) (9,12) (0,20) (4,18) (11,24) (4,29) (25,32) (11,1) (17,4) (24,7) (25,6) (0,2) (17,19) (32,19) (13,25) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1676", "image": "data/cycle/graph_visual/hard/graph1676.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (28,12) (16,20) (8,22) (20,21) (25,27) (0,2) (6,27) (10,18) (30,26) (22,12) (17,6) (15,26) (20,19) (1,6) (9,16) (29,24) (16,14) (18,17) (23,4) (4,24) (3,0) (13,6) (31,25) (6,4) (7,12) (7,2) (0,1) (25,5) (12,3) (9,11) (1,26) (1,19) (29,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph157", "image": "data/cycle/graph_visual/hard/graph157.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (19,24) (9,10) (15,12) (22,26) (26,21) (8,17) (10,6) (10,0) (25,23) (12,16) (20,24) (11,23) (15,26) (9,21) (14,4) (3,14) (7,9) (21,14) (1,16) (11,7) (0,17) (0,19) (13,17) (5,18) (5,4) (26,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph908", "image": "data/cycle/graph_visual/hard/graph908.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (2,10) (16,2) (32,33) (30,6) (28,9) (21,19) (33,27) (27,29) (26,31) (34,23) (20,17) (30,19) (1,32) (26,3) (24,23) (10,22) (14,25) (34,6) (0,15) (14,5) (31,15) (20,18) (17,21) (25,22) (29,12) (23,4) (5,33) (24,0) (13,23) (30,9) (27,7) (8,6) (11,4) (9,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph698", "image": "data/cycle/graph_visual/hard/graph698.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (16,8) (17,14) (15,4) (29,18) (27,1) (12,0) (28,8) (14,7) (29,15) (8,12) (4,6) (0,31) (30,11) (5,11) (3,8) (26,19) (25,12) (22,13) (23,10) (17,11) (28,14) (9,13) (26,6) (1,26) (20,8) (21,13) (9,25) (10,8) (26,20) (2,7) (24,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1750", "image": "data/cycle/graph_visual/hard/graph1750.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (9,1) (6,16) (24,0) (23,13) (6,30) (9,30) (0,15) (10,22) (29,27) (28,9) (20,17) (15,27) (3,26) (8,6) (4,11) (23,4) (21,17) (2,18) (27,7) (5,31) (12,29) (25,14) (26,25) (5,14) (24,23) (2,0) (1,0) (21,19) (32,16) (20,22) (2,10) (19,30) (31,1) (23,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1601", "image": "data/cycle/graph_visual/hard/graph1601.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (20,22) (25,14) (1,0) (5,31) (21,19) (30,6) (30,9) (10,22) (14,5) (12,29) (6,16) (27,7) (26,25) (0,24) (4,11) (27,15) (10,2) (0,15) (6,8) (23,24) (9,1) (23,13) (2,18) (0,2) (30,19) (4,23) (16,31) (9,28) (17,20) (27,29) (17,21) (1,23) (26,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph34", "image": "data/cycle/graph_visual/hard/graph34.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,3) (1,3) (12,5) (13,25) (20,16) (17,8) (0,6) (4,22) (19,6) (21,6) (4,7) (14,17) (22,10) (7,15) (18,13) (19,9) (6,24) (6,20) (11,5) (2,23) (14,24) (5,4) (23,12) (4,19) (13,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph87", "image": "data/cycle/graph_visual/hard/graph87.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (2,0) (24,21) (8,24) (12,25) (17,10) (1,23) (10,3) (14,4) (25,19) (19,7) (1,13) (5,13) (23,14) (4,8) (11,16) (22,23) (17,16) (20,1) (24,9) (15,21) (11,2) (6,3) (20,17) (16,7) (1,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1478", "image": "data/cycle/graph_visual/hard/graph1478.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,18) (7,19) (1,0) (7,4) (6,26) (8,2) (27,8) (11,10) (26,25) (3,9) (16,0) (6,10) (17,20) (12,7) (22,17) (15,28) (21,20) (26,14) (24,27) (26,0) (16,21) (23,19) (0,3) (0,2) (8,0) (17,4) (5,25) (6,29) (5,15) (15,9) (13,6) (1,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph945", "image": "data/cycle/graph_visual/hard/graph945.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (8,34) (17,24) (28,11) (32,27) (31,7) (25,15) (18,22) (26,13) (28,7) (4,31) (1,16) (1,33) (10,29) (8,18) (2,31) (14,20) (32,22) (9,13) (28,16) (24,23) (4,25) (7,0) (8,12) (3,18) (15,26) (28,24) (4,8) (17,20) (5,2) (5,6) (29,20) (6,30) (6,19) (9,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1382", "image": "data/cycle/graph_visual/hard/graph1382.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (3,17) (25,4) (14,26) (1,9) (8,27) (13,9) (5,23) (24,15) (10,7) (22,25) (23,3) (19,17) (26,21) (25,7) (0,2) (9,8) (27,2) (25,18) (14,12) (6,13) (4,16) (22,11) (27,20) (28,5) (0,3) (1,0) (23,11) (16,14) (2,22) (15,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph800", "image": "data/cycle/graph_visual/hard/graph800.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,23) (33,10) (18,30) (11,4) (13,9) (19,32) (23,25) (27,0) (2,33) (16,1) (24,30) (1,2) (6,20) (12,18) (29,12) (5,21) (15,31) (4,13) (19,9) (31,0) (17,6) (7,21) (3,33) (28,12) (33,8) (20,21) (31,2) (3,22) (32,7) (28,5) (26,8) (7,10) (15,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1681", "image": "data/cycle/graph_visual/hard/graph1681.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,28) (4,29) (8,18) (9,12) (3,1) (31,9) (7,27) (25,6) (25,30) (29,7) (2,13) (5,25) (18,21) (3,19) (1,2) (26,29) (30,4) (21,28) (0,2) (23,9) (14,11) (8,1) (17,9) (4,15) (27,14) (5,20) (5,0) (2,10) (14,21) (0,3) (4,0) (24,23) (0,1) (20,16) (30,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1975", "image": "data/cycle/graph_visual/hard/graph1975.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,29) (18,6) (29,22) (2,0) (23,5) (26,14) (13,34) (27,10) (21,2) (12,17) (27,28) (24,4) (3,7) (28,30) (3,0) (10,31) (0,21) (1,0) (32,20) (15,10) (5,17) (9,23) (5,26) (10,29) (8,16) (4,32) (8,32) (15,3) (8,7) (18,13) (33,14) (17,13) (11,19) (2,24) (21,25) (0,11) (24,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1120", "image": "data/cycle/graph_visual/hard/graph1120.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (18,25) (20,17) (12,0) (25,16) (1,0) (23,22) (11,21) (8,15) (20,3) (24,19) (20,24) (2,13) (14,6) (15,1) (12,9) (7,19) (4,20) (25,24) (6,26) (26,22) (8,22) (21,6) (4,2) (17,10) (6,0) (3,5) (14,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1572", "image": "data/cycle/graph_visual/hard/graph1572.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,6) (4,18) (7,13) (3,0) (5,26) (27,12) (14,24) (2,7) (2,3) (9,4) (5,16) (13,0) (4,0) (0,6) (22,15) (6,29) (4,19) (10,17) (0,2) (23,8) (17,7) (24,6) (11,19) (25,4) (30,3) (21,20) (28,4) (12,5) (14,20) (1,3) (0,1) (23,6) (22,13) (26,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph847", "image": "data/cycle/graph_visual/hard/graph847.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (25,27) (18,28) (17,5) (20,14) (33,3) (29,14) (5,1) (19,29) (11,16) (18,12) (24,19) (32,10) (20,22) (30,9) (7,25) (17,13) (33,13) (8,17) (26,25) (4,15) (22,16) (10,9) (21,1) (16,23) (10,0) (17,31) (23,33) (28,16) (2,6) (4,0) (7,4) (6,15) (7,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1398", "image": "data/cycle/graph_visual/hard/graph1398.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,10) (27,16) (27,25) (9,26) (14,13) (0,5) (24,28) (4,24) (0,1) (24,0) (25,1) (0,4) (21,23) (26,3) (26,7) (17,6) (2,22) (15,2) (12,23) (2,0) (17,16) (16,3) (20,9) (12,3) (23,18) (0,11) (10,23) (20,19) (26,13) (14,28) (0,3) (26,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1559", "image": "data/cycle/graph_visual/hard/graph1559.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (9,16) (18,8) (22,7) (24,9) (5,27) (3,7) (2,10) (18,24) (24,0) (6,18) (13,26) (0,28) (1,6) (11,19) (15,20) (0,14) (10,20) (1,0) (30,29) (27,6) (29,1) (25,17) (2,19) (29,17) (21,15) (12,17) (13,22) (11,3) (2,0) (4,30) (20,8) (23,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph579", "image": "data/cycle/graph_visual/hard/graph579.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (18,2) (9,18) (6,14) (18,19) (13,15) (22,12) (27,0) (16,6) (8,13) (30,17) (25,8) (23,16) (24,26) (10,15) (0,3) (3,4) (9,21) (17,15) (11,17) (14,5) (3,14) (12,16) (5,20) (28,11) (2,15) (0,13) (13,29) (24,27) (16,7) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1730", "image": "data/cycle/graph_visual/hard/graph1730.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (2,17) (21,23) (5,3) (20,29) (2,1) (18,25) (24,30) (11,10) (23,29) (27,24) (20,11) (14,1) (22,28) (4,5) (19,32) (2,12) (15,14) (20,32) (23,5) (15,31) (28,23) (10,27) (17,26) (6,10) (3,0) (25,32) (11,1) (19,7) (16,8) (0,2) (9,13) (0,1) (27,16) (13,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph844", "image": "data/cycle/graph_visual/hard/graph844.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (16,9) (28,18) (12,5) (6,10) (33,5) (31,4) (13,30) (21,13) (22,23) (0,31) (5,32) (2,20) (13,25) (4,30) (4,7) (4,3) (25,11) (23,25) (27,10) (15,22) (2,7) (14,26) (7,17) (21,18) (24,7) (5,6) (10,19) (18,29) (30,14) (7,8) (22,1) (3,10) (9,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1000", "image": "data/cycle/graph_visual/hard/graph1000.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (24,25) (22,15) (6,4) (0,1) (9,4) (5,2) (11,15) (14,1) (13,23) (16,1) (17,24) (1,10) (20,16) (7,9) (22,8) (3,18) (10,21) (10,3) (19,0) (12,0) (11,19) (7,15) (17,0) (25,23) (6,2) (16,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1899", "image": "data/cycle/graph_visual/hard/graph1899.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,10) (31,2) (1,0) (9,3) (31,17) (12,16) (8,13) (12,13) (21,19) (25,11) (21,2) (12,28) (6,22) (5,2) (4,31) (30,12) (3,30) (8,32) (1,22) (24,19) (26,33) (27,0) (14,18) (23,22) (18,25) (25,10) (7,26) (20,2) (32,17) (12,26) (24,0) (4,15) (11,32) (23,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph786", "image": "data/cycle/graph_visual/hard/graph786.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (8,30) (28,18) (0,7) (10,26) (9,26) (32,22) (16,22) (7,18) (5,15) (2,11) (17,8) (20,16) (16,14) (9,17) (19,2) (4,26) (30,24) (1,4) (11,20) (23,21) (17,6) (19,5) (31,12) (21,1) (4,27) (4,29) (19,7) (9,3) (31,13) (27,13) (25,0) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1709", "image": "data/cycle/graph_visual/hard/graph1709.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,29) (10,19) (15,21) (30,22) (2,3) (17,10) (8,6) (17,5) (4,27) (18,1) (20,10) (1,10) (24,10) (11,31) (14,9) (32,9) (25,7) (13,4) (1,0) (26,21) (10,11) (26,23) (12,10) (27,23) (16,3) (6,30) (2,26) (11,14) (7,9) (26,0) (2,17) (14,30) (29,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph288", "image": "data/cycle/graph_visual/hard/graph288.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,5) (22,1) (9,23) (5,6) (14,27) (4,25) (26,7) (14,25) (21,9) (22,2) (24,22) (4,18) (23,26) (3,12) (19,22) (13,6) (14,0) (2,16) (24,0) (23,20) (27,20) (15,21) (18,8) (11,6) (5,21) (17,24) (5,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph753", "image": "data/cycle/graph_visual/hard/graph753.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (29,20) (32,20) (32,25) (6,10) (0,3) (13,9) (11,20) (11,10) (2,1) (23,28) (10,13) (17,2) (18,25) (3,5) (5,23) (16,8) (30,24) (4,5) (1,14) (32,19) (31,15) (19,7) (10,27) (24,27) (22,28) (27,16) (14,15) (17,26) (23,29) (12,2) (23,21) (1,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph878", "image": "data/cycle/graph_visual/hard/graph878.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (31,0) (33,4) (4,26) (24,27) (33,12) (21,4) (8,2) (32,23) (4,23) (32,0) (3,5) (27,2) (23,10) (26,29) (7,32) (18,22) (26,5) (18,15) (23,25) (20,9) (27,17) (13,28) (11,28) (2,33) (13,32) (6,29) (30,0) (16,24) (3,9) (14,6) (18,23) (28,19) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph818", "image": "data/cycle/graph_visual/hard/graph818.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (14,19) (16,3) (20,7) (24,10) (12,9) (17,29) (29,1) (11,9) (17,24) (11,4) (19,13) (13,3) (18,32) (27,7) (14,21) (10,7) (25,6) (13,25) (27,15) (22,8) (31,21) (28,5) (29,25) (26,23) (9,0) (2,29) (33,7) (29,5) (13,26) (30,16) (11,32) (12,22) (22,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1094", "image": "data/cycle/graph_visual/hard/graph1094.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,0) (1,4) (22,14) (11,19) (3,22) (9,18) (24,15) (18,10) (18,12) (9,13) (8,9) (21,7) (6,15) (20,25) (2,17) (23,17) (1,0) (0,3) (8,11) (0,2) (5,2) (21,25) (15,8) (6,0) (20,16) (23,4) (18,14) (1,21) (11,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph91", "image": "data/cycle/graph_visual/hard/graph91.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,13) (12,18) (7,21) (25,21) (14,18) (23,4) (4,1) (24,15) (11,19) (10,18) (6,15) (0,6) (5,2) (3,22) (8,9) (20,25) (22,14) (1,21) (8,11) (11,2) (17,23) (18,9) (17,2) (15,8) (16,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph894", "image": "data/cycle/graph_visual/hard/graph894.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (5,32) (20,27) (21,4) (33,16) (25,10) (14,22) (12,30) (11,19) (17,32) (30,28) (24,0) (19,6) (13,15) (16,25) (22,6) (8,23) (16,2) (6,31) (21,30) (20,13) (28,33) (26,9) (19,9) (4,29) (16,32) (8,18) (18,24) (1,26) (31,7) (8,6) (3,2) (27,22) (13,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph206", "image": "data/cycle/graph_visual/hard/graph206.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,13) (3,17) (11,24) (21,1) (5,22) (15,14) (2,3) (6,20) (7,10) (19,5) (23,14) (25,3) (9,7) (23,12) (2,23) (6,10) (1,8) (26,17) (14,4) (16,25) (13,11) (0,4) (8,14) (24,18) (27,9) (22,12) (20,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1146", "image": "data/cycle/graph_visual/hard/graph1146.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,26) (1,24) (0,20) (1,0) (2,22) (18,9) (3,2) (7,25) (19,14) (23,4) (21,18) (13,12) (15,26) (7,19) (9,13) (14,8) (2,17) (4,11) (6,23) (11,16) (0,2) (9,5) (0,14) (8,6) (0,3) (22,15) (24,0) (12,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1744", "image": "data/cycle/graph_visual/hard/graph1744.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,17) (22,18) (2,16) (3,20) (24,29) (0,3) (25,0) (23,15) (16,31) (8,15) (31,1) (5,7) (12,27) (10,12) (7,19) (21,11) (0,17) (14,13) (11,24) (32,28) (5,32) (4,12) (21,20) (4,5) (11,26) (1,0) (30,13) (14,12) (0,2) (9,32) (18,30) (30,16) (7,20) (15,9) (12,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1401", "image": "data/cycle/graph_visual/hard/graph1401.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,24) (10,17) (0,21) (26,16) (25,29) (29,9) (27,13) (2,19) (11,7) (15,25) (8,10) (1,0) (14,23) (10,16) (3,0) (25,19) (18,14) (13,22) (28,17) (18,13) (17,21) (11,29) (1,4) (6,5) (25,3) (0,2) (12,27) (25,17) (26,14) (20,27) (5,2) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph96", "image": "data/cycle/graph_visual/hard/graph96.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,12) (21,18) (10,23) (8,9) (13,20) (19,1) (25,12) (9,17) (23,16) (6,22) (23,24) (5,21) (19,6) (19,8) (25,14) (3,2) (18,1) (4,2) (1,0) (2,11) (15,21) (11,16) (25,11) (7,5) (5,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1814", "image": "data/cycle/graph_visual/hard/graph1814.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (16,30) (20,3) (2,16) (20,21) (13,14) (33,12) (6,12) (22,18) (5,4) (29,24) (7,19) (13,30) (9,32) (16,31) (27,12) (10,12) (18,30) (24,11) (8,15) (15,9) (11,26) (0,25) (1,0) (23,15) (4,32) (31,1) (32,28) (20,7) (2,0) (5,7) (1,17) (14,12) (5,12) (17,0) (21,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph19", "image": "data/cycle/graph_visual/hard/graph19.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (11,14) (16,9) (14,23) (3,8) (17,0) (13,20) (13,11) (11,25) (8,19) (9,5) (13,9) (3,4) (8,17) (25,24) (0,7) (18,19) (23,0) (0,21) (1,17) (15,12) (2,5) (15,11) (6,13) (21,10) (13,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1672", "image": "data/cycle/graph_visual/hard/graph1672.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (13,9) (27,23) (15,10) (29,5) (0,1) (11,28) (11,21) (8,5) (30,20) (6,11) (18,5) (5,30) (29,9) (22,12) (2,25) (12,26) (7,14) (23,24) (21,5) (13,26) (12,4) (31,19) (14,8) (31,0) (16,24) (0,17) (24,3) (2,17) (24,13) (25,20) (15,16) (25,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph124", "image": "data/cycle/graph_visual/hard/graph124.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,24) (6,23) (4,11) (26,10) (0,14) (21,18) (22,15) (23,4) (7,25) (9,18) (2,22) (20,0) (9,5) (17,2) (7,19) (11,16) (6,8) (26,15) (16,12) (2,3) (9,13) (13,12) (0,3) (14,19) (1,24) (14,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1978", "image": "data/cycle/graph_visual/hard/graph1978.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (16,33) (2,9) (23,31) (13,6) (13,3) (14,25) (29,32) (28,22) (34,24) (0,4) (19,5) (29,18) (18,9) (3,0) (34,16) (12,17) (27,21) (19,30) (27,22) (12,9) (27,8) (6,12) (11,26) (20,24) (1,0) (15,11) (21,26) (3,23) (11,30) (25,0) (6,4) (23,11) (9,33) (10,2) (15,0) (2,0) (12,1) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1228", "image": "data/cycle/graph_visual/hard/graph1228.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (24,19) (26,5) (18,12) (18,6) (7,17) (1,10) (22,25) (8,25) (17,9) (3,23) (15,5) (13,0) (27,1) (0,1) (25,11) (10,20) (13,8) (17,21) (0,2) (18,21) (26,25) (20,21) (18,3) (15,16) (18,2) (16,4) (2,26) (14,25) (24,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph843", "image": "data/cycle/graph_visual/hard/graph843.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (32,26) (1,17) (25,5) (25,13) (31,5) (4,24) (31,28) (7,24) (6,33) (3,23) (2,5) (0,14) (31,14) (9,8) (30,26) (22,31) (15,8) (20,1) (16,6) (10,12) (33,17) (1,14) (29,12) (23,29) (11,2) (30,24) (8,18) (13,19) (25,12) (15,32) (27,24) (29,21) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1096", "image": "data/cycle/graph_visual/hard/graph1096.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,17) (17,21) (23,3) (2,18) (5,2) (5,15) (25,11) (18,3) (8,13) (24,19) (12,18) (18,21) (16,24) (0,13) (4,16) (25,1) (20,21) (18,6) (1,10) (8,25) (9,17) (25,22) (15,16) (14,25) (10,20) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph697", "image": "data/cycle/graph_visual/hard/graph697.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,9) (21,13) (17,11) (31,21) (7,17) (16,20) (28,7) (15,24) (11,14) (0,26) (9,12) (23,6) (29,5) (4,7) (19,2) (26,21) (1,18) (20,25) (26,19) (19,4) (3,25) (13,27) (30,5) (16,23) (1,15) (8,24) (8,12) (22,26) (26,9) (8,3) (18,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph12", "image": "data/cycle/graph_visual/hard/graph12.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,16) (15,1) (4,22) (2,6) (19,4) (11,20) (18,21) (23,13) (14,22) (12,8) (5,7) (0,6) (5,16) (12,24) (0,17) (8,23) (1,0) (1,25) (11,25) (22,11) (10,14) (10,3) (11,8) (7,21) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1364", "image": "data/cycle/graph_visual/hard/graph1364.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,25) (10,23) (2,0) (0,3) (28,2) (28,22) (10,26) (5,27) (16,4) (17,27) (3,9) (1,0) (2,7) (14,11) (26,7) (7,9) (17,21) (14,12) (22,19) (20,24) (18,16) (17,14) (15,19) (13,0) (9,1) (6,8) (13,28) (20,6) (4,0) (14,16) (14,8) (15,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph286", "image": "data/cycle/graph_visual/hard/graph286.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (8,6) (15,9) (15,13) (11,10) (10,3) (4,14) (7,6) (23,6) (15,18) (27,5) (5,25) (14,9) (21,16) (19,5) (25,24) (24,21) (27,26) (7,12) (2,21) (22,8) (15,20) (22,3) (1,3) (17,20) (14,8) (10,16) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1077", "image": "data/cycle/graph_visual/hard/graph1077.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,15) (3,10) (2,21) (0,2) (11,10) (8,14) (20,6) (12,7) (5,0) (0,3) (25,23) (15,18) (22,3) (14,4) (14,9) (20,17) (24,25) (6,7) (15,13) (1,0) (24,21) (1,3) (5,19) (8,6) (10,16) (8,22) (9,15) (21,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph348", "image": "data/cycle/graph_visual/hard/graph348.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (16,17) (19,22) (5,4) (26,21) (15,3) (16,14) (0,17) (27,17) (13,5) (9,12) (20,15) (7,20) (6,7) (16,24) (8,17) (27,28) (18,6) (10,1) (13,23) (25,9) (17,11) (24,22) (25,4) (4,2) (27,25) (10,22) (21,3) (24,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph440", "image": "data/cycle/graph_visual/hard/graph440.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (6,0) (29,26) (9,14) (4,24) (28,27) (27,3) (22,8) (12,27) (2,12) (7,26) (16,20) (3,18) (9,1) (18,25) (24,20) (10,26) (13,24) (26,23) (18,9) (1,15) (15,17) (18,21) (23,21) (27,19) (13,3) (6,29) (29,5) (8,1) (11,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1017", "image": "data/cycle/graph_visual/hard/graph1017.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,8) (21,5) (18,9) (2,22) (21,2) (7,20) (13,0) (6,9) (0,3) (18,15) (4,11) (0,2) (17,25) (1,0) (12,1) (7,1) (1,10) (9,3) (24,25) (25,19) (16,8) (4,12) (10,14) (15,14) (23,0) (25,20) (5,4) (13,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph309", "image": "data/cycle/graph_visual/hard/graph309.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (5,13) (10,11) (6,3) (4,2) (16,7) (26,22) (19,11) (15,20) (27,9) (4,1) (17,7) (14,5) (13,15) (9,5) (25,22) (6,0) (15,26) (22,11) (14,8) (23,15) (21,4) (11,2) (3,23) (24,0) (28,19) (22,18) (7,23) (19,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1285", "image": "data/cycle/graph_visual/hard/graph1285.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,2) (12,27) (2,0) (19,22) (12,5) (21,4) (23,11) (26,25) (23,16) (21,8) (7,6) (26,14) (25,11) (0,4) (1,0) (8,7) (3,0) (27,6) (21,3) (18,14) (14,17) (14,10) (6,15) (25,13) (25,6) (14,20) (26,19) (18,1) (15,24) (9,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph123", "image": "data/cycle/graph_visual/hard/graph123.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (5,10) (18,22) (15,21) (25,6) (14,12) (14,10) (26,2) (2,22) (25,17) (7,6) (3,5) (16,0) (15,11) (10,8) (1,15) (22,16) (10,9) (25,5) (10,20) (0,20) (24,12) (2,11) (13,9) (4,17) (23,11) (0,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1280", "image": "data/cycle/graph_visual/hard/graph1280.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (6,0) (3,18) (22,18) (0,3) (1,15) (3,13) (0,10) (21,18) (26,27) (2,0) (9,1) (8,1) (24,4) (24,27) (13,20) (9,11) (27,6) (7,26) (15,14) (21,23) (12,20) (1,0) (2,12) (8,19) (3,25) (23,26) (17,24) (27,16) (26,5) (9,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1284", "image": "data/cycle/graph_visual/hard/graph1284.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (13,0) (11,5) (13,20) (14,24) (14,18) (6,21) (0,3) (23,4) (1,0) (23,2) (4,19) (0,6) (5,12) (24,12) (27,7) (6,19) (19,9) (25,4) (2,0) (26,5) (20,17) (4,16) (7,15) (7,13) (3,4) (26,6) (22,10) (8,17) (22,6) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1426", "image": "data/cycle/graph_visual/hard/graph1426.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,9) (27,12) (14,7) (19,26) (25,23) (10,15) (20,28) (24,0) (27,0) (16,29) (19,11) (7,16) (0,3) (3,20) (13,20) (8,0) (28,29) (0,2) (16,5) (12,3) (6,19) (22,12) (0,1) (13,9) (1,11) (17,10) (2,1) (12,11) (28,21) (5,23) (18,26) (18,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1930", "image": "data/cycle/graph_visual/hard/graph1930.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,26) (28,19) (0,1) (24,16) (23,10) (17,27) (33,12) (25,27) (24,18) (29,6) (13,32) (26,30) (34,22) (0,31) (33,2) (23,4) (9,20) (3,0) (2,28) (21,4) (0,2) (5,3) (32,0) (3,9) (5,1) (26,5) (32,7) (34,4) (13,29) (27,23) (14,6) (11,28) (2,8) (23,32) (33,0) (15,18) (18,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1587", "image": "data/cycle/graph_visual/hard/graph1587.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (7,11) (28,30) (19,9) (13,23) (17,2) (12,1) (28,25) (16,21) (1,0) (19,26) (0,3) (6,15) (2,14) (7,5) (23,19) (13,29) (18,6) (20,8) (23,8) (5,10) (2,30) (3,6) (12,24) (4,7) (12,16) (6,25) (12,0) (27,15) (22,21) (24,4) (0,2) (17,22) (18,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1323", "image": "data/cycle/graph_visual/hard/graph1323.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (24,16) (12,22) (4,2) (16,19) (18,26) (0,13) (19,15) (1,12) (10,25) (17,3) (7,0) (14,23) (20,12) (5,26) (26,27) (14,0) (20,17) (4,20) (28,16) (8,1) (7,25) (0,1) (0,2) (6,8) (5,2) (19,9) (26,19) (9,11) (21,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1304", "image": "data/cycle/graph_visual/hard/graph1304.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,0) (16,21) (8,2) (28,4) (11,16) (7,19) (3,10) (1,19) (6,2) (2,0) (1,0) (22,27) (13,4) (1,23) (6,19) (17,24) (22,16) (16,5) (0,26) (24,14) (26,11) (15,26) (4,24) (9,25) (16,6) (18,6) (8,20) (0,10) (14,26) (8,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph217", "image": "data/cycle/graph_visual/hard/graph217.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (23,15) (11,15) (5,24) (24,4) (8,17) (26,21) (19,25) (12,2) (16,4) (11,18) (26,9) (12,25) (12,20) (18,6) (8,25) (4,9) (10,1) (8,1) (14,15) (13,7) (27,0) (13,16) (24,3) (6,16) (17,27) (22,9) (3,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph592", "image": "data/cycle/graph_visual/hard/graph592.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (8,6) (22,29) (9,13) (16,17) (15,20) (30,29) (12,0) (11,8) (4,15) (23,9) (25,9) (3,14) (24,25) (1,7) (5,24) (5,26) (3,8) (4,2) (17,12) (30,6) (17,11) (2,21) (0,2) (3,26) (10,7) (23,18) (28,24) (27,1) (12,19) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph923", "image": "data/cycle/graph_visual/hard/graph923.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (2,13) (29,10) (19,3) (32,8) (15,22) (20,6) (12,9) (7,27) (31,10) (9,19) (1,29) (17,16) (6,18) (17,26) (25,17) (30,12) (14,30) (21,31) (12,8) (23,22) (20,5) (29,11) (28,29) (5,16) (2,32) (33,31) (22,31) (27,24) (0,28) (4,3) (24,34) (4,34) (19,1) (26,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1414", "image": "data/cycle/graph_visual/hard/graph1414.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,4) (18,6) (22,21) (0,12) (2,14) (13,27) (19,23) (24,4) (13,23) (16,21) (5,10) (15,6) (7,5) (17,2) (15,26) (18,19) (17,22) (25,6) (6,3) (12,24) (0,1) (23,8) (2,19) (16,12) (12,1) (28,29) (25,28) (11,7) (8,20) (9,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph63", "image": "data/cycle/graph_visual/hard/graph63.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (12,20) (2,14) (2,17) (16,12) (15,6) (23,13) (7,5) (17,22) (19,9) (21,16) (8,18) (23,8) (0,12) (4,7) (15,24) (3,6) (5,10) (25,19) (22,21) (7,11) (2,19) (24,4) (1,12) (6,13) (19,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph866", "image": "data/cycle/graph_visual/hard/graph866.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,9) (30,5) (24,16) (5,19) (17,0) (27,12) (23,28) (4,12) (15,10) (16,15) (5,32) (5,21) (20,25) (33,31) (14,8) (22,31) (24,23) (11,21) (6,11) (33,0) (13,24) (14,7) (18,33) (30,20) (26,13) (12,26) (1,25) (13,9) (25,2) (24,3) (5,8) (2,17) (29,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1517", "image": "data/cycle/graph_visual/hard/graph1517.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,18) (14,0) (17,2) (15,16) (9,14) (27,1) (4,2) (16,21) (22,30) (15,20) (14,12) (0,1) (25,19) (9,4) (29,5) (24,18) (25,17) (5,3) (22,28) (3,14) (27,8) (24,11) (23,27) (25,26) (19,20) (6,5) (16,27) (13,14) (7,17) (25,28) (0,2) (10,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1250", "image": "data/cycle/graph_visual/hard/graph1250.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,7) (2,10) (27,18) (19,12) (15,22) (10,13) (19,14) (2,20) (18,2) (21,22) (22,9) (21,10) (9,6) (11,17) (5,14) (5,26) (27,4) (0,1) (4,23) (27,7) (11,27) (19,0) (2,1) (16,8) (24,3) (4,8) (0,3) (2,0) (0,4) (6,25) (24,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph308", "image": "data/cycle/graph_visual/hard/graph308.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,17) (1,23) (26,8) (10,2) (11,28) (25,22) (18,22) (11,20) (13,9) (24,5) (15,18) (24,18) (4,6) (12,10) (23,25) (3,24) (8,13) (8,20) (14,4) (24,16) (17,0) (25,27) (19,16) (21,27) (10,27) (7,23) (3,11) (4,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1603", "image": "data/cycle/graph_visual/hard/graph1603.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,17) (13,31) (30,0) (3,0) (13,22) (7,26) (19,21) (24,8) (10,14) (25,24) (11,24) (20,16) (1,9) (12,13) (13,4) (8,3) (24,9) (13,16) (11,15) (19,5) (0,4) (6,12) (0,2) (6,14) (29,6) (1,0) (4,18) (26,1) (30,28) (11,28) (4,8) (23,3) (21,1) (15,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1913", "image": "data/cycle/graph_visual/hard/graph1913.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,21) (17,10) (23,28) (20,29) (9,32) (4,0) (26,28) (8,25) (19,22) (32,5) (31,5) (10,16) (26,34) (15,22) (20,22) (14,11) (12,6) (30,31) (5,27) (4,31) (33,23) (19,12) (31,11) (18,13) (0,3) (30,7) (8,7) (15,0) (3,9) (1,34) (1,19) (16,18) (27,2) (0,11) (2,10) (1,0) (0,2) (24,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph990", "image": "data/cycle/graph_visual/hard/graph990.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (23,16) (31,2) (6,0) (12,34) (7,33) (9,20) (9,2) (18,32) (27,2) (0,15) (16,33) (32,28) (14,21) (29,2) (25,26) (25,21) (24,29) (10,20) (18,34) (13,29) (17,31) (6,33) (11,12) (5,0) (33,31) (34,22) (3,2) (31,4) (18,1) (12,15) (19,23) (9,30) (8,14) (30,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1223", "image": "data/cycle/graph_visual/hard/graph1223.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (6,0) (12,20) (14,15) (22,18) (21,18) (10,0) (7,26) (2,12) (8,1) (26,27) (3,13) (3,25) (23,21) (23,26) (1,0) (16,27) (5,26) (27,6) (15,1) (8,19) (24,27) (9,11) (18,9) (17,24) (4,24) (9,1) (18,3) (20,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1708", "image": "data/cycle/graph_visual/hard/graph1708.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,0) (21,29) (7,29) (28,12) (3,9) (16,21) (14,11) (31,26) (4,21) (0,11) (12,14) (19,8) (2,12) (27,8) (23,7) (11,25) (8,18) (20,27) (5,11) (0,1) (28,30) (6,0) (28,15) (10,19) (8,24) (7,10) (29,17) (26,20) (14,22) (21,3) (15,9) (25,1) (13,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph379", "image": "data/cycle/graph_visual/hard/graph379.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,10) (8,23) (0,24) (14,21) (18,16) (3,0) (20,5) (21,5) (11,17) (5,4) (15,26) (18,1) (5,27) (14,12) (19,5) (2,6) (16,0) (3,25) (9,13) (15,27) (8,20) (16,15) (2,26) (22,0) (9,28) (7,28) (11,5) (28,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1894", "image": "data/cycle/graph_visual/hard/graph1894.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (9,19) (24,2) (31,32) (0,1) (28,24) (26,0) (1,14) (18,15) (22,30) (16,20) (9,13) (2,15) (2,21) (18,12) (4,33) (32,3) (2,0) (17,15) (26,10) (14,16) (7,19) (25,21) (11,9) (5,11) (9,30) (4,0) (9,1) (29,23) (0,3) (8,19) (6,19) (8,10) (17,4) (5,27) (6,3) (18,14) (29,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1372", "image": "data/cycle/graph_visual/hard/graph1372.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (23,12) (27,17) (3,17) (10,6) (16,13) (0,1) (6,20) (1,21) (18,24) (26,28) (0,4) (14,15) (23,2) (14,4) (23,14) (7,9) (3,25) (26,9) (11,24) (14,8) (12,22) (11,13) (1,8) (16,25) (21,20) (5,19) (10,7) (5,22) (2,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph414", "image": "data/cycle/graph_visual/hard/graph414.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,18) (17,15) (29,20) (20,12) (15,23) (29,0) (5,17) (15,12) (11,19) (29,10) (15,22) (8,17) (16,18) (17,27) (19,2) (4,9) (6,22) (8,24) (18,2) (28,26) (11,4) (21,26) (7,25) (20,14) (7,6) (13,15) (7,1) (17,26) (0,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1839", "image": "data/cycle/graph_visual/hard/graph1839.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,27) (8,16) (33,0) (12,8) (14,17) (9,25) (26,6) (3,8) (33,31) (26,19) (13,9) (2,0) (3,0) (1,0) (7,14) (4,15) (28,14) (32,17) (28,8) (21,13) (24,12) (12,25) (20,26) (0,12) (10,23) (7,2) (8,20) (26,1) (13,22) (29,18) (10,8) (11,32) (4,6) (11,5) (30,11) (15,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph232", "image": "data/cycle/graph_visual/hard/graph232.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,27) (24,13) (23,13) (17,8) (9,13) (0,12) (16,21) (17,1) (20,9) (9,6) (3,26) (15,11) (7,13) (13,11) (14,26) (25,0) (5,2) (23,0) (22,8) (19,21) (26,19) (0,17) (5,8) (18,15) (14,11) (27,11) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph76", "image": "data/cycle/graph_visual/hard/graph76.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (14,0) (11,16) (4,9) (25,17) (24,22) (14,9) (4,2) (6,5) (18,12) (24,7) (16,15) (19,20) (15,20) (19,25) (17,2) (21,16) (13,6) (22,25) (8,14) (23,5) (3,14) (14,10) (18,25) (3,5) (1,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1706", "image": "data/cycle/graph_visual/hard/graph1706.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (25,7) (1,5) (29,19) (0,4) (22,16) (10,31) (4,7) (13,17) (14,20) (28,15) (28,16) (15,3) (1,0) (9,10) (32,24) (2,0) (3,0) (13,24) (27,25) (30,17) (23,16) (7,21) (22,20) (14,29) (2,6) (25,26) (8,16) (19,18) (0,10) (1,21) (12,4) (9,23) (6,17) (18,11) (5,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph964", "image": "data/cycle/graph_visual/hard/graph964.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (16,33) (14,25) (11,30) (30,19) (0,15) (18,29) (34,16) (24,34) (27,21) (8,27) (12,6) (16,7) (11,23) (20,24) (31,23) (6,13) (17,12) (21,26) (4,6) (15,11) (2,10) (0,25) (27,22) (33,9) (18,9) (9,12) (13,3) (26,11) (2,9) (22,28) (1,12) (23,3) (19,5) (32,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1079", "image": "data/cycle/graph_visual/hard/graph1079.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,17) (4,3) (15,25) (15,7) (24,2) (9,6) (3,15) (23,18) (19,5) (21,20) (25,12) (1,22) (6,24) (13,1) (1,0) (3,18) (8,5) (0,4) (9,11) (14,5) (15,13) (21,8) (5,24) (16,10) (17,9) (2,0) (25,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1808", "image": "data/cycle/graph_visual/hard/graph1808.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (13,25) (27,7) (19,14) (13,3) (5,29) (7,33) (24,17) (4,11) (19,13) (22,12) (32,18) (2,29) (28,5) (31,21) (7,20) (24,10) (16,3) (30,16) (29,1) (11,9) (14,21) (26,13) (15,27) (8,22) (0,1) (10,7) (26,23) (9,12) (9,0) (23,22) (17,29) (25,6) (11,32) (29,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1430", "image": "data/cycle/graph_visual/hard/graph1430.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (24,17) (2,8) (7,27) (13,14) (0,4) (18,0) (21,12) (1,0) (0,2) (26,24) (7,5) (29,4) (23,17) (12,7) (0,11) (27,10) (1,19) (16,5) (20,17) (28,19) (6,17) (11,22) (16,18) (25,12) (28,8) (12,1) (11,15) (29,26) (22,9) (3,12) (11,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph771", "image": "data/cycle/graph_visual/hard/graph771.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (29,23) (16,0) (32,21) (9,31) (21,0) (16,26) (7,27) (19,13) (1,11) (22,18) (10,15) (5,15) (12,25) (2,7) (20,11) (19,16) (11,15) (11,14) (21,4) (6,12) (31,8) (30,12) (31,13) (12,15) (20,7) (23,32) (31,12) (28,10) (18,29) (17,30) (24,16) (3,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph487", "image": "data/cycle/graph_visual/hard/graph487.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,8) (8,20) (4,14) (2,8) (0,17) (3,21) (27,22) (0,12) (22,26) (19,4) (7,17) (7,28) (16,6) (19,21) (10,5) (21,0) (16,4) (12,18) (25,20) (14,11) (29,10) (15,24) (23,11) (27,19) (21,9) (5,11) (25,14) (13,11) (15,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1631", "image": "data/cycle/graph_visual/hard/graph1631.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (27,25) (23,27) (8,2) (2,0) (11,28) (23,4) (9,3) (0,30) (28,2) (1,14) (0,29) (4,14) (28,19) (26,5) (0,3) (18,15) (23,18) (24,16) (9,21) (12,6) (22,4) (24,18) (2,13) (23,0) (26,13) (27,17) (5,7) (5,3) (20,31) (29,6) (4,26) (20,1) (10,23) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1777", "image": "data/cycle/graph_visual/hard/graph1777.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (21,8) (27,20) (0,20) (0,25) (6,0) (9,16) (14,26) (30,16) (28,30) (15,28) (12,21) (13,25) (24,11) (1,19) (23,22) (15,14) (2,23) (22,3) (4,5) (22,21) (12,15) (6,1) (10,32) (29,7) (4,27) (32,27) (2,17) (15,32) (29,22) (1,0) (2,31) (18,26) (0,2) (24,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph247", "image": "data/cycle/graph_visual/hard/graph247.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (3,14) (8,13) (18,2) (13,11) (5,20) (23,8) (18,9) (15,2) (12,16) (24,25) (0,26) (3,4) (8,1) (16,22) (27,24) (19,18) (12,15) (16,7) (15,10) (17,27) (6,14) (6,16) (17,11) (0,13) (5,14) (0,3) (21,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph103", "image": "data/cycle/graph_visual/hard/graph103.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,5) (6,10) (20,17) (6,13) (10,11) (8,23) (5,25) (19,7) (14,3) (15,9) (4,17) (20,21) (4,7) (24,15) (7,12) (17,18) (6,26) (0,26) (8,0) (25,1) (22,19) (16,0) (21,16) (25,26) (9,3) (8,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph270", "image": "data/cycle/graph_visual/hard/graph270.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,13) (15,16) (22,8) (1,5) (16,9) (9,10) (0,9) (18,4) (12,11) (21,2) (19,4) (16,7) (21,3) (24,3) (25,8) (10,24) (11,16) (6,17) (12,6) (25,1) (23,13) (18,20) (27,0) (3,26) (8,26) (3,14) (8,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph455", "image": "data/cycle/graph_visual/hard/graph455.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,18) (11,22) (19,28) (16,20) (4,1) (15,6) (24,25) (28,15) (20,29) (18,10) (21,7) (8,9) (3,22) (21,1) (18,28) (26,27) (23,4) (2,5) (9,13) (9,26) (12,18) (17,2) (17,23) (14,25) (11,2) (15,8) (21,20) (6,0) (11,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1699", "image": "data/cycle/graph_visual/hard/graph1699.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (28,17) (26,25) (17,12) (11,29) (0,20) (1,21) (1,26) (14,29) (12,8) (1,27) (4,18) (28,2) (6,24) (5,31) (1,9) (3,22) (23,31) (19,10) (16,24) (8,19) (0,4) (23,13) (2,0) (0,14) (18,22) (3,13) (27,22) (30,23) (1,0) (23,2) (27,15) (5,7) (5,6) (3,0) (13,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1445", "image": "data/cycle/graph_visual/hard/graph1445.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,2) (9,26) (21,7) (15,8) (16,20) (11,8) (0,3) (13,9) (25,14) (18,10) (17,23) (11,2) (2,5) (12,18) (3,22) (2,17) (0,1) (21,1) (11,22) (14,18) (15,28) (29,20) (1,4) (0,6) (8,9) (28,19) (21,20) (24,25) (6,15) (18,28) (23,4) (27,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph319", "image": "data/cycle/graph_visual/hard/graph319.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (10,27) (0,4) (25,12) (22,11) (2,8) (22,9) (12,21) (20,17) (28,4) (11,13) (11,0) (18,16) (15,11) (5,16) (6,17) (0,18) (28,8) (7,26) (12,3) (24,26) (12,1) (23,17) (7,12) (1,19) (27,19) (13,14) (17,24) (7,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1960", "image": "data/cycle/graph_visual/hard/graph1960.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (14,20) (18,29) (23,17) (3,0) (14,29) (32,14) (1,11) (15,7) (19,28) (29,34) (13,22) (5,29) (15,10) (21,22) (22,20) (8,2) (26,33) (9,23) (25,17) (16,24) (3,1) (15,12) (13,27) (31,26) (10,2) (4,13) (25,14) (0,6) (30,26) (1,0) (22,16) (32,19) (3,9) (21,7) (0,33) (5,31) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1867", "image": "data/cycle/graph_visual/hard/graph1867.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (11,1) (21,11) (19,24) (24,23) (3,10) (13,23) (30,22) (25,4) (24,25) (15,14) (33,2) (5,26) (27,31) (28,19) (8,29) (24,22) (18,13) (1,0) (5,0) (31,17) (24,11) (28,7) (29,9) (5,28) (16,13) (29,6) (21,32) (16,10) (15,12) (16,2) (12,23) (27,11) (5,29) (13,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1788", "image": "data/cycle/graph_visual/hard/graph1788.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (26,10) (15,9) (7,28) (2,4) (1,0) (22,10) (16,6) (1,27) (13,0) (8,23) (6,31) (7,24) (19,32) (29,31) (25,29) (13,20) (20,30) (19,3) (23,1) (18,8) (18,14) (3,0) (8,24) (28,12) (32,26) (21,4) (29,11) (19,30) (17,11) (29,13) (15,16) (27,5) (0,2) (23,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph621", "image": "data/cycle/graph_visual/hard/graph621.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,5) (8,16) (8,7) (10,27) (24,2) (21,0) (14,26) (25,10) (0,11) (24,6) (15,3) (13,18) (12,17) (23,9) (24,4) (31,17) (23,21) (29,1) (5,26) (29,20) (15,10) (6,18) (2,21) (30,10) (3,7) (5,22) (29,28) (11,19) (14,13) (27,28) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph37", "image": "data/cycle/graph_visual/hard/graph37.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (1,6) (8,15) (17,2) (9,5) (18,10) (18,23) (6,12) (7,13) (0,4) (2,19) (9,15) (23,21) (22,6) (14,3) (25,15) (25,17) (14,7) (14,19) (12,20) (12,11) (4,17) (16,10) (1,15) (23,17) (24,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph769", "image": "data/cycle/graph_visual/hard/graph769.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (24,8) (2,12) (0,32) (13,0) (20,26) (21,16) (12,14) (0,11) (15,28) (8,18) (15,9) (29,17) (10,19) (27,8) (14,11) (4,21) (3,21) (10,7) (23,7) (6,0) (29,21) (9,3) (11,5) (29,7) (22,14) (11,25) (8,19) (20,27) (30,28) (1,25) (26,31) (12,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1388", "image": "data/cycle/graph_visual/hard/graph1388.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,19) (5,4) (24,22) (9,7) (15,12) (11,23) (14,20) (5,18) (4,28) (26,24) (10,26) (3,0) (17,13) (2,0) (7,11) (16,12) (17,0) (16,1) (10,9) (2,26) (27,23) (19,25) (21,14) (0,28) (4,21) (8,17) (15,26) (21,9) (6,10) (1,0) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1121", "image": "data/cycle/graph_visual/hard/graph1121.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (16,0) (15,22) (21,3) (0,1) (4,7) (18,11) (4,14) (24,17) (23,0) (9,21) (5,22) (19,14) (9,1) (13,12) (18,25) (12,26) (1,2) (22,10) (19,17) (11,8) (6,24) (20,25) (13,24) (14,3) (19,15) (11,19) (13,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1396", "image": "data/cycle/graph_visual/hard/graph1396.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,7) (11,26) (18,7) (27,22) (13,15) (23,0) (2,0) (3,12) (14,1) (3,25) (19,18) (4,23) (27,24) (1,0) (24,20) (19,16) (6,26) (3,0) (17,20) (16,9) (21,23) (10,21) (14,10) (14,17) (28,3) (5,11) (17,5) (8,15) (2,22) (25,24) (23,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1005", "image": "data/cycle/graph_visual/hard/graph1005.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,24) (23,4) (17,12) (11,5) (24,25) (11,8) (1,16) (20,2) (18,21) (0,19) (7,15) (4,16) (19,11) (14,0) (24,4) (8,3) (1,0) (18,16) (6,18) (10,9) (0,7) (13,9) (12,11) (10,3) (22,3) (13,2) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1124", "image": "data/cycle/graph_visual/hard/graph1124.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,16) (3,4) (7,12) (23,19) (8,14) (9,14) (21,17) (0,2) (22,6) (24,12) (25,13) (12,20) (3,15) (1,0) (9,1) (21,22) (22,5) (14,10) (26,4) (4,11) (2,16) (0,3) (18,21) (21,13) (20,2) (0,4) (6,19) (25,7) (26,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1182", "image": "data/cycle/graph_visual/hard/graph1182.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (3,0) (24,5) (11,17) (23,1) (12,17) (3,25) (26,3) (20,2) (3,13) (9,25) (6,7) (14,23) (5,26) (18,12) (2,4) (1,0) (15,19) (11,8) (24,8) (9,10) (7,16) (17,16) (1,7) (15,4) (12,0) (24,22) (9,21) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph139", "image": "data/cycle/graph_visual/hard/graph139.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,0) (5,8) (23,26) (7,15) (8,4) (0,3) (20,1) (25,21) (2,4) (23,9) (3,9) (8,25) (2,12) (23,25) (13,6) (1,19) (14,10) (19,2) (9,13) (11,8) (15,0) (3,22) (17,15) (20,24) (9,18) (16,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1237", "image": "data/cycle/graph_visual/hard/graph1237.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (24,13) (12,19) (21,10) (0,19) (19,14) (11,27) (3,0) (13,10) (9,6) (11,17) (0,7) (22,9) (25,6) (15,22) (5,26) (20,2) (2,10) (1,2) (2,18) (16,8) (27,7) (4,23) (2,0) (18,27) (5,14) (22,21) (27,4) (1,0) (8,4) (24,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph226", "image": "data/cycle/graph_visual/hard/graph226.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (2,10) (13,19) (24,9) (16,24) (17,14) (21,25) (27,0) (2,8) (14,15) (24,26) (0,15) (1,4) (15,11) (24,0) (19,24) (12,20) (3,6) (20,18) (12,13) (22,6) (12,25) (26,23) (15,3) (7,25) (5,27) (4,18) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph174", "image": "data/cycle/graph_visual/hard/graph174.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (18,10) (20,2) (5,23) (4,9) (0,26) (14,21) (24,9) (25,15) (16,19) (26,21) (17,9) (22,11) (18,23) (15,12) (14,6) (1,7) (0,13) (25,17) (10,21) (0,7) (24,5) (12,22) (2,3) (0,19) (15,20) (8,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph548", "image": "data/cycle/graph_visual/hard/graph548.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (4,15) (0,2) (1,27) (16,17) (1,7) (7,16) (9,23) (30,29) (11,17) (3,26) (18,23) (28,24) (25,9) (19,12) (3,8) (30,6) (24,25) (13,9) (10,7) (11,8) (5,24) (21,2) (6,8) (12,0) (5,26) (3,14) (4,2) (15,20) (29,22) (12,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1732", "image": "data/cycle/graph_visual/hard/graph1732.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,17) (23,15) (15,9) (6,12) (12,27) (18,22) (28,32) (26,11) (8,15) (0,1) (2,0) (18,30) (11,24) (29,24) (0,17) (16,30) (25,0) (2,16) (4,5) (30,13) (14,13) (5,32) (7,20) (4,12) (31,1) (21,20) (10,12) (11,21) (14,12) (16,31) (19,7) (32,9) (3,20) (7,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1090", "image": "data/cycle/graph_visual/hard/graph1090.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,18) (25,11) (15,7) (2,17) (5,12) (17,6) (0,3) (23,6) (4,0) (21,10) (0,1) (24,2) (0,13) (5,22) (3,9) (23,9) (8,1) (4,21) (8,21) (21,16) (19,7) (25,21) (4,13) (7,20) (0,9) (20,23) (0,2) (20,14) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph656", "image": "data/cycle/graph_visual/hard/graph656.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,26) (17,18) (12,3) (6,17) (12,28) (20,19) (29,7) (18,10) (12,7) (1,6) (9,11) (7,2) (14,16) (5,25) (6,4) (24,4) (31,25) (26,30) (16,20) (2,0) (29,24) (22,12) (9,16) (13,6) (27,25) (1,26) (21,20) (6,27) (23,4) (19,1) (22,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph613", "image": "data/cycle/graph_visual/hard/graph613.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,17) (18,9) (8,21) (0,6) (5,20) (14,3) (1,23) (20,15) (21,26) (21,29) (22,0) (1,3) (2,21) (4,10) (27,12) (31,30) (3,28) (23,25) (5,10) (15,1) (16,13) (27,31) (0,24) (7,8) (6,31) (30,4) (10,21) (23,19) (16,17) (9,11) (6,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1920", "image": "data/cycle/graph_visual/hard/graph1920.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (14,30) (16,9) (22,1) (4,3) (6,10) (10,27) (7,24) (11,25) (2,7) (22,15) (13,30) (5,33) (7,8) (23,22) (20,2) (26,14) (6,5) (10,3) (13,25) (28,18) (4,30) (19,10) (4,7) (9,11) (25,23) (21,13) (5,12) (18,34) (32,4) (31,0) (1,0) (17,7) (5,18) (29,18) (31,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph345", "image": "data/cycle/graph_visual/hard/graph345.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (28,12) (8,7) (16,25) (25,6) (3,21) (14,10) (19,23) (21,4) (24,11) (18,14) (18,1) (27,13) (15,26) (5,2) (25,11) (5,9) (14,21) (12,6) (8,22) (6,7) (20,14) (2,0) (14,26) (27,25) (19,26) (6,15) (5,12) (23,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph686", "image": "data/cycle/graph_visual/hard/graph686.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,21) (29,27) (28,22) (24,11) (13,17) (10,15) (8,29) (12,14) (19,24) (6,28) (19,26) (5,25) (16,13) (3,25) (21,11) (28,5) (11,1) (7,29) (29,4) (24,22) (11,27) (20,5) (12,23) (13,31) (10,2) (18,24) (9,16) (24,23) (13,23) (0,5) (31,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph369", "image": "data/cycle/graph_visual/hard/graph369.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (28,19) (21,1) (20,16) (3,22) (15,27) (23,17) (2,5) (17,2) (18,12) (8,9) (0,6) (4,1) (28,18) (18,10) (26,9) (2,11) (18,14) (8,15) (25,22) (7,21) (23,4) (24,14) (11,8) (26,25) (15,6) (21,28) (20,11) (13,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1789", "image": "data/cycle/graph_visual/hard/graph1789.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (26,0) (24,5) (2,14) (31,20) (32,22) (21,6) (0,1) (15,22) (9,20) (28,20) (26,19) (20,23) (7,32) (13,6) (20,1) (2,1) (10,1) (25,11) (17,25) (2,0) (30,0) (10,3) (27,30) (17,8) (10,18) (13,12) (3,7) (32,8) (22,21) (28,29) (5,16) (23,4) (15,30) (21,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph881", "image": "data/cycle/graph_visual/hard/graph881.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (32,31) (3,32) (8,19) (15,18) (1,9) (26,0) (14,18) (2,24) (27,5) (11,5) (30,22) (29,0) (9,30) (29,23) (4,33) (20,16) (8,10) (11,9) (2,21) (16,14) (17,4) (17,15) (3,6) (14,1) (28,24) (6,19) (13,9) (25,21) (7,19) (18,12) (15,2) (10,26) (19,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1627", "image": "data/cycle/graph_visual/hard/graph1627.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (1,0) (8,5) (17,4) (23,19) (6,3) (13,18) (22,25) (12,15) (31,0) (24,26) (0,2) (11,31) (27,15) (2,21) (7,31) (14,17) (21,17) (15,25) (27,16) (10,20) (31,23) (4,26) (29,13) (18,11) (18,1) (0,10) (7,28) (20,30) (24,22) (5,0) (3,0) (10,25) (9,11) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph556", "image": "data/cycle/graph_visual/hard/graph556.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,11) (15,17) (27,4) (13,27) (1,13) (15,16) (26,22) (3,18) (0,18) (7,2) (30,4) (6,14) (2,10) (16,26) (5,1) (25,20) (11,1) (29,23) (10,15) (21,15) (28,30) (12,13) (9,1) (24,8) (8,20) (6,0) (7,30) (5,25) (19,18) (14,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1483", "image": "data/cycle/graph_visual/hard/graph1483.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,13) (0,1) (27,13) (27,12) (11,7) (25,3) (9,29) (29,11) (10,8) (25,19) (1,3) (0,21) (19,2) (14,18) (23,14) (17,25) (25,29) (5,2) (2,0) (10,17) (13,22) (5,6) (20,27) (26,14) (24,26) (28,17) (4,1) (26,16) (21,17) (16,10) (15,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1019", "image": "data/cycle/graph_visual/hard/graph1019.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,4) (22,17) (2,15) (22,19) (2,24) (25,22) (0,1) (0,11) (8,9) (0,3) (10,14) (1,4) (10,21) (23,4) (3,23) (8,0) (17,20) (16,15) (12,8) (12,24) (18,20) (16,19) (7,3) (22,10) (11,3) (13,24) (17,6) (6,5) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1617", "image": "data/cycle/graph_visual/hard/graph1617.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (1,17) (15,4) (18,11) (10,8) (31,17) (2,7) (30,10) (8,13) (30,26) (27,10) (26,16) (0,2) (4,10) (12,2) (24,22) (28,14) (5,3) (3,30) (0,15) (28,19) (26,9) (31,24) (28,23) (2,21) (0,20) (1,0) (11,22) (26,7) (31,29) (24,2) (0,25) (23,6) (14,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1838", "image": "data/cycle/graph_visual/hard/graph1838.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (14,24) (29,22) (4,25) (6,17) (0,33) (3,13) (10,33) (3,25) (29,5) (32,8) (10,26) (0,1) (1,15) (1,25) (19,8) (0,2) (0,20) (11,13) (7,31) (17,7) (9,1) (1,23) (16,12) (18,5) (4,22) (25,28) (3,0) (15,17) (30,27) (4,24) (33,19) (31,19) (21,15) (2,18) (6,27) (8,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph939", "image": "data/cycle/graph_visual/hard/graph939.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (27,16) (1,14) (15,33) (19,7) (14,15) (23,30) (17,28) (23,5) (16,8) (0,3) (27,33) (13,10) (28,25) (21,23) (3,5) (9,13) (1,11) (20,11) (10,6) (20,34) (32,26) (22,34) (12,2) (24,27) (20,29) (2,17) (18,25) (10,32) (11,10) (31,24) (32,19) (29,23) (1,2) (5,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1068", "image": "data/cycle/graph_visual/hard/graph1068.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (22,12) (23,19) (20,21) (13,3) (17,6) (18,24) (0,14) (24,4) (3,12) (16,17) (0,1) (7,10) (9,20) (23,8) (0,10) (11,24) (16,3) (18,0) (2,15) (24,25) (1,25) (22,2) (23,16) (9,23) (14,13) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1207", "image": "data/cycle/graph_visual/hard/graph1207.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,0) (13,20) (2,0) (27,26) (22,1) (13,5) (20,10) (6,12) (26,3) (14,21) (0,27) (6,3) (8,2) (24,18) (23,2) (8,11) (8,4) (0,25) (10,17) (9,10) (10,24) (11,10) (21,0) (4,16) (15,12) (16,25) (11,7) (1,19) (5,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1541", "image": "data/cycle/graph_visual/hard/graph1541.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,22) (29,2) (13,0) (14,15) (12,4) (7,20) (27,5) (24,29) (0,28) (3,9) (1,12) (18,15) (11,4) (28,14) (10,19) (13,30) (0,1) (21,2) (25,23) (25,20) (27,26) (7,1) (8,16) (10,28) (9,18) (5,4) (2,0) (7,8) (6,9) (25,17) (21,27) (28,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1926", "image": "data/cycle/graph_visual/hard/graph1926.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (9,10) (5,1) (23,16) (31,9) (17,32) (29,19) (18,12) (10,0) (1,0) (4,0) (33,3) (33,10) (14,30) (16,22) (2,0) (16,29) (28,18) (17,13) (6,2) (17,8) (4,7) (24,34) (25,27) (21,1) (5,17) (20,22) (20,14) (7,25) (23,33) (21,7) (26,19) (15,6) (11,16) (4,15) (13,24) (25,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph980", "image": "data/cycle/graph_visual/hard/graph980.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (15,20) (34,21) (25,4) (21,2) (26,28) (31,7) (10,18) (27,32) (33,31) (13,16) (23,0) (18,11) (1,23) (0,15) (22,0) (2,14) (4,9) (34,5) (29,14) (30,12) (33,19) (8,26) (2,28) (32,17) (10,3) (26,6) (30,14) (32,11) (26,27) (9,5) (7,23) (13,30) (9,1) (24,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph374", "image": "data/cycle/graph_visual/hard/graph374.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (6,12) (15,6) (24,25) (7,12) (27,23) (27,14) (17,2) (25,4) (3,20) (9,22) (22,21) (5,6) (8,26) (0,14) (16,21) (18,24) (1,22) (26,14) (3,28) (18,10) (5,13) (0,24) (4,19) (2,22) (5,11) (21,5) (20,23) (23,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1371", "image": "data/cycle/graph_visual/hard/graph1371.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (2,21) (16,7) (23,18) (10,7) (0,2) (14,3) (1,25) (16,17) (12,19) (8,11) (20,15) (0,1) (1,7) (24,27) (9,25) (5,24) (6,8) (0,4) (3,26) (15,4) (9,13) (28,6) (2,4) (0,12) (8,3) (5,26) (9,22) (24,23) (17,12) (17,11) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph186", "image": "data/cycle/graph_visual/hard/graph186.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (2,16) (0,26) (10,19) (17,8) (4,11) (17,5) (6,22) (13,20) (0,18) (8,20) (19,2) (17,15) (26,12) (7,6) (15,22) (15,19) (11,15) (12,15) (18,3) (7,21) (26,24) (17,25) (17,23) (7,1) (14,18) (4,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph332", "image": "data/cycle/graph_visual/hard/graph332.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (17,22) (18,21) (20,4) (2,1) (7,28) (0,22) (22,25) (27,12) (17,14) (10,26) (13,22) (4,12) (10,7) (22,24) (19,21) (16,11) (4,19) (2,25) (5,8) (5,11) (11,9) (22,23) (23,6) (9,23) (19,15) (20,0) (19,3) (25,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1159", "image": "data/cycle/graph_visual/hard/graph1159.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (26,8) (0,4) (12,11) (17,13) (18,10) (0,2) (7,0) (5,4) (26,6) (17,24) (0,3) (16,2) (17,3) (21,11) (1,0) (14,25) (12,19) (7,5) (12,8) (16,20) (21,18) (22,17) (17,16) (20,10) (1,26) (26,7) (23,14) (9,7) (22,23) (15,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph922", "image": "data/cycle/graph_visual/hard/graph922.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,15) (8,21) (22,23) (17,23) (10,21) (30,23) (31,32) (3,14) (3,1) (33,21) (25,32) (19,6) (5,10) (10,4) (20,15) (3,31) (13,16) (9,11) (28,1) (27,12) (5,20) (2,21) (24,0) (27,23) (4,30) (34,23) (6,0) (33,16) (21,29) (8,7) (9,18) (31,6) (0,26) (17,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1954", "image": "data/cycle/graph_visual/hard/graph1954.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (23,25) (9,24) (30,0) (1,25) (9,2) (3,0) (11,9) (34,14) (16,2) (22,8) (34,19) (3,8) (25,10) (15,23) (4,0) (34,13) (3,2) (8,14) (7,1) (12,32) (15,13) (21,25) (26,13) (0,2) (17,8) (14,20) (26,29) (0,1) (30,5) (33,21) (28,27) (31,21) (7,18) (7,5) (28,33) (7,6) (12,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1800", "image": "data/cycle/graph_visual/hard/graph1800.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (32,22) (32,5) (17,21) (33,7) (28,29) (14,12) (32,25) (30,6) (3,25) (2,10) (27,23) (0,1) (28,12) (20,31) (2,0) (29,4) (0,13) (13,29) (3,16) (10,3) (11,23) (24,16) (1,2) (15,1) (30,8) (20,32) (14,23) (22,18) (8,19) (9,17) (10,26) (3,21) (8,22) (14,8) (9,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1192", "image": "data/cycle/graph_visual/hard/graph1192.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (4,18) (7,23) (3,0) (26,23) (17,0) (0,26) (16,13) (17,12) (25,7) (0,2) (19,12) (2,26) (22,15) (12,15) (3,9) (6,5) (1,20) (9,21) (4,20) (1,13) (21,6) (6,22) (8,23) (11,23) (20,24) (0,1) (3,10) (14,8) (21,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph71", "image": "data/cycle/graph_visual/hard/graph71.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (11,24) (25,6) (25,9) (14,13) (22,5) (3,2) (20,17) (18,14) (23,13) (15,18) (21,7) (15,10) (4,10) (16,8) (3,19) (4,3) (24,2) (21,8) (23,1) (13,0) (4,12) (18,21) (20,10) (13,6) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph358", "image": "data/cycle/graph_visual/hard/graph358.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (5,0) (8,23) (19,5) (8,28) (3,1) (25,5) (7,12) (24,21) (25,24) (16,21) (7,6) (17,20) (15,9) (13,15) (22,3) (20,15) (28,5) (4,14) (6,26) (18,15) (2,21) (10,3) (27,22) (10,11) (8,6) (9,14) (16,10) (28,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1879", "image": "data/cycle/graph_visual/hard/graph1879.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (27,20) (7,22) (14,30) (3,18) (33,22) (16,2) (27,31) (0,17) (31,14) (26,28) (11,8) (14,10) (22,16) (11,19) (1,27) (0,3) (25,0) (29,8) (16,8) (13,18) (4,21) (27,23) (5,9) (9,17) (6,11) (27,28) (0,1) (12,9) (18,1) (0,4) (32,23) (0,2) (13,4) (16,5) (8,24) (15,14) (7,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph789", "image": "data/cycle/graph_visual/hard/graph789.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (27,28) (21,14) (16,5) (20,22) (24,12) (23,3) (30,8) (31,1) (18,9) (26,21) (2,17) (14,15) (14,20) (11,5) (6,12) (4,21) (6,19) (32,12) (17,21) (27,6) (31,0) (21,10) (13,20) (17,27) (22,9) (14,0) (23,22) (25,4) (29,5) (4,5) (15,7) (30,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph940", "image": "data/cycle/graph_visual/hard/graph940.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,16) (20,14) (4,8) (24,17) (20,17) (26,13) (28,11) (33,1) (7,31) (6,19) (22,18) (9,21) (20,29) (23,24) (16,28) (18,8) (29,10) (31,2) (6,5) (12,8) (7,28) (24,28) (9,13) (4,25) (26,15) (32,22) (8,34) (3,18) (5,2) (7,0) (25,15) (30,6) (32,27) (31,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph931", "image": "data/cycle/graph_visual/hard/graph931.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (25,26) (32,10) (13,4) (7,15) (10,0) (2,17) (29,3) (20,34) (8,33) (16,28) (32,3) (21,18) (19,26) (17,20) (31,15) (4,22) (24,19) (18,33) (7,23) (20,3) (11,20) (7,20) (5,30) (31,28) (33,12) (19,33) (30,27) (4,23) (14,30) (18,13) (9,11) (6,34) (27,17) (14,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph61", "image": "data/cycle/graph_visual/hard/graph61.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (19,24) (6,1) (7,23) (20,10) (1,17) (11,9) (18,2) (19,13) (8,14) (9,18) (6,4) (13,9) (18,3) (25,22) (20,14) (12,11) (6,16) (15,6) (0,15) (23,8) (25,6) (12,21) (0,3) (5,6) (14,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1810", "image": "data/cycle/graph_visual/hard/graph1810.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (32,17) (22,13) (26,6) (8,16) (29,15) (26,1) (8,12) (13,9) (27,1) (28,8) (0,33) (15,4) (9,25) (19,26) (20,8) (17,14) (33,31) (28,14) (13,21) (10,23) (2,0) (20,26) (7,2) (11,32) (12,0) (0,3) (1,0) (11,5) (8,3) (18,29) (11,30) (25,12) (6,4) (24,12) (14,7) (10,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1610", "image": "data/cycle/graph_visual/hard/graph1610.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,23) (27,8) (0,2) (18,16) (29,15) (10,13) (20,4) (12,17) (31,15) (26,18) (0,6) (28,22) (2,10) (7,29) (31,9) (14,31) (3,0) (1,2) (13,0) (22,24) (19,11) (27,3) (16,29) (26,2) (2,25) (26,24) (11,30) (5,30) (29,8) (8,23) (17,20) (4,15) (21,23) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph450", "image": "data/cycle/graph_visual/hard/graph450.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (16,21) (22,21) (6,15) (22,17) (9,19) (0,12) (19,2) (13,23) (7,11) (4,24) (13,27) (17,2) (12,1) (10,5) (16,12) (23,19) (23,8) (25,6) (2,14) (24,12) (29,28) (15,26) (6,18) (3,6) (19,18) (20,8) (7,5) (4,7) (28,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1962", "image": "data/cycle/graph_visual/hard/graph1962.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,2) (18,30) (28,27) (1,0) (8,1) (5,11) (5,3) (16,19) (30,12) (7,10) (29,6) (28,34) (31,27) (28,20) (26,30) (33,24) (17,15) (4,29) (12,11) (21,6) (9,1) (33,0) (2,34) (32,24) (23,25) (10,23) (21,16) (34,22) (13,32) (0,2) (12,0) (14,7) (33,8) (9,22) (15,27) (3,21) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1971", "image": "data/cycle/graph_visual/hard/graph1971.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,1) (12,22) (1,17) (21,10) (23,7) (22,13) (2,9) (4,12) (34,8) (27,26) (31,29) (20,28) (30,18) (1,19) (16,33) (16,11) (34,18) (13,28) (31,32) (30,12) (21,7) (5,24) (27,20) (0,17) (0,23) (25,24) (12,3) (20,15) (6,17) (6,9) (14,34) (26,17) (5,19) (5,11) (4,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph434", "image": "data/cycle/graph_visual/hard/graph434.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,18) (28,4) (16,22) (23,29) (5,28) (23,4) (12,1) (17,8) (9,19) (4,14) (7,24) (29,10) (6,5) (0,14) (12,8) (21,7) (2,10) (12,27) (15,28) (24,22) (23,20) (27,24) (25,18) (7,3) (12,11) (13,18) (21,26) (17,9) (0,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1262", "image": "data/cycle/graph_visual/hard/graph1262.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,14) (1,0) (3,9) (14,17) (4,0) (1,22) (10,26) (24,10) (19,15) (22,19) (9,4) (8,14) (2,0) (18,14) (7,13) (7,11) (21,16) (27,1) (2,7) (20,25) (26,13) (17,23) (13,0) (3,0) (17,2) (6,20) (6,8) (12,14) (27,9) (16,5) (20,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph710", "image": "data/cycle/graph_visual/hard/graph710.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (13,19) (25,4) (25,22) (32,29) (5,22) (1,6) (14,28) (21,26) (18,9) (2,10) (18,26) (30,13) (29,10) (6,31) (20,7) (13,6) (28,17) (6,24) (4,24) (19,9) (0,2) (16,4) (28,12) (23,32) (15,20) (12,9) (26,8) (11,27) (4,3) (9,20) (23,16) (26,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph435", "image": "data/cycle/graph_visual/hard/graph435.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (17,29) (20,3) (5,1) (19,16) (5,24) (15,16) (20,21) (20,5) (26,6) (2,20) (22,17) (26,7) (18,28) (23,16) (19,26) (9,21) (27,10) (8,11) (16,28) (14,15) (29,2) (13,28) (0,18) (25,28) (20,12) (14,9) (15,8) (4,7) (10,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1998", "image": "data/cycle/graph_visual/hard/graph1998.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,13) (1,27) (10,17) (31,19) (0,3) (19,11) (2,0) (0,4) (33,15) (23,0) (21,5) (28,14) (10,9) (21,11) (26,14) (1,0) (21,32) (22,18) (28,9) (24,7) (15,28) (3,29) (11,24) (13,32) (2,32) (16,1) (18,34) (34,6) (22,25) (29,19) (28,1) (27,22) (24,14) (8,30) (8,4) (20,18) (12,30) (0,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph58", "image": "data/cycle/graph_visual/hard/graph58.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (13,23) (14,11) (18,16) (7,23) (12,23) (17,11) (25,14) (0,21) (16,25) (20,1) (20,3) (3,21) (22,19) (25,19) (5,2) (10,16) (20,8) (9,12) (9,24) (21,14) (1,15) (6,21) (19,2) (14,13) (19,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph707", "image": "data/cycle/graph_visual/hard/graph707.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,9) (5,3) (31,7) (20,1) (4,9) (5,23) (21,29) (12,1) (30,25) (2,30) (16,28) (18,9) (27,24) (7,12) (24,6) (29,6) (17,15) (22,4) (15,31) (31,5) (23,26) (11,26) (22,19) (16,31) (10,14) (32,6) (15,10) (19,11) (2,21) (22,13) (3,29) (28,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1136", "image": "data/cycle/graph_visual/hard/graph1136.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (20,14) (18,8) (0,5) (26,1) (17,13) (6,1) (20,8) (2,19) (17,4) (25,0) (11,3) (10,20) (9,16) (9,24) (19,11) (21,17) (3,7) (24,18) (15,12) (6,23) (22,13) (16,15) (10,2) (18,6) (7,22) (0,24) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph872", "image": "data/cycle/graph_visual/hard/graph872.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (25,9) (18,32) (1,30) (16,31) (7,6) (28,15) (29,11) (4,3) (5,30) (22,14) (0,13) (11,3) (27,6) (19,12) (29,23) (2,9) (4,27) (19,20) (33,4) (6,26) (16,19) (8,33) (10,5) (1,7) (13,7) (13,18) (28,8) (23,17) (24,2) (23,24) (21,17) (32,31) (22,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1342", "image": "data/cycle/graph_visual/hard/graph1342.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,7) (5,3) (24,28) (12,18) (8,27) (22,16) (24,12) (0,4) (12,20) (0,3) (27,18) (24,5) (18,21) (22,20) (5,0) (11,5) (9,22) (0,23) (13,1) (6,22) (1,0) (16,2) (17,4) (2,0) (25,16) (17,0) (15,9) (10,3) (7,19) (9,26) (12,13) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1512", "image": "data/cycle/graph_visual/hard/graph1512.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (4,13) (17,22) (8,28) (4,22) (7,26) (21,10) (25,4) (24,14) (21,13) (28,19) (16,15) (20,10) (1,12) (0,2) (19,5) (6,2) (1,0) (14,5) (23,21) (9,5) (13,14) (27,0) (30,7) (3,27) (6,10) (11,20) (3,22) (12,0) (29,10) (16,24) (30,4) (18,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph486", "image": "data/cycle/graph_visual/hard/graph486.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (19,6) (3,4) (22,6) (7,12) (9,22) (14,4) (2,16) (29,0) (9,5) (2,20) (15,14) (3,18) (21,26) (21,13) (4,26) (29,8) (12,20) (1,3) (13,25) (16,10) (17,10) (22,21) (24,8) (24,10) (25,12) (28,7) (27,19) (14,11) (23,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph888", "image": "data/cycle/graph_visual/hard/graph888.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (19,2) (4,29) (16,22) (8,17) (17,6) (1,21) (30,8) (16,32) (18,28) (7,19) (20,11) (12,31) (1,4) (20,22) (14,16) (26,4) (33,20) (19,5) (31,13) (17,9) (24,30) (11,2) (27,4) (26,10) (9,26) (3,9) (2,3) (21,23) (0,25) (18,7) (13,27) (15,5) (7,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph612", "image": "data/cycle/graph_visual/hard/graph612.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,28) (14,10) (8,22) (26,11) (26,30) (1,2) (24,10) (17,14) (20,21) (26,21) (7,5) (31,30) (19,27) (22,12) (9,25) (14,15) (27,25) (6,28) (22,3) (4,18) (28,26) (18,5) (29,12) (14,26) (17,19) (31,5) (1,13) (2,6) (4,0) (12,27) (22,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1171", "image": "data/cycle/graph_visual/hard/graph1171.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (17,2) (4,5) (20,23) (22,5) (6,23) (10,21) (26,4) (25,21) (0,13) (3,9) (9,0) (18,4) (20,7) (23,9) (7,15) (24,2) (4,13) (25,11) (5,12) (6,17) (8,1) (21,26) (8,21) (20,14) (0,1) (16,21) (7,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph324", "image": "data/cycle/graph_visual/hard/graph324.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,2) (23,22) (20,0) (22,17) (22,0) (28,7) (14,17) (19,4) (10,7) (9,23) (21,19) (22,25) (24,22) (6,23) (5,11) (2,1) (13,22) (4,20) (12,4) (7,25) (8,5) (19,3) (16,11) (21,18) (27,12) (11,9) (10,26) (19,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1500", "image": "data/cycle/graph_visual/hard/graph1500.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,20) (13,20) (24,0) (19,11) (13,9) (25,23) (0,2) (0,8) (1,11) (3,0) (0,27) (28,23) (2,1) (16,29) (10,17) (19,27) (11,12) (20,3) (12,22) (23,30) (0,1) (28,21) (12,29) (5,26) (3,12) (19,6) (7,14) (16,5) (18,26) (9,15) (16,7) (4,18) (10,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph263", "image": "data/cycle/graph_visual/hard/graph263.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (15,2) (26,27) (12,13) (18,2) (20,9) (25,27) (2,26) (1,19) (23,24) (5,8) (21,16) (6,17) (15,8) (2,11) (23,12) (2,14) (9,4) (9,6) (9,26) (27,21) (21,7) (20,22) (10,21) (1,7) (14,0) (23,19) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph889", "image": "data/cycle/graph_visual/hard/graph889.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (30,9) (27,28) (0,15) (11,22) (17,31) (24,5) (5,33) (23,2) (16,2) (17,14) (0,28) (20,11) (7,2) (14,30) (32,31) (8,10) (4,10) (24,25) (12,23) (26,31) (29,10) (26,13) (1,17) (22,0) (7,26) (28,21) (24,2) (3,32) (18,8) (6,3) (4,15) (30,10) (26,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1714", "image": "data/cycle/graph_visual/hard/graph1714.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,13) (22,3) (19,8) (3,0) (11,13) (1,32) (27,15) (5,7) (25,26) (6,24) (31,5) (16,24) (20,0) (11,30) (27,28) (8,12) (1,0) (23,31) (27,22) (2,23) (29,2) (1,26) (6,5) (4,18) (1,9) (23,32) (13,3) (14,0) (18,22) (2,0) (17,28) (17,12) (1,21) (14,29) (19,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1648", "image": "data/cycle/graph_visual/hard/graph1648.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (8,7) (19,12) (5,29) (14,10) (11,30) (9,18) (23,1) (0,1) (31,5) (0,15) (3,9) (10,16) (7,30) (18,30) (1,19) (21,6) (31,4) (26,20) (3,0) (2,27) (22,19) (6,12) (2,10) (27,31) (28,31) (22,15) (5,25) (22,20) (0,11) (23,28) (8,24) (11,13) (2,0) (16,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph977", "image": "data/cycle/graph_visual/hard/graph977.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (26,17) (24,10) (10,3) (28,8) (26,27) (11,17) (32,0) (30,28) (8,0) (11,24) (29,4) (34,22) (25,13) (31,8) (29,1) (34,10) (7,23) (20,15) (0,13) (8,4) (10,13) (24,21) (16,2) (6,15) (13,33) (18,7) (14,15) (12,1) (0,15) (22,5) (6,23) (19,30) (9,33) (3,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph833", "image": "data/cycle/graph_visual/hard/graph833.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (7,33) (30,27) (21,16) (1,2) (20,1) (32,8) (25,11) (10,18) (7,3) (0,30) (17,8) (22,33) (14,2) (5,16) (29,28) (17,25) (4,23) (10,1) (15,30) (6,21) (13,6) (20,28) (21,22) (26,19) (22,15) (13,12) (32,20) (3,10) (23,20) (5,24) (26,0) (20,9) (31,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph721", "image": "data/cycle/graph_visual/hard/graph721.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (25,29) (11,17) (16,6) (7,28) (0,13) (13,29) (21,4) (31,6) (8,18) (10,22) (20,13) (23,8) (4,23) (29,11) (32,19) (23,1) (15,9) (14,18) (24,7) (12,28) (26,10) (2,4) (19,3) (29,31) (24,8) (30,20) (27,1) (0,1) (16,15) (30,19) (26,32) (5,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph393", "image": "data/cycle/graph_visual/hard/graph393.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,12) (10,16) (12,25) (19,26) (21,13) (15,10) (22,21) (4,14) (21,18) (26,4) (22,6) (16,2) (12,7) (27,7) (4,3) (10,24) (9,1) (8,28) (5,22) (20,2) (17,3) (6,19) (23,21) (24,8) (14,9) (0,3) (14,11) (13,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph507", "image": "data/cycle/graph_visual/hard/graph507.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,19) (21,27) (14,25) (22,29) (8,28) (3,12) (3,11) (16,26) (9,5) (1,27) (15,3) (14,3) (27,7) (16,19) (29,27) (25,24) (8,16) (11,6) (30,0) (28,20) (4,16) (18,9) (8,10) (14,5) (10,5) (6,23) (19,0) (14,29) (25,17) (13,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1040", "image": "data/cycle/graph_visual/hard/graph1040.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (16,15) (5,11) (0,16) (5,18) (7,2) (21,9) (0,2) (5,17) (12,9) (7,14) (15,23) (4,5) (0,3) (16,14) (1,0) (3,5) (6,2) (10,24) (25,10) (21,8) (11,13) (0,24) (20,5) (0,19) (20,8) (18,1) (22,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1107", "image": "data/cycle/graph_visual/hard/graph1107.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (2,15) (18,15) (11,10) (17,4) (20,24) (16,1) (12,24) (7,26) (3,0) (25,3) (21,4) (15,8) (0,2) (26,13) (13,23) (2,9) (1,0) (10,24) (11,22) (25,6) (6,23) (0,24) (18,19) (18,5) (8,14) (15,25) (0,8) (23,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1666", "image": "data/cycle/graph_visual/hard/graph1666.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (28,25) (26,9) (1,8) (2,29) (0,24) (19,24) (20,9) (30,23) (0,1) (24,5) (27,18) (3,7) (17,22) (10,14) (13,4) (13,18) (15,0) (8,30) (2,0) (10,16) (21,11) (28,9) (23,4) (24,17) (1,15) (1,7) (12,14) (10,20) (21,18) (16,3) (27,2) (6,31) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph222", "image": "data/cycle/graph_visual/hard/graph222.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (18,21) (11,15) (19,27) (22,1) (17,12) (12,22) (7,24) (11,18) (27,23) (21,24) (19,2) (8,6) (26,17) (4,26) (7,16) (0,6) (3,5) (13,24) (27,14) (7,17) (6,7) (24,10) (10,3) (18,19) (20,21) (27,25) (9,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1781", "image": "data/cycle/graph_visual/hard/graph1781.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (9,13) (11,6) (4,0) (32,27) (11,21) (14,8) (31,19) (21,5) (7,14) (10,15) (1,0) (22,12) (15,16) (11,29) (0,2) (13,24) (2,17) (31,5) (17,0) (20,30) (3,0) (18,5) (20,25) (3,24) (9,29) (25,1) (5,8) (27,0) (24,16) (13,26) (23,24) (30,5) (26,12) (25,2) (23,28) (12,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1910", "image": "data/cycle/graph_visual/hard/graph1910.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (31,25) (19,28) (26,22) (17,8) (24,12) (5,6) (27,5) (27,21) (30,31) (20,9) (15,2) (4,0) (5,12) (20,26) (12,2) (6,7) (13,32) (18,30) (0,1) (1,10) (34,12) (28,21) (2,0) (33,6) (26,14) (3,0) (15,13) (10,11) (23,13) (16,4) (25,5) (0,9) (20,8) (16,3) (20,21) (33,29) (4,6) (1,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph415", "image": "data/cycle/graph_visual/hard/graph415.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,3) (27,4) (13,3) (20,27) (16,19) (9,5) (16,25) (27,0) (14,3) (28,14) (28,18) (10,8) (3,11) (17,9) (14,5) (29,19) (29,26) (14,24) (10,5) (16,8) (27,8) (2,16) (11,6) (1,19) (15,25) (25,23) (21,29) (12,10) (22,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph429", "image": "data/cycle/graph_visual/hard/graph429.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,15) (9,13) (27,7) (5,12) (14,2) (19,26) (1,15) (0,20) (9,6) (2,6) (11,26) (16,8) (8,4) (10,8) (17,21) (5,7) (24,12) (3,22) (17,10) (29,23) (29,25) (26,2) (11,8) (22,26) (20,18) (15,26) (18,29) (23,2) (28,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph634", "image": "data/cycle/graph_visual/hard/graph634.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,7) (29,23) (13,18) (31,4) (2,24) (27,4) (6,27) (30,5) (29,1) (16,31) (20,19) (2,9) (11,8) (17,21) (7,13) (14,22) (8,28) (25,9) (28,15) (5,10) (4,22) (19,16) (12,19) (7,1) (23,24) (4,3) (23,17) (11,3) (0,13) (26,6) (30,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph439", "image": "data/cycle/graph_visual/hard/graph439.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,1) (11,8) (26,18) (27,11) (1,12) (7,1) (2,17) (24,0) (24,22) (23,15) (20,25) (9,16) (17,21) (25,22) (12,6) (10,13) (24,29) (21,19) (9,23) (26,5) (11,0) (15,14) (15,29) (24,28) (2,25) (26,6) (4,18) (20,1) (11,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph307", "image": "data/cycle/graph_visual/hard/graph307.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,15) (12,3) (27,24) (18,7) (17,20) (14,1) (3,28) (23,21) (23,8) (25,3) (24,20) (16,19) (27,22) (15,13) (2,22) (13,7) (11,5) (16,9) (10,14) (26,6) (18,19) (4,23) (24,25) (23,0) (14,17) (21,10) (11,26) (17,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph166", "image": "data/cycle/graph_visual/hard/graph166.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (18,9) (3,26) (3,4) (26,19) (23,13) (10,0) (0,23) (11,13) (11,15) (11,14) (14,25) (6,9) (26,11) (17,0) (8,17) (13,7) (21,8) (5,2) (20,19) (21,12) (15,16) (13,9) (13,22) (24,0) (5,8) (1,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1232", "image": "data/cycle/graph_visual/hard/graph1232.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,3) (25,23) (15,7) (16,2) (23,24) (25,8) (22,3) (5,8) (11,8) (26,20) (2,4) (1,19) (20,1) (0,1) (9,13) (2,19) (9,18) (21,25) (17,15) (27,23) (10,14) (9,27) (4,8) (0,15) (10,0) (3,9) (12,2) (13,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph848", "image": "data/cycle/graph_visual/hard/graph848.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (18,19) (0,22) (23,16) (22,17) (14,23) (20,24) (9,0) (3,5) (30,5) (33,9) (4,15) (4,27) (6,29) (13,33) (20,13) (2,33) (19,10) (26,21) (19,25) (1,12) (24,18) (3,24) (9,28) (11,14) (16,3) (27,32) (17,6) (22,7) (1,8) (10,32) (24,1) (23,31) (6,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1952", "image": "data/cycle/graph_visual/hard/graph1952.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (12,33) (4,13) (32,3) (33,18) (0,10) (18,21) (19,24) (28,16) (9,11) (20,17) (17,27) (7,15) (17,2) (14,30) (34,20) (23,7) (26,25) (19,33) (10,32) (1,14) (19,26) (30,5) (29,3) (0,1) (23,4) (3,20) (31,15) (6,34) (28,31) (13,18) (22,4) (20,7) (8,33) (11,20) (27,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1216", "image": "data/cycle/graph_visual/hard/graph1216.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (8,16) (26,15) (4,8) (22,26) (9,6) (11,8) (17,10) (2,26) (12,24) (11,26) (15,7) (17,21) (6,2) (22,3) (20,0) (23,2) (0,1) (9,13) (0,2) (18,20) (10,8) (27,18) (7,5) (23,20) (26,19) (7,25) (14,2) (15,1) (12,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1513", "image": "data/cycle/graph_visual/hard/graph1513.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,9) (7,11) (10,5) (4,24) (18,6) (22,17) (0,12) (17,2) (8,20) (30,2) (16,21) (22,21) (27,15) (1,12) (28,25) (6,15) (19,26) (23,8) (6,3) (4,7) (19,23) (6,25) (0,2) (18,19) (12,24) (14,2) (30,28) (1,0) (23,13) (7,5) (13,29) (12,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph323", "image": "data/cycle/graph_visual/hard/graph323.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,5) (6,27) (1,8) (20,7) (7,24) (20,23) (21,10) (7,18) (9,23) (9,0) (17,27) (3,9) (21,19) (17,2) (4,5) (5,15) (25,11) (28,14) (23,6) (21,4) (27,22) (13,0) (13,4) (4,28) (26,2) (8,21) (16,20) (12,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1725", "image": "data/cycle/graph_visual/hard/graph1725.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (18,8) (6,32) (13,25) (10,12) (12,25) (3,23) (32,15) (30,26) (5,31) (29,21) (0,1) (14,31) (20,1) (7,24) (5,25) (28,31) (8,9) (12,29) (29,23) (8,15) (2,11) (5,2) (24,30) (19,13) (31,22) (14,0) (0,2) (24,27) (6,16) (24,4) (1,17) (16,7) (17,26) (14,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph853", "image": "data/cycle/graph_visual/hard/graph853.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (21,0) (27,1) (3,4) (1,26) (24,13) (9,30) (27,19) (14,32) (5,7) (11,13) (10,24) (8,2) (24,18) (4,16) (20,1) (31,15) (30,0) (13,27) (7,31) (14,17) (33,31) (31,28) (1,29) (17,23) (6,20) (14,28) (33,1) (6,25) (22,28) (8,28) (16,1) (24,0) (12,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1938", "image": "data/cycle/graph_visual/hard/graph1938.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (19,13) (0,3) (10,29) (1,9) (4,26) (0,27) (21,17) (21,8) (1,0) (8,0) (28,14) (5,2) (33,4) (25,17) (3,20) (5,25) (10,24) (32,9) (11,22) (20,5) (12,4) (3,29) (14,9) (6,16) (19,21) (22,13) (5,30) (7,8) (21,18) (26,30) (16,26) (32,34) (9,15) (4,23) (29,31) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1264", "image": "data/cycle/graph_visual/hard/graph1264.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,12) (12,11) (3,14) (0,3) (6,23) (4,0) (14,7) (23,24) (25,17) (18,23) (1,15) (6,12) (0,2) (10,17) (4,17) (14,19) (6,1) (2,19) (27,16) (15,9) (14,26) (16,10) (5,9) (15,25) (15,8) (0,1) (2,17) (13,7) (18,21) (20,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph904", "image": "data/cycle/graph_visual/hard/graph904.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (18,17) (33,21) (11,9) (8,21) (34,23) (26,0) (4,30) (19,6) (8,7) (23,17) (30,23) (1,3) (16,13) (21,2) (10,21) (28,1) (27,12) (31,32) (31,6) (9,18) (31,3) (27,23) (10,4) (16,33) (21,29) (5,20) (6,0) (10,5) (25,32) (0,24) (22,23) (14,3) (20,15) (15,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph773", "image": "data/cycle/graph_visual/hard/graph773.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,16) (18,7) (3,28) (30,0) (11,15) (29,15) (23,20) (2,17) (3,26) (5,27) (0,22) (19,16) (21,14) (23,25) (25,6) (15,31) (6,9) (30,1) (12,4) (4,5) (18,21) (31,4) (16,8) (32,25) (21,8) (16,17) (11,24) (27,26) (9,14) (10,12) (13,4) (28,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1196", "image": "data/cycle/graph_visual/hard/graph1196.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,6) (2,14) (6,3) (23,13) (19,23) (25,15) (11,7) (15,6) (12,0) (5,7) (18,26) (19,18) (21,16) (8,20) (7,4) (17,2) (12,16) (24,12) (2,19) (12,1) (19,9) (21,22) (1,0) (24,4) (10,5) (23,8) (22,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph606", "image": "data/cycle/graph_visual/hard/graph606.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,3) (0,20) (23,6) (0,25) (30,10) (13,8) (22,11) (24,22) (9,26) (15,4) (30,26) (4,10) (14,17) (11,18) (10,27) (26,16) (31,17) (21,2) (1,17) (3,5) (19,28) (24,31) (8,10) (26,7) (12,2) (2,24) (14,28) (0,15) (28,23) (29,31) (7,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1018", "image": "data/cycle/graph_visual/hard/graph1018.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,0) (0,2) (12,3) (13,14) (21,20) (11,24) (4,24) (17,16) (20,9) (24,25) (7,10) (23,8) (13,3) (18,24) (22,2) (23,9) (14,0) (16,23) (12,22) (1,0) (10,0) (0,5) (2,15) (3,16) (1,25) (19,23) (6,17) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1784", "image": "data/cycle/graph_visual/hard/graph1784.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (25,26) (27,3) (24,21) (17,12) (19,2) (6,11) (19,10) (4,1) (30,13) (6,16) (15,30) (9,20) (18,25) (29,11) (14,3) (23,14) (5,23) (25,8) (24,32) (0,15) (28,17) (16,17) (10,12) (16,1) (22,4) (1,0) (5,21) (5,9) (18,23) (31,32) (7,6) (1,13) (18,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph471", "image": "data/cycle/graph_visual/hard/graph471.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (24,29) (27,13) (12,6) (28,25) (11,26) (16,25) (21,3) (12,24) (14,18) (21,4) (0,2) (22,8) (5,9) (7,6) (21,14) (27,15) (6,25) (8,7) (26,14) (26,19) (25,11) (20,14) (5,2) (12,5) (17,23) (23,19) (15,6) (14,10) (1,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1949", "image": "data/cycle/graph_visual/hard/graph1949.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (13,9) (26,6) (26,1) (29,19) (4,6) (8,10) (16,14) (20,8) (7,11) (0,1) (28,8) (22,13) (2,0) (8,12) (26,21) (4,15) (7,2) (23,13) (8,18) (26,20) (12,25) (8,3) (17,14) (11,32) (25,9) (14,28) (29,1) (24,10) (0,34) (27,12) (0,3) (32,33) (34,5) (15,30) (33,17) (31,11) (0,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1115", "image": "data/cycle/graph_visual/hard/graph1115.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (9,25) (0,4) (1,7) (25,3) (7,6) (11,8) (7,16) (11,17) (15,4) (5,26) (26,3) (0,12) (3,13) (20,2) (21,9) (5,24) (14,23) (22,24) (1,0) (12,17) (1,23) (18,12) (10,9) (19,15) (5,0) (17,16) (4,2) (24,8) (3,0) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph86", "image": "data/cycle/graph_visual/hard/graph86.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (8,15) (23,4) (14,1) (19,10) (12,18) (18,21) (13,15) (7,13) (9,3) (7,16) (22,24) (21,11) (25,24) (8,23) (11,5) (5,17) (23,0) (24,20) (17,20) (22,2) (19,3) (10,14) (17,14) (23,25) (16,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph291", "image": "data/cycle/graph_visual/hard/graph291.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,12) (11,0) (6,17) (3,12) (12,24) (11,13) (19,1) (8,22) (2,8) (17,15) (9,27) (4,27) (7,25) (12,20) (21,11) (24,17) (19,26) (23,26) (17,22) (18,0) (0,4) (7,5) (1,12) (5,16) (18,16) (13,10) (11,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph601", "image": "data/cycle/graph_visual/hard/graph601.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (5,22) (8,27) (8,28) (0,13) (23,26) (10,4) (13,31) (0,29) (30,13) (15,12) (9,1) (17,25) (6,21) (15,0) (30,18) (7,16) (3,14) (1,29) (13,22) (16,2) (28,26) (24,11) (7,23) (19,15) (6,15) (10,3) (8,0) (8,4) (20,24) (17,11) (24,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph42", "image": "data/cycle/graph_visual/hard/graph42.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (23,8) (6,3) (4,7) (7,11) (12,20) (22,17) (8,18) (19,25) (19,2) (5,7) (6,13) (12,0) (5,10) (9,19) (23,13) (21,22) (6,15) (14,2) (24,15) (17,2) (23,19) (16,21) (12,16) (1,12) (4,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1600", "image": "data/cycle/graph_visual/hard/graph1600.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (13,11) (30,18) (14,10) (30,11) (0,11) (23,28) (30,7) (25,5) (28,31) (19,12) (16,10) (8,7) (0,3) (8,24) (15,22) (17,16) (29,5) (6,12) (31,5) (0,15) (31,27) (23,1) (4,31) (20,26) (0,1) (18,9) (9,3) (20,22) (19,22) (27,2) (21,6) (10,2) (1,19) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph971", "image": "data/cycle/graph_visual/hard/graph971.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (22,24) (20,29) (12,13) (17,13) (14,27) (25,9) (8,7) (24,8) (29,30) (29,1) (33,30) (16,3) (1,2) (5,23) (11,24) (19,12) (26,19) (28,10) (31,1) (3,26) (5,6) (11,20) (2,10) (0,31) (11,18) (32,22) (22,9) (2,15) (21,19) (30,12) (28,14) (34,20) (29,4) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1868", "image": "data/cycle/graph_visual/hard/graph1868.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,4) (9,30) (14,31) (28,17) (27,6) (24,20) (7,20) (9,29) (14,18) (26,3) (7,11) (29,2) (1,32) (2,32) (20,22) (25,17) (23,18) (22,5) (32,12) (3,19) (13,26) (13,4) (24,27) (2,21) (15,8) (22,17) (33,16) (25,3) (1,0) (25,23) (15,1) (4,16) (6,8) (26,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1394", "image": "data/cycle/graph_visual/hard/graph1394.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (9,1) (5,22) (10,22) (18,11) (8,11) (19,27) (21,9) (25,20) (24,6) (24,27) (14,4) (25,18) (12,13) (24,13) (2,1) (17,28) (28,12) (22,15) (17,26) (11,19) (3,14) (0,2) (0,16) (14,19) (4,7) (19,15) (21,3) (1,0) (0,23) (16,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph927", "image": "data/cycle/graph_visual/hard/graph927.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,4) (34,7) (32,5) (11,22) (32,29) (21,16) (31,12) (26,33) (7,3) (19,1) (12,8) (14,18) (16,26) (24,4) (2,33) (4,6) (22,20) (6,1) (25,10) (12,7) (6,27) (33,13) (34,27) (6,17) (16,9) (26,1) (9,15) (19,20) (29,24) (28,12) (6,18) (23,17) (0,2) (20,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph295", "image": "data/cycle/graph_visual/hard/graph295.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,6) (4,21) (27,4) (4,5) (11,7) (9,21) (9,10) (16,1) (23,11) (26,2) (22,24) (9,7) (23,26) (16,12) (8,17) (24,26) (14,20) (0,10) (19,25) (0,19) (12,15) (3,14) (17,13) (26,15) (5,18) (0,17) (21,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph496", "image": "data/cycle/graph_visual/hard/graph496.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,15) (26,19) (23,3) (19,21) (28,17) (2,16) (29,0) (17,27) (26,11) (4,5) (11,12) (21,3) (25,24) (11,2) (28,3) (8,29) (13,11) (5,18) (15,7) (20,4) (18,9) (6,27) (23,10) (5,25) (28,14) (18,1) (22,12) (1,19) (29,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1338", "image": "data/cycle/graph_visual/hard/graph1338.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (9,22) (23,0) (12,20) (0,17) (6,22) (7,19) (18,12) (13,1) (5,11) (0,5) (13,12) (5,24) (27,18) (1,0) (27,8) (24,12) (3,0) (5,3) (17,4) (16,25) (18,21) (9,15) (3,10) (7,3) (0,4) (16,22) (16,2) (22,20) (24,28) (9,26) (14,7) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1711", "image": "data/cycle/graph_visual/hard/graph1711.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,0) (19,15) (9,23) (11,7) (7,3) (31,20) (26,4) (10,9) (5,29) (18,24) (0,30) (11,27) (16,27) (17,13) (11,22) (14,28) (18,2) (8,26) (32,14) (6,31) (4,1) (19,29) (13,2) (12,17) (23,0) (10,2) (26,28) (0,2) (17,21) (25,31) (1,0) (7,6) (25,10) (15,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph699", "image": "data/cycle/graph_visual/hard/graph699.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (3,13) (31,19) (4,22) (14,24) (9,1) (1,15) (25,4) (7,17) (5,29) (5,18) (10,25) (25,1) (16,8) (15,17) (23,4) (3,25) (8,30) (27,28) (19,29) (20,0) (22,26) (6,17) (11,13) (2,18) (6,27) (21,1) (0,15) (12,16) (24,10) (8,19) (7,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1503", "image": "data/cycle/graph_visual/hard/graph1503.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (20,8) (12,18) (5,10) (4,0) (12,0) (11,14) (19,21) (30,28) (4,16) (2,0) (21,0) (0,1) (27,22) (15,24) (8,2) (7,29) (7,17) (15,8) (3,0) (21,3) (9,21) (11,23) (22,26) (5,11) (19,27) (25,14) (19,4) (1,15) (4,14) (0,17) (11,13) (16,6) (20,25) (10,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1521", "image": "data/cycle/graph_visual/hard/graph1521.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (20,27) (1,4) (5,6) (29,11) (25,3) (24,26) (25,14) (17,29) (23,14) (28,26) (27,13) (1,0) (7,11) (10,16) (25,19) (2,5) (3,1) (17,10) (21,17) (21,0) (25,17) (9,29) (14,18) (10,8) (13,18) (25,15) (27,12) (14,30) (2,19) (26,16) (22,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph112", "image": "data/cycle/graph_visual/hard/graph112.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (22,24) (1,20) (1,21) (14,23) (8,4) (17,20) (3,6) (24,10) (7,19) (3,10) (7,16) (24,23) (12,16) (13,5) (21,18) (25,8) (16,17) (15,1) (23,1) (11,17) (0,2) (14,4) (26,9) (19,9) (13,25) (11,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph239", "image": "data/cycle/graph_visual/hard/graph239.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (4,18) (3,12) (24,23) (27,0) (16,19) (9,13) (0,22) (17,10) (20,13) (16,7) (14,7) (1,2) (21,12) (11,19) (25,5) (8,0) (19,6) (26,18) (12,11) (26,12) (10,15) (27,23) (20,23) (15,9) (20,3) (1,11) (16,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph68", "image": "data/cycle/graph_visual/hard/graph68.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,11) (4,22) (8,3) (24,12) (9,14) (20,14) (7,25) (23,15) (3,0) (3,24) (8,16) (2,19) (19,1) (8,7) (23,18) (21,12) (16,10) (8,13) (6,20) (9,22) (24,5) (2,21) (17,9) (23,12) (21,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1287", "image": "data/cycle/graph_visual/hard/graph1287.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (4,12) (27,6) (13,25) (27,19) (5,0) (3,2) (27,21) (9,25) (3,0) (0,13) (23,18) (14,13) (16,8) (11,24) (10,15) (21,8) (14,18) (1,23) (6,13) (20,3) (24,5) (3,4) (26,2) (0,1) (7,21) (22,10) (20,17) (2,0) (15,18) (4,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph290", "image": "data/cycle/graph_visual/hard/graph290.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,11) (4,17) (10,20) (23,6) (9,15) (17,25) (6,12) (24,23) (16,10) (9,5) (27,16) (25,15) (4,0) (10,17) (15,8) (2,19) (22,12) (14,26) (14,7) (14,19) (13,7) (1,6) (1,15) (18,23) (14,3) (21,18) (17,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph751", "image": "data/cycle/graph_visual/hard/graph751.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (6,17) (0,10) (7,21) (22,16) (24,32) (8,16) (13,24) (5,1) (25,7) (17,13) (17,30) (9,23) (11,18) (29,14) (14,20) (10,31) (23,16) (4,7) (10,9) (2,6) (28,15) (19,29) (25,27) (3,15) (17,5) (18,19) (28,16) (25,26) (12,4) (20,22) (4,0) (1,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph216", "image": "data/cycle/graph_visual/hard/graph216.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,1) (15,19) (8,6) (2,7) (25,20) (7,11) (5,16) (10,26) (21,16) (0,13) (17,2) (13,26) (27,1) (9,27) (22,19) (14,17) (12,14) (18,14) (20,15) (9,3) (24,10) (4,9) (17,23) (13,7) (14,8) (20,6) (14,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1522", "image": "data/cycle/graph_visual/hard/graph1522.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,0) (17,10) (7,28) (13,30) (11,8) (0,4) (23,29) (0,3) (20,0) (3,22) (21,26) (6,9) (19,8) (22,17) (2,0) (15,26) (23,2) (24,26) (8,4) (29,20) (11,26) (10,8) (6,2) (20,18) (5,7) (15,1) (27,29) (26,2) (18,30) (12,25) (9,14) (12,5) (16,2) (7,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1974", "image": "data/cycle/graph_visual/hard/graph1974.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,0) (18,14) (1,31) (2,0) (17,15) (0,18) (9,21) (5,26) (0,11) (9,32) (14,28) (26,16) (19,22) (25,19) (34,5) (30,16) (30,4) (21,24) (12,26) (8,14) (1,9) (27,1) (16,13) (19,23) (14,15) (2,23) (19,14) (3,30) (29,18) (16,23) (6,18) (29,1) (29,33) (28,10) (7,26) (20,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph196", "image": "data/cycle/graph_visual/hard/graph196.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (26,2) (8,10) (0,20) (10,5) (3,5) (20,10) (22,16) (10,9) (18,22) (11,15) (24,12) (6,25) (2,11) (15,1) (16,0) (2,22) (17,4) (7,6) (25,17) (25,5) (14,10) (13,9) (15,21) (11,23) (19,0) (14,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph108", "image": "data/cycle/graph_visual/hard/graph108.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,25) (5,23) (24,20) (3,8) (7,2) (0,14) (0,7) (12,17) (16,13) (8,23) (25,21) (10,15) (19,4) (20,0) (11,5) (26,13) (9,16) (11,14) (11,15) (1,18) (1,17) (22,13) (14,12) (1,6) (26,2) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1492", "image": "data/cycle/graph_visual/hard/graph1492.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,2) (11,26) (7,26) (18,15) (27,23) (6,23) (15,8) (0,24) (1,16) (25,3) (0,8) (4,21) (24,12) (6,25) (2,9) (15,25) (24,21) (14,8) (13,29) (18,20) (5,18) (13,27) (17,29) (28,17) (0,3) (11,10) (22,23) (4,19) (0,2) (24,10) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1446", "image": "data/cycle/graph_visual/hard/graph1446.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,25) (27,6) (29,12) (5,24) (3,0) (4,9) (16,8) (0,1) (13,1) (10,13) (9,22) (2,12) (15,11) (8,1) (0,2) (23,15) (20,25) (24,3) (18,28) (12,17) (0,27) (6,16) (28,9) (4,24) (28,7) (11,18) (25,19) (4,16) (3,19) (15,14) (21,26) (29,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph893", "image": "data/cycle/graph_visual/hard/graph893.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (26,0) (20,16) (32,3) (24,2) (15,2) (16,14) (18,12) (10,26) (4,17) (30,9) (6,3) (6,19) (24,28) (31,32) (18,15) (23,29) (9,11) (8,19) (9,19) (29,0) (27,5) (4,33) (9,1) (8,10) (21,2) (13,9) (1,14) (22,30) (17,15) (18,14) (7,19) (21,25) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph993", "image": "data/cycle/graph_visual/hard/graph993.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,5) (13,31) (12,18) (6,13) (1,2) (23,31) (16,11) (5,24) (18,9) (20,5) (3,19) (10,14) (21,33) (28,7) (28,15) (30,16) (21,2) (15,17) (21,8) (27,14) (23,27) (25,12) (28,0) (17,1) (2,32) (29,10) (4,19) (14,3) (34,21) (18,4) (6,2) (27,30) (26,8) (22,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph80", "image": "data/cycle/graph_visual/hard/graph80.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,25) (1,5) (25,2) (0,11) (6,12) (9,23) (15,6) (21,16) (0,24) (15,13) (25,24) (18,17) (15,19) (1,20) (9,14) (17,2) (4,18) (8,13) (12,1) (3,11) (7,11) (21,22) (23,11) (24,22) (1,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph460", "image": "data/cycle/graph_visual/hard/graph460.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (25,4) (14,27) (28,14) (0,14) (9,23) (6,5) (20,23) (4,19) (21,16) (2,22) (5,21) (17,2) (23,27) (22,1) (12,7) (29,25) (11,5) (21,22) (29,3) (12,6) (6,15) (24,26) (26,8) (3,20) (10,18) (13,5) (0,24) (18,24) (22,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph780", "image": "data/cycle/graph_visual/hard/graph780.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,21) (5,20) (1,0) (1,25) (14,10) (6,20) (16,5) (16,17) (2,17) (28,9) (7,26) (31,9) (27,14) (23,14) (23,12) (10,8) (22,11) (6,1) (11,13) (10,15) (30,0) (19,25) (3,29) (17,13) (3,24) (24,26) (25,4) (15,24) (18,23) (0,32) (28,8) (23,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph581", "image": "data/cycle/graph_visual/hard/graph581.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,30) (1,18) (14,26) (19,26) (5,12) (25,17) (10,5) (16,27) (18,23) (6,7) (24,19) (15,27) (30,12) (25,11) (20,14) (30,28) (7,8) (14,22) (30,3) (9,21) (4,21) (15,6) (8,23) (2,0) (26,11) (21,14) (25,6) (5,2) (25,29) (13,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1463", "image": "data/cycle/graph_visual/hard/graph1463.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,9) (25,28) (14,15) (1,12) (20,7) (0,29) (9,6) (7,1) (5,27) (27,21) (24,27) (0,2) (28,0) (25,20) (12,4) (14,28) (0,1) (25,22) (21,2) (2,26) (8,13) (4,5) (1,19) (28,10) (15,17) (16,25) (11,4) (18,9) (23,29) (3,0) (7,8) (0,4) (10,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph145", "image": "data/cycle/graph_visual/hard/graph145.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (18,10) (20,16) (17,16) (7,0) (17,3) (9,7) (17,13) (5,4) (26,1) (21,11) (16,2) (8,12) (24,17) (23,14) (10,20) (7,5) (22,17) (26,8) (18,21) (7,26) (26,6) (19,12) (8,15) (14,25) (22,23) (11,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph967", "image": "data/cycle/graph_visual/hard/graph967.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (13,10) (24,28) (10,2) (15,4) (31,9) (2,27) (19,11) (24,34) (26,32) (29,16) (21,20) (2,1) (33,11) (0,13) (25,23) (30,8) (26,18) (17,31) (31,22) (7,29) (33,14) (29,15) (24,22) (6,0) (4,20) (28,15) (5,30) (18,16) (2,26) (23,8) (12,17) (27,3) (19,23) (29,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1091", "image": "data/cycle/graph_visual/hard/graph1091.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (6,3) (3,23) (0,2) (1,4) (5,13) (5,14) (9,24) (22,18) (15,13) (6,0) (7,23) (8,14) (19,15) (22,25) (15,21) (0,11) (12,19) (0,1) (23,22) (11,2) (15,22) (4,2) (11,10) (4,20) (7,17) (9,5) (7,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1098", "image": "data/cycle/graph_visual/hard/graph1098.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (13,1) (9,11) (10,16) (25,15) (2,24) (22,1) (5,24) (5,19) (2,0) (8,21) (5,14) (4,17) (16,25) (3,18) (23,18) (3,4) (8,5) (20,21) (15,3) (9,6) (15,7) (0,4) (9,17) (1,0) (24,6) (12,25) (13,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1929", "image": "data/cycle/graph_visual/hard/graph1929.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (9,17) (22,8) (12,28) (32,6) (8,31) (20,32) (10,3) (23,29) (26,16) (22,32) (1,18) (27,10) (4,0) (14,8) (9,5) (30,7) (8,24) (16,3) (14,23) (22,19) (0,1) (33,20) (11,33) (0,2) (32,25) (13,23) (10,2) (12,14) (30,28) (2,1) (13,0) (15,29) (21,3) (3,0) (3,25) (21,17) (34,5) (29,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1453", "image": "data/cycle/graph_visual/hard/graph1453.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (10,21) (25,20) (23,4) (6,21) (12,20) (21,24) (26,0) (27,14) (5,6) (18,13) (29,6) (29,9) (12,15) (8,23) (7,3) (0,2) (8,16) (28,13) (0,17) (28,22) (0,3) (26,2) (15,22) (27,24) (1,20) (4,28) (11,23) (19,1) (26,29) (1,0) (12,17) (9,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1003", "image": "data/cycle/graph_visual/hard/graph1003.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,2) (23,21) (0,6) (0,3) (11,13) (11,18) (24,10) (3,4) (17,22) (14,25) (6,7) (18,21) (7,17) (6,5) (2,19) (20,12) (0,1) (17,12) (22,1) (7,15) (14,8) (14,18) (10,3) (24,19) (19,18) (24,7) (16,21) (9,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph198", "image": "data/cycle/graph_visual/hard/graph198.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,18) (24,1) (20,4) (16,22) (21,1) (4,19) (7,17) (3,13) (24,6) (11,1) (17,23) (9,4) (26,14) (0,2) (21,25) (8,12) (7,15) (4,7) (23,14) (4,1) (15,0) (22,23) (5,3) (3,17) (4,12) (10,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1542", "image": "data/cycle/graph_visual/hard/graph1542.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (13,14) (6,0) (17,10) (6,23) (29,11) (1,15) (30,23) (15,0) (24,26) (25,24) (21,25) (27,13) (24,20) (20,19) (6,28) (26,22) (16,8) (1,0) (19,7) (4,20) (29,17) (5,3) (18,25) (22,29) (9,12) (6,14) (27,2) (12,21) (4,2) (20,3) (22,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1340", "image": "data/cycle/graph_visual/hard/graph1340.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (10,24) (3,0) (13,10) (28,5) (8,19) (18,4) (28,10) (4,0) (8,25) (17,6) (3,24) (18,20) (3,26) (15,16) (1,0) (7,16) (11,16) (25,1) (3,14) (9,27) (8,22) (6,12) (2,0) (4,19) (28,9) (12,11) (3,21) (0,21) (1,2) (23,13) (26,8) (9,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1564", "image": "data/cycle/graph_visual/hard/graph1564.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,30) (5,30) (30,16) (17,0) (2,8) (13,14) (17,18) (27,30) (28,6) (0,2) (3,12) (21,11) (24,12) (22,26) (11,13) (12,20) (27,9) (7,5) (7,26) (17,4) (29,25) (7,12) (0,3) (30,10) (8,22) (29,16) (19,1) (0,11) (15,11) (19,28) (4,0) (1,12) (17,24) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1687", "image": "data/cycle/graph_visual/hard/graph1687.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,30) (7,12) (19,31) (2,0) (16,20) (28,12) (0,1) (19,8) (28,4) (12,1) (6,3) (8,6) (22,15) (12,10) (13,30) (18,19) (11,18) (26,21) (14,25) (17,18) (2,11) (6,25) (31,0) (0,26) (4,29) (22,18) (0,3) (9,2) (5,13) (3,23) (28,16) (24,28) (27,13) (23,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph941", "image": "data/cycle/graph_visual/hard/graph941.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (20,7) (4,6) (17,14) (26,34) (26,16) (23,7) (1,2) (17,23) (15,20) (12,0) (34,33) (8,29) (22,30) (1,18) (1,4) (13,2) (16,25) (11,12) (21,28) (4,34) (3,1) (15,28) (27,12) (34,15) (5,27) (24,19) (32,34) (6,11) (8,31) (23,9) (8,6) (30,4) (3,10) (19,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1205", "image": "data/cycle/graph_visual/hard/graph1205.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,15) (7,12) (27,23) (14,3) (6,10) (16,21) (7,19) (17,18) (17,4) (15,9) (13,6) (0,8) (1,25) (19,22) (2,8) (0,1) (26,0) (9,3) (2,0) (5,15) (24,8) (27,25) (7,4) (11,10) (16,0) (21,20) (26,6) (20,17) (25,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph339", "image": "data/cycle/graph_visual/hard/graph339.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (21,27) (3,15) (1,20) (11,13) (9,1) (16,19) (14,10) (9,25) (19,8) (19,18) (8,12) (4,24) (6,22) (28,8) (5,14) (1,5) (15,28) (3,21) (5,3) (13,15) (21,23) (17,13) (7,13) (6,20) (24,5) (2,0) (26,14) (2,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1811", "image": "data/cycle/graph_visual/hard/graph1811.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (23,19) (29,16) (11,31) (9,14) (32,12) (24,17) (28,10) (25,17) (6,10) (2,0) (16,2) (11,22) (7,27) (30,0) (25,0) (3,33) (18,33) (22,19) (23,21) (26,24) (16,13) (20,21) (28,23) (1,12) (32,5) (8,15) (28,1) (7,1) (30,10) (4,15) (25,14) (29,15) (30,2) (0,3) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph569", "image": "data/cycle/graph_visual/hard/graph569.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (20,13) (0,21) (2,13) (2,5) (19,1) (29,30) (12,19) (30,27) (12,16) (18,12) (9,18) (25,15) (1,25) (10,11) (22,30) (15,23) (4,11) (17,23) (30,8) (8,10) (8,26) (24,3) (14,7) (17,6) (28,25) (17,0) (21,13) (0,29) (3,0) (14,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph160", "image": "data/cycle/graph_visual/hard/graph160.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,18) (8,22) (5,18) (9,13) (5,3) (26,2) (24,0) (0,16) (25,15) (7,14) (10,24) (8,20) (5,19) (11,14) (12,7) (9,21) (11,5) (21,0) (3,0) (5,4) (17,16) (16,15) (10,26) (6,2) (5,20) (23,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1211", "image": "data/cycle/graph_visual/hard/graph1211.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (17,5) (0,15) (20,2) (16,19) (23,18) (4,17) (25,11) (8,24) (10,17) (4,13) (27,20) (0,19) (0,21) (2,22) (2,0) (12,27) (20,6) (0,3) (26,1) (25,4) (1,0) (25,8) (16,23) (14,15) (6,25) (23,9) (7,16) (6,19) (0,4) (3,24) (18,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1742", "image": "data/cycle/graph_visual/hard/graph1742.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (21,6) (9,5) (24,20) (19,10) (3,16) (11,1) (14,8) (24,18) (24,1) (5,3) (2,0) (21,25) (1,0) (32,13) (32,26) (16,23) (14,4) (15,19) (27,9) (0,22) (12,23) (17,6) (27,4) (20,13) (1,7) (10,30) (23,29) (3,24) (9,0) (31,13) (22,17) (28,6) (18,19) (22,2) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1443", "image": "data/cycle/graph_visual/hard/graph1443.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,0) (7,16) (24,25) (0,27) (19,6) (26,17) (11,0) (2,4) (13,2) (9,14) (7,25) (21,16) (15,9) (20,15) (24,29) (28,18) (13,18) (8,22) (15,25) (6,25) (16,5) (0,1) (22,5) (11,29) (4,25) (13,3) (23,16) (1,5) (12,20) (13,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1842", "image": "data/cycle/graph_visual/hard/graph1842.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,7) (0,1) (28,1) (10,16) (30,24) (16,18) (32,10) (10,11) (27,33) (14,32) (5,20) (21,31) (23,21) (6,29) (5,13) (13,10) (30,1) (2,11) (7,22) (2,0) (25,19) (4,3) (9,22) (0,17) (8,19) (0,29) (12,10) (11,15) (26,30) (0,33) (15,4) (19,21) (25,1) (23,29) (28,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1081", "image": "data/cycle/graph_visual/hard/graph1081.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,12) (3,2) (6,10) (4,0) (22,5) (23,14) (23,12) (4,14) (24,9) (17,24) (14,7) (21,1) (20,21) (3,22) (2,23) (1,8) (6,20) (17,3) (25,16) (16,13) (0,1) (11,13) (14,8) (19,11) (25,10) (5,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1119", "image": "data/cycle/graph_visual/hard/graph1119.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (26,14) (12,3) (20,9) (10,8) (0,5) (14,13) (15,2) (10,23) (3,16) (12,23) (22,26) (26,7) (11,0) (1,25) (24,4) (2,22) (24,0) (23,21) (26,9) (23,18) (24,16) (1,0) (17,16) (3,26) (6,17) (20,19) (13,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1224", "image": "data/cycle/graph_visual/hard/graph1224.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (2,4) (19,15) (0,3) (9,19) (14,23) (19,26) (0,2) (6,21) (26,18) (0,13) (8,6) (25,10) (24,16) (0,1) (11,9) (8,1) (20,12) (26,5) (7,0) (1,12) (19,27) (17,20) (14,0) (25,26) (3,17) (4,20) (2,5) (22,12) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph868", "image": "data/cycle/graph_visual/hard/graph868.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (31,5) (15,12) (23,17) (21,22) (15,7) (0,33) (0,6) (26,31) (19,32) (32,14) (22,16) (23,9) (8,2) (2,10) (22,13) (28,19) (24,16) (29,14) (29,18) (25,14) (33,5) (27,13) (22,20) (30,26) (3,1) (29,26) (20,14) (7,21) (4,13) (25,17) (10,15) (1,11) (9,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1534", "image": "data/cycle/graph_visual/hard/graph1534.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (16,22) (14,7) (30,21) (0,4) (9,27) (0,1) (11,5) (9,22) (22,21) (23,18) (0,25) (0,17) (1,13) (2,0) (20,28) (29,18) (8,27) (3,0) (12,13) (2,16) (3,10) (26,16) (12,24) (6,22) (17,4) (12,18) (7,3) (22,24) (7,19) (3,5) (12,20) (9,15) (24,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1575", "image": "data/cycle/graph_visual/hard/graph1575.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,2) (15,28) (28,19) (9,13) (9,8) (28,18) (21,20) (11,22) (23,4) (15,6) (1,0) (1,21) (22,3) (1,4) (18,12) (24,25) (2,0) (17,23) (2,11) (30,20) (25,14) (8,11) (5,2) (10,18) (0,3) (20,16) (30,29) (7,21) (26,27) (0,6) (18,14) (8,15) (9,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph82", "image": "data/cycle/graph_visual/hard/graph82.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,2) (17,9) (25,1) (25,22) (11,25) (18,6) (20,10) (24,19) (16,4) (21,17) (13,8) (21,18) (3,23) (25,8) (18,3) (12,18) (15,5) (21,20) (7,17) (16,15) (0,13) (2,5) (14,25) (10,1) (24,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph605", "image": "data/cycle/graph_visual/hard/graph605.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (28,17) (16,6) (21,5) (19,10) (15,0) (16,17) (30,13) (1,4) (23,18) (18,19) (5,9) (3,14) (14,23) (1,16) (18,25) (29,11) (7,6) (5,23) (17,12) (21,24) (20,9) (15,30) (24,31) (8,25) (2,19) (6,11) (22,4) (25,26) (3,27) (1,13) (12,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph574", "image": "data/cycle/graph_visual/hard/graph574.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (15,6) (1,6) (3,0) (8,28) (25,24) (9,23) (28,26) (14,25) (30,6) (6,5) (9,13) (1,20) (2,18) (19,25) (6,4) (21,14) (17,6) (27,18) (20,10) (22,12) (14,29) (30,8) (18,3) (30,16) (30,11) (12,11) (23,7) (9,27) (0,15) (13,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1830", "image": "data/cycle/graph_visual/hard/graph1830.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,0) (21,6) (4,27) (9,19) (0,3) (8,10) (14,23) (22,31) (1,4) (32,21) (27,29) (32,24) (1,13) (10,31) (12,27) (14,13) (8,4) (6,15) (15,17) (32,25) (0,4) (28,13) (3,18) (7,32) (19,5) (8,3) (18,21) (9,26) (30,9) (10,16) (11,12) (8,2) (17,33) (20,0) (31,30) (6,20) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph720", "image": "data/cycle/graph_visual/hard/graph720.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (7,19) (28,0) (2,14) (16,2) (19,10) (24,3) (15,30) (12,27) (2,23) (24,17) (12,32) (18,24) (32,5) (8,5) (25,21) (27,31) (29,14) (20,27) (5,11) (11,9) (19,32) (26,32) (24,14) (1,5) (4,12) (29,0) (6,9) (16,25) (14,5) (22,13) (20,22) (30,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1940", "image": "data/cycle/graph_visual/hard/graph1940.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (20,28) (5,19) (16,33) (13,22) (9,2) (29,31) (0,23) (24,5) (7,21) (19,1) (7,23) (12,4) (6,9) (10,21) (26,17) (12,22) (27,20) (1,0) (14,34) (13,28) (0,17) (17,1) (32,31) (25,24) (32,4) (11,5) (18,34) (11,16) (12,30) (3,12) (27,26) (20,15) (6,17) (0,2) (30,18) (8,34)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1911", "image": "data/cycle/graph_visual/hard/graph1911.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (5,21) (20,18) (22,18) (9,10) (21,11) (13,32) (25,22) (28,1) (0,1) (4,13) (31,19) (2,0) (32,2) (16,1) (14,24) (12,30) (3,29) (27,22) (24,7) (14,28) (17,10) (33,15) (8,30) (11,19) (34,6) (34,18) (24,11) (28,15) (1,27) (9,28) (19,29) (4,8) (0,23) (26,14) (32,21) (0,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1738", "image": "data/cycle/graph_visual/hard/graph1738.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (24,7) (21,29) (2,11) (25,12) (17,26) (1,20) (30,24) (3,23) (25,13) (31,14) (29,23) (12,10) (0,2) (0,14) (31,5) (17,1) (5,25) (2,5) (32,6) (29,12) (8,18) (4,24) (31,22) (8,9) (16,7) (28,31) (13,19) (26,30) (32,15) (1,0) (1,14) (16,6) (27,24) (8,15) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1086", "image": "data/cycle/graph_visual/hard/graph1086.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,1) (10,9) (12,18) (3,25) (4,2) (4,15) (9,25) (17,16) (23,1) (3,13) (20,2) (2,0) (8,24) (7,16) (6,7) (11,17) (5,24) (3,5) (11,8) (9,21) (12,17) (14,23) (12,0) (15,19) (1,0) (22,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph685", "image": "data/cycle/graph_visual/hard/graph685.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,13) (31,28) (3,24) (9,17) (7,24) (15,5) (6,11) (10,16) (9,18) (26,28) (10,1) (31,25) (31,21) (7,1) (27,19) (13,20) (4,23) (10,12) (5,16) (29,22) (19,4) (20,21) (13,8) (20,10) (0,28) (30,19) (2,23) (14,12) (18,0) (10,11) (5,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1297", "image": "data/cycle/graph_visual/hard/graph1297.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (18,22) (23,21) (27,6) (19,8) (11,9) (6,0) (0,1) (27,24) (21,18) (15,1) (26,5) (16,27) (8,1) (12,2) (1,9) (13,20) (24,17) (4,24) (27,26) (12,20) (18,9) (15,14) (26,7) (3,0) (23,26) (0,2) (3,25) (3,18) (3,13) (10,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1319", "image": "data/cycle/graph_visual/hard/graph1319.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,10) (23,10) (4,24) (16,27) (3,26) (18,23) (20,9) (26,7) (16,3) (0,2) (1,0) (17,16) (24,28) (28,14) (0,3) (9,26) (0,4) (20,19) (23,12) (3,12) (24,0) (0,5) (11,0) (26,13) (2,15) (22,2) (13,14) (25,27) (22,26) (21,23) (1,25) (6,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph896", "image": "data/cycle/graph_visual/hard/graph896.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (24,16) (11,13) (26,1) (23,13) (17,12) (25,6) (2,30) (32,1) (23,32) (4,18) (8,12) (1,24) (9,1) (22,19) (28,17) (29,14) (22,3) (33,23) (31,11) (18,33) (27,15) (8,20) (6,5) (13,3) (27,29) (26,28) (2,23) (21,0) (7,5) (10,19) (5,31) (22,27) (14,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1945", "image": "data/cycle/graph_visual/hard/graph1945.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (29,11) (27,20) (28,29) (6,2) (5,12) (14,34) (6,14) (24,9) (7,22) (26,8) (4,27) (14,30) (22,12) (22,10) (21,7) (9,32) (24,15) (3,20) (19,29) (7,26) (32,14) (34,17) (13,14) (14,31) (0,24) (23,0) (27,30) (1,12) (0,10) (25,4) (1,0) (28,30) (16,34) (33,8) (14,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph484", "image": "data/cycle/graph_visual/hard/graph484.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,28) (11,22) (26,9) (17,2) (6,15) (8,9) (22,3) (16,20) (20,29) (19,28) (1,21) (13,9) (20,21) (25,14) (8,11) (1,4) (25,24) (26,27) (5,2) (10,18) (21,7) (0,6) (17,23) (15,8) (28,15) (23,4) (14,18) (2,11) (18,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph349", "image": "data/cycle/graph_visual/hard/graph349.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,21) (28,1) (26,5) (14,25) (15,16) (28,17) (3,18) (6,18) (11,25) (9,17) (13,0) (5,15) (26,27) (22,24) (25,23) (8,13) (3,24) (25,8) (21,18) (16,4) (1,10) (19,21) (10,20) (17,7) (18,12) (2,18) (2,26) (25,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph73", "image": "data/cycle/graph_visual/hard/graph73.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (21,0) (21,19) (24,7) (2,8) (23,22) (10,4) (12,0) (1,15) (8,15) (17,0) (18,25) (11,9) (7,17) (14,4) (13,12) (16,11) (6,21) (16,5) (22,19) (19,4) (3,21) (15,11) (14,20) (25,14) (8,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1139", "image": "data/cycle/graph_visual/hard/graph1139.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (3,0) (5,19) (19,10) (0,1) (2,7) (1,8) (15,22) (25,11) (22,1) (13,23) (6,4) (13,22) (0,19) (0,2) (5,17) (10,25) (1,26) (16,3) (12,14) (20,18) (7,8) (0,9) (14,5) (21,23) (3,23) (7,4) (11,20) (17,21) (2,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1886", "image": "data/cycle/graph_visual/hard/graph1886.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (27,5) (24,15) (14,23) (19,30) (3,0) (21,32) (5,33) (15,16) (1,4) (11,19) (6,9) (1,0) (22,31) (0,26) (19,18) (26,13) (19,14) (17,18) (8,24) (24,26) (29,1) (15,6) (21,29) (28,21) (12,3) (14,21) (20,28) (5,15) (31,3) (12,10) (4,25) (23,2) (25,9) (29,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1554", "image": "data/cycle/graph_visual/hard/graph1554.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,26) (6,15) (26,14) (3,30) (29,25) (0,2) (10,5) (12,5) (30,6) (25,6) (14,20) (21,14) (19,24) (18,1) (11,25) (23,8) (25,17) (12,30) (14,13) (4,0) (0,1) (16,27) (27,15) (26,11) (9,21) (6,7) (18,23) (2,5) (3,0) (30,28) (7,8) (4,21) (14,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1493", "image": "data/cycle/graph_visual/hard/graph1493.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,11) (16,18) (26,8) (21,14) (17,20) (29,2) (22,1) (25,19) (15,26) (14,29) (6,19) (26,3) (14,13) (25,9) (19,27) (20,11) (23,13) (5,2) (23,10) (20,1) (23,12) (29,9) (3,21) (1,0) (19,4) (21,7) (16,24) (12,28) (25,16) (0,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1710", "image": "data/cycle/graph_visual/hard/graph1710.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (16,21) (25,23) (30,18) (28,24) (12,11) (30,2) (27,28) (7,9) (9,22) (30,12) (15,27) (16,19) (0,3) (28,20) (2,0) (32,7) (23,10) (29,4) (6,29) (0,12) (8,1) (21,3) (2,26) (4,0) (1,9) (0,1) (10,7) (17,15) (6,21) (3,5) (32,13) (0,27) (5,11) (22,31) (8,24) (14,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph944", "image": "data/cycle/graph_visual/hard/graph944.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,21) (22,29) (2,5) (30,26) (30,24) (7,24) (26,33) (27,29) (4,6) (12,11) (24,9) (10,8) (32,15) (5,31) (17,33) (13,20) (14,0) (14,1) (23,3) (1,17) (5,25) (31,23) (4,34) (8,19) (12,25) (16,6) (7,16) (8,15) (18,2) (32,12) (31,14) (24,28) (25,13) (29,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1013", "image": "data/cycle/graph_visual/hard/graph1013.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (17,25) (10,16) (3,1) (4,14) (7,5) (24,14) (17,23) (14,20) (18,13) (4,25) (10,17) (2,0) (1,6) (17,15) (3,25) (25,12) (0,21) (1,0) (5,2) (13,19) (0,3) (2,19) (11,8) (21,13) (14,18) (11,25) (16,22) (10,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1731", "image": "data/cycle/graph_visual/hard/graph1731.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (6,19) (15,17) (0,12) (20,10) (32,12) (28,9) (1,32) (17,16) (26,9) (10,24) (28,7) (20,4) (20,17) (11,13) (28,14) (22,17) (2,8) (0,29) (7,5) (27,0) (19,7) (21,29) (18,11) (8,14) (30,32) (26,15) (28,23) (13,22) (27,16) (1,0) (31,2) (3,7) (32,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph27", "image": "data/cycle/graph_visual/hard/graph27.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (25,16) (17,4) (25,2) (0,22) (18,11) (4,14) (16,9) (7,20) (18,15) (1,20) (5,12) (18,17) (4,0) (3,2) (23,2) (1,21) (0,1) (10,24) (6,1) (12,7) (16,13) (18,8) (20,10) (25,19) (9,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph819", "image": "data/cycle/graph_visual/hard/graph819.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (14,25) (18,25) (18,32) (15,11) (30,4) (22,26) (23,3) (12,28) (26,6) (19,8) (17,22) (11,2) (31,2) (28,16) (24,23) (29,13) (16,21) (3,6) (13,30) (12,7) (20,18) (24,28) (0,27) (1,12) (2,9) (13,5) (11,19) (8,6) (15,33) (28,4) (18,19) (31,0) (12,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1858", "image": "data/cycle/graph_visual/hard/graph1858.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,21) (1,27) (29,1) (0,3) (31,28) (15,31) (8,2) (23,17) (12,6) (11,13) (27,19) (20,6) (13,24) (33,1) (14,28) (30,0) (5,7) (8,28) (26,1) (4,16) (0,1) (4,3) (24,0) (1,20) (9,30) (24,18) (10,24) (16,1) (25,6) (22,28) (31,33) (2,0) (32,14) (17,14) (13,27) (7,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1636", "image": "data/cycle/graph_visual/hard/graph1636.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,29) (29,24) (29,1) (1,23) (8,12) (4,27) (31,18) (14,6) (19,9) (29,7) (20,22) (26,17) (10,30) (13,22) (17,16) (20,6) (11,2) (31,28) (1,0) (28,0) (31,21) (3,31) (4,0) (27,8) (30,2) (15,5) (2,0) (3,19) (0,3) (16,5) (9,12) (1,19) (24,25) (12,26) (22,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph635", "image": "data/cycle/graph_visual/hard/graph635.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (29,25) (14,12) (8,18) (3,30) (25,7) (5,9) (2,16) (1,5) (19,13) (1,29) (26,1) (16,14) (28,25) (12,17) (27,5) (0,30) (28,23) (25,13) (4,11) (9,21) (1,15) (2,6) (24,12) (17,20) (8,31) (0,4) (26,22) (6,11) (5,12) (18,13) (7,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph476", "image": "data/cycle/graph_visual/hard/graph476.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,17) (16,4) (18,9) (20,26) (22,1) (1,27) (7,14) (29,17) (12,27) (19,18) (11,18) (1,8) (28,13) (7,20) (25,10) (10,20) (2,25) (1,26) (25,21) (4,17) (5,2) (28,3) (28,29) (0,23) (0,4) (2,24) (0,26) (6,12) (15,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1890", "image": "data/cycle/graph_visual/hard/graph1890.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (6,19) (16,17) (12,33) (2,32) (0,1) (22,13) (28,24) (20,17) (2,8) (12,0) (10,20) (7,5) (18,11) (30,0) (21,29) (14,28) (31,32) (9,26) (29,32) (16,27) (14,8) (1,32) (4,20) (33,22) (0,27) (17,23) (13,11) (7,3) (15,17) (26,15) (25,10) (9,28) (7,19) (7,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1204", "image": "data/cycle/graph_visual/hard/graph1204.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,0) (11,19) (5,22) (17,26) (0,3) (19,15) (24,13) (4,14) (18,11) (12,27) (1,9) (16,13) (8,11) (14,3) (12,13) (25,20) (19,27) (0,1) (0,23) (18,25) (2,0) (2,1) (6,24) (15,22) (19,14) (17,24) (21,3) (21,9) (4,7) (22,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1716", "image": "data/cycle/graph_visual/hard/graph1716.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (19,9) (7,20) (8,18) (6,0) (27,8) (14,21) (24,30) (31,2) (6,31) (2,0) (18,1) (15,12) (11,29) (0,15) (16,29) (9,2) (21,23) (20,16) (27,12) (18,32) (0,5) (1,0) (31,4) (28,2) (8,14) (25,22) (23,17) (2,25) (12,10) (29,9) (3,2) (31,13) (30,18) (26,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1373", "image": "data/cycle/graph_visual/hard/graph1373.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,4) (0,3) (2,0) (5,11) (14,24) (15,23) (4,13) (18,11) (0,21) (28,5) (11,14) (1,15) (20,8) (21,19) (26,19) (12,16) (9,21) (0,17) (2,8) (22,25) (10,11) (0,12) (8,15) (20,25) (0,1) (6,16) (22,27) (17,7) (0,4) (7,27) (21,3) (19,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph533", "image": "data/cycle/graph_visual/hard/graph533.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,23) (21,8) (22,3) (28,14) (16,4) (21,7) (4,10) (19,20) (15,30) (27,5) (29,18) (5,0) (4,3) (28,13) (20,27) (8,17) (1,28) (27,23) (24,11) (28,26) (13,0) (2,3) (25,18) (28,21) (18,30) (10,15) (13,2) (24,10) (25,9) (28,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph168", "image": "data/cycle/graph_visual/hard/graph168.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (6,7) (26,5) (24,25) (24,21) (12,7) (5,19) (14,9) (16,10) (2,21) (4,14) (13,15) (20,17) (14,8) (22,3) (21,16) (3,10) (18,15) (5,25) (22,8) (20,15) (15,9) (8,6) (11,10) (5,0) (6,23) (1,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1809", "image": "data/cycle/graph_visual/hard/graph1809.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (28,32) (9,30) (11,14) (21,14) (7,29) (23,9) (12,33) (7,27) (20,19) (26,23) (3,20) (17,33) (10,2) (30,29) (17,28) (25,30) (6,25) (4,29) (4,16) (4,0) (5,24) (1,0) (8,1) (22,21) (13,9) (2,15) (33,18) (3,1) (21,32) (8,18) (31,4) (5,25) (1,2) (27,14) (0,2) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1499", "image": "data/cycle/graph_visual/hard/graph1499.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (23,2) (12,24) (8,10) (5,12) (13,9) (7,15) (22,3) (20,18) (11,8) (29,18) (9,6) (26,19) (7,27) (10,17) (22,26) (7,5) (4,8) (29,23) (8,16) (2,6) (20,28) (1,0) (14,2) (0,20) (11,26) (26,15) (15,1) (2,26) (17,21) (25,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph767", "image": "data/cycle/graph_visual/hard/graph767.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,20) (22,29) (21,7) (16,3) (18,22) (12,19) (18,32) (3,11) (32,17) (5,12) (26,1) (25,1) (1,7) (4,14) (31,4) (11,9) (15,25) (16,23) (24,26) (2,7) (5,29) (11,27) (17,0) (6,32) (26,22) (31,27) (10,29) (12,16) (30,8) (28,27) (13,19) (31,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph563", "image": "data/cycle/graph_visual/hard/graph563.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,26) (17,12) (29,12) (6,18) (10,20) (22,28) (28,2) (5,26) (16,4) (30,27) (25,0) (23,1) (14,29) (10,29) (10,9) (5,13) (6,3) (27,0) (20,13) (10,11) (11,8) (21,24) (8,4) (10,19) (11,7) (15,21) (8,2) (22,1) (16,25) (0,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph36", "image": "data/cycle/graph_visual/hard/graph36.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (25,11) (10,9) (14,24) (4,14) (2,19) (16,22) (25,4) (17,25) (17,23) (14,18) (25,12) (3,25) (1,6) (19,13) (14,20) (2,5) (1,3) (5,7) (11,8) (21,13) (17,15) (13,18) (16,10) (17,10) (0,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph121", "image": "data/cycle/graph_visual/hard/graph121.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,6) (17,24) (3,21) (22,6) (20,5) (5,16) (6,2) (14,4) (15,1) (16,19) (10,19) (24,21) (0,23) (7,23) (6,26) (13,22) (17,11) (24,4) (19,21) (13,23) (15,18) (25,7) (1,12) (9,13) (13,20) (1,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph519", "image": "data/cycle/graph_visual/hard/graph519.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (27,7) (23,16) (21,2) (5,24) (11,30) (12,26) (15,8) (6,20) (19,23) (14,21) (9,23) (25,12) (14,9) (3,8) (17,8) (27,28) (22,4) (19,1) (3,29) (21,27) (7,8) (7,13) (24,12) (16,10) (20,2) (28,30) (22,14) (18,9) (3,0) (29,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1337", "image": "data/cycle/graph_visual/hard/graph1337.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (2,12) (21,12) (20,0) (15,25) (8,12) (1,2) (11,5) (0,2) (15,23) (6,28) (3,7) (25,7) (18,15) (12,26) (0,3) (9,4) (7,4) (10,6) (14,12) (0,14) (1,13) (16,19) (1,0) (4,17) (6,16) (26,27) (28,2) (6,18) (22,20) (22,11) (24,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph20", "image": "data/cycle/graph_visual/hard/graph20.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (14,9) (15,23) (6,20) (9,17) (14,20) (0,3) (21,2) (21,14) (22,9) (24,5) (25,7) (3,24) (23,12) (1,19) (24,12) (8,13) (10,16) (23,18) (21,12) (8,7) (3,8) (4,22) (8,16) (11,7) (2,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1055", "image": "data/cycle/graph_visual/hard/graph1055.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (15,9) (13,15) (6,20) (19,5) (14,4) (8,6) (24,25) (12,7) (0,5) (8,14) (18,15) (16,10) (22,3) (25,23) (22,8) (3,10) (6,7) (10,11) (16,21) (2,21) (5,15) (24,21) (9,14) (17,20) (3,1) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph763", "image": "data/cycle/graph_visual/hard/graph763.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (13,22) (27,23) (14,17) (15,2) (19,28) (32,9) (19,25) (1,27) (20,21) (15,5) (1,16) (0,8) (11,22) (17,3) (7,30) (20,18) (7,3) (9,31) (20,3) (3,24) (28,6) (12,26) (29,26) (12,11) (11,25) (21,16) (10,7) (14,5) (11,16) (4,1) (11,8) (19,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph814", "image": "data/cycle/graph_visual/hard/graph814.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (11,14) (14,21) (29,7) (28,32) (18,8) (25,30) (16,4) (22,21) (4,31) (20,3) (6,25) (33,12) (13,9) (18,33) (30,9) (17,28) (29,30) (0,4) (24,5) (1,2) (29,4) (3,1) (8,1) (23,26) (5,25) (2,15) (33,17) (14,27) (10,2) (19,20) (32,21) (7,27) (9,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph480", "image": "data/cycle/graph_visual/hard/graph480.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (28,24) (6,23) (5,27) (8,2) (3,8) (24,16) (1,4) (3,15) (29,22) (10,2) (13,12) (19,13) (15,14) (15,0) (15,11) (4,18) (21,25) (28,25) (22,0) (0,24) (24,9) (12,26) (14,17) (26,27) (7,25) (3,6) (20,12) (20,18) (19,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph459", "image": "data/cycle/graph_visual/hard/graph459.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,11) (6,19) (0,8) (22,12) (10,15) (3,12) (26,18) (13,20) (23,25) (21,28) (27,0) (15,9) (5,23) (20,3) (13,9) (0,24) (7,14) (29,28) (27,12) (17,10) (26,19) (1,2) (16,5) (12,11) (29,16) (20,28) (19,11) (4,18) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph376", "image": "data/cycle/graph_visual/hard/graph376.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (5,18) (1,18) (6,15) (21,27) (3,13) (15,4) (23,8) (0,27) (22,25) (21,19) (12,16) (9,11) (19,1) (4,5) (11,12) (11,2) (28,3) (5,23) (2,14) (28,10) (26,11) (19,26) (3,12) (17,24) (7,18) (17,28) (25,3) (3,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph9", "image": "data/cycle/graph_visual/hard/graph9.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,7) (16,1) (15,14) (6,17) (22,25) (9,12) (11,21) (5,7) (19,22) (16,17) (13,17) (18,21) (0,7) (20,10) (23,14) (8,7) (3,5) (24,8) (22,12) (17,23) (2,17) (16,20) (12,11) (12,8) (10,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph39", "image": "data/cycle/graph_visual/hard/graph39.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (19,22) (20,17) (9,8) (2,15) (0,11) (8,0) (7,3) (10,14) (10,22) (12,24) (24,2) (10,21) (25,22) (18,20) (6,5) (16,15) (3,11) (23,4) (23,3) (16,19) (22,17) (4,1) (6,17) (13,24) (12,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph600", "image": "data/cycle/graph_visual/hard/graph600.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,5) (7,15) (22,20) (19,6) (9,18) (21,25) (21,4) (12,24) (15,14) (21,17) (0,30) (3,23) (21,14) (14,20) (27,29) (27,26) (6,27) (30,8) (28,5) (16,5) (20,13) (4,5) (23,22) (12,4) (2,17) (17,27) (21,10) (22,9) (0,14) (31,1) (6,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1754", "image": "data/cycle/graph_visual/hard/graph1754.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (12,13) (14,19) (13,32) (8,14) (10,25) (29,12) (7,1) (25,1) (17,8) (22,9) (13,15) (7,5) (28,14) (28,21) (18,7) (3,0) (20,8) (26,24) (5,27) (0,5) (25,23) (13,26) (4,0) (11,9) (25,21) (2,3) (6,7) (30,0) (16,2) (30,21) (9,2) (15,23) (3,8) (0,2) (0,1) (13,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph128", "image": "data/cycle/graph_visual/hard/graph128.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,7) (7,6) (9,3) (7,8) (18,13) (0,17) (19,16) (23,11) (0,19) (21,23) (2,25) (0,10) (3,21) (4,15) (1,13) (26,17) (16,7) (18,24) (17,22) (8,12) (2,6) (2,23) (1,0) (23,4) (3,20) (5,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph50", "image": "data/cycle/graph_visual/hard/graph50.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (22,24) (8,22) (20,24) (4,19) (0,16) (0,9) (1,15) (18,15) (16,8) (7,1) (23,11) (14,25) (16,14) (21,23) (3,9) (10,6) (19,11) (2,23) (17,4) (13,10) (17,15) (21,12) (24,17) (14,6) (5,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph693", "image": "data/cycle/graph_visual/hard/graph693.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (31,24) (0,17) (31,18) (11,5) (9,21) (29,16) (12,22) (12,4) (6,17) (27,20) (13,22) (19,1) (17,1) (5,19) (27,26) (30,12) (20,28) (28,13) (10,20) (12,3) (6,8) (2,9) (24,21) (5,23) (14,7) (15,0) (17,26) (30,18) (7,23) (11,16) (4,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1923", "image": "data/cycle/graph_visual/hard/graph1923.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (22,20) (32,13) (17,8) (16,33) (2,3) (34,6) (12,26) (7,19) (26,9) (11,2) (30,25) (21,24) (16,22) (2,19) (1,4) (5,19) (30,4) (6,20) (4,26) (3,9) (17,9) (13,27) (31,14) (0,1) (29,18) (21,1) (7,18) (0,2) (5,23) (0,7) (17,10) (20,11) (27,4) (8,31) (0,28) (16,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph525", "image": "data/cycle/graph_visual/hard/graph525.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,25) (13,10) (10,28) (0,30) (26,8) (7,28) (15,3) (16,11) (12,6) (23,8) (27,30) (4,18) (2,21) (6,20) (14,16) (21,18) (4,19) (17,16) (24,10) (0,9) (28,9) (29,8) (5,1) (11,12) (26,3) (3,22) (8,19) (25,13) (9,16) (24,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1832", "image": "data/cycle/graph_visual/hard/graph1832.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (23,25) (7,18) (30,0) (21,14) (1,30) (16,8) (8,21) (28,22) (27,5) (14,33) (6,25) (15,11) (31,4) (12,10) (2,0) (32,9) (6,9) (30,16) (25,33) (26,27) (29,15) (24,11) (22,0) (3,26) (21,18) (16,19) (0,1) (17,2) (3,28) (4,13) (4,5) (16,17) (3,0) (31,15) (23,20) (12,4) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph742", "image": "data/cycle/graph_visual/hard/graph742.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (26,16) (10,19) (20,1) (24,29) (32,5) (0,25) (9,1) (2,4) (9,19) (5,18) (14,23) (13,24) (16,17) (18,4) (30,14) (11,3) (20,28) (7,23) (31,15) (23,29) (26,1) (22,6) (12,14) (0,28) (8,21) (32,22) (14,21) (15,22) (22,17) (11,8) (31,23) (27,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph325", "image": "data/cycle/graph_visual/hard/graph325.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (22,12) (23,1) (0,20) (4,25) (23,18) (24,11) (3,27) (8,4) (2,19) (1,5) (6,14) (1,21) (27,5) (7,28) (28,1) (28,8) (19,14) (10,16) (23,14) (17,16) (11,16) (23,26) (15,13) (5,22) (9,6) (23,11) (27,0) (22,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph852", "image": "data/cycle/graph_visual/hard/graph852.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,29) (19,13) (16,3) (30,16) (3,13) (6,25) (29,1) (10,7) (11,4) (33,7) (25,13) (10,24) (22,8) (14,21) (29,5) (20,7) (26,13) (9,11) (27,7) (14,19) (29,25) (5,28) (17,29) (18,32) (15,27) (23,26) (0,9) (22,23) (12,22) (31,21) (17,24) (32,11) (12,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1797", "image": "data/cycle/graph_visual/hard/graph1797.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,3) (13,22) (8,7) (5,25) (0,27) (1,32) (9,14) (1,0) (16,6) (26,4) (22,11) (29,3) (9,15) (18,21) (17,25) (21,17) (3,20) (2,5) (5,30) (5,20) (29,10) (16,26) (21,8) (9,29) (30,26) (14,28) (19,13) (4,23) (2,0) (21,19) (24,10) (0,8) (12,4) (31,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph999", "image": "data/cycle/graph_visual/hard/graph999.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,12) (30,13) (1,30) (7,33) (2,32) (8,13) (9,14) (2,0) (19,2) (34,11) (15,1) (27,10) (13,5) (27,14) (18,34) (32,7) (30,17) (24,28) (23,15) (29,34) (0,29) (26,25) (22,15) (32,20) (8,9) (31,34) (3,8) (12,26) (21,10) (24,23) (6,27) (4,12) (3,16) (18,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph746", "image": "data/cycle/graph_visual/hard/graph746.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,9) (22,23) (32,5) (14,25) (30,32) (17,27) (16,20) (30,28) (7,27) (6,14) (28,13) (3,18) (16,2) (15,21) (24,2) (1,18) (19,4) (28,25) (7,16) (12,21) (0,26) (26,10) (8,22) (12,30) (23,29) (8,7) (10,8) (14,18) (14,23) (29,4) (14,31) (11,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1619", "image": "data/cycle/graph_visual/hard/graph1619.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (9,19) (14,6) (24,29) (31,21) (18,31) (7,29) (24,25) (22,17) (8,27) (1,29) (12,26) (17,16) (15,5) (16,5) (12,8) (9,12) (30,10) (31,3) (19,3) (11,2) (22,13) (0,28) (27,4) (17,26) (31,28) (22,20) (19,1) (29,10) (1,0) (23,1) (2,30) (20,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph534", "image": "data/cycle/graph_visual/hard/graph534.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (9,19) (6,13) (15,13) (8,18) (23,19) (0,9) (7,11) (29,23) (21,10) (21,16) (26,28) (25,30) (9,5) (8,7) (0,14) (27,13) (14,12) (2,15) (20,22) (20,7) (25,0) (22,17) (1,11) (27,9) (15,3) (24,9) (7,0) (4,21) (30,4) (26,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1333", "image": "data/cycle/graph_visual/hard/graph1333.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,6) (6,0) (27,15) (27,25) (24,7) (7,20) (13,24) (3,5) (24,21) (22,21) (27,26) (10,14) (23,12) (19,18) (19,28) (7,17) (21,18) (1,22) (4,26) (3,10) (8,28) (11,16) (18,11) (9,6) (24,14) (12,17) (17,27) (1,0) (2,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1177", "image": "data/cycle/graph_visual/hard/graph1177.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (20,25) (8,2) (7,25) (13,12) (12,0) (11,26) (17,0) (11,16) (7,17) (8,15) (4,14) (2,0) (21,3) (19,22) (0,21) (3,0) (22,24) (4,19) (0,1) (21,6) (21,19) (9,11) (8,20) (11,14) (16,5) (4,10) (18,15) (23,14) (15,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1045", "image": "data/cycle/graph_visual/hard/graph1045.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (23,0) (25,6) (18,8) (6,18) (20,12) (1,0) (2,19) (10,20) (17,13) (16,14) (24,0) (5,15) (16,17) (2,0) (21,7) (13,22) (0,4) (3,7) (11,3) (18,24) (24,9) (2,10) (1,17) (22,6) (11,19) (15,9) (8,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph473", "image": "data/cycle/graph_visual/hard/graph473.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,16) (18,13) (25,17) (17,10) (25,19) (10,8) (1,3) (1,4) (29,25) (14,18) (11,7) (10,16) (29,9) (12,27) (21,17) (29,11) (2,5) (17,28) (25,15) (14,26) (23,14) (3,25) (13,27) (20,27) (13,22) (21,0) (24,26) (19,2) (5,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph56", "image": "data/cycle/graph_visual/hard/graph56.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (21,3) (1,13) (2,24) (7,6) (7,8) (17,22) (23,21) (4,15) (6,2) (0,1) (0,19) (12,8) (4,23) (3,9) (0,10) (20,5) (18,13) (16,19) (7,14) (20,3) (23,11) (17,2) (23,18) (7,16) (25,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1122", "image": "data/cycle/graph_visual/hard/graph1122.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,14) (6,26) (20,8) (6,15) (14,18) (6,25) (3,21) (7,8) (14,17) (18,1) (5,9) (26,19) (2,0) (24,25) (21,4) (11,25) (22,11) (1,0) (16,14) (13,23) (12,5) (14,26) (15,23) (19,21) (12,25) (7,6) (5,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1661", "image": "data/cycle/graph_visual/hard/graph1661.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (16,28) (8,2) (3,0) (31,2) (10,0) (26,23) (20,6) (1,0) (12,30) (22,12) (6,2) (7,16) (12,18) (19,26) (1,14) (6,28) (5,23) (25,5) (16,26) (13,20) (31,15) (31,4) (5,21) (1,17) (4,0) (12,17) (0,2) (21,27) (9,30) (0,9) (23,11) (6,18) (24,16) (27,29) (3,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1931", "image": "data/cycle/graph_visual/hard/graph1931.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (13,23) (0,2) (27,29) (31,15) (28,9) (33,5) (18,20) (10,2) (30,6) (34,6) (21,19) (14,25) (14,5) (4,23) (10,22) (4,11) (6,8) (25,22) (26,3) (27,7) (24,0) (32,33) (26,31) (16,2) (0,15) (17,20) (24,23) (23,34) (12,29) (17,21) (30,19) (0,1) (33,27) (9,1) (9,30) (1,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1289", "image": "data/cycle/graph_visual/hard/graph1289.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,26) (18,3) (3,25) (7,26) (19,8) (0,10) (8,1) (24,27) (3,13) (9,18) (0,1) (18,21) (6,27) (9,1) (23,26) (16,27) (0,6) (0,3) (27,26) (17,24) (23,21) (9,11) (15,1) (2,12) (15,14) (12,20) (20,13) (24,4) (4,0) (2,0) (18,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph195", "image": "data/cycle/graph_visual/hard/graph195.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (16,8) (13,0) (2,21) (18,9) (13,25) (15,14) (4,11) (7,20) (4,5) (9,3) (1,7) (24,0) (21,5) (7,8) (20,25) (9,6) (25,17) (26,23) (22,2) (19,25) (10,1) (14,10) (25,23) (4,12) (1,12) (18,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1536", "image": "data/cycle/graph_visual/hard/graph1536.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,23) (25,20) (4,30) (5,25) (3,18) (4,0) (16,26) (6,0) (7,2) (0,2) (18,19) (7,30) (1,0) (4,27) (9,1) (10,15) (26,22) (18,0) (13,12) (11,1) (26,14) (13,27) (16,15) (24,8) (30,28) (23,29) (3,0) (1,5) (10,2) (8,20) (17,15) (1,13) (21,15) (14,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph447", "image": "data/cycle/graph_visual/hard/graph447.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,3) (16,12) (7,16) (12,22) (18,19) (27,0) (8,1) (2,15) (16,6) (11,17) (8,25) (13,15) (5,14) (4,3) (2,18) (26,24) (8,13) (17,13) (11,28) (20,5) (14,6) (27,24) (18,9) (13,0) (16,23) (9,21) (14,3) (15,29) (10,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1357", "image": "data/cycle/graph_visual/hard/graph1357.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,27) (27,15) (5,3) (1,0) (2,0) (0,6) (19,28) (6,7) (24,7) (27,26) (14,10) (24,13) (11,16) (1,22) (21,22) (10,3) (7,17) (19,2) (12,23) (27,17) (11,18) (9,6) (18,19) (4,26) (21,24) (18,21) (7,20) (17,12) (14,24) (8,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph962", "image": "data/cycle/graph_visual/hard/graph962.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (22,20) (31,7) (8,0) (3,33) (19,25) (24,27) (34,17) (23,11) (11,8) (3,18) (14,5) (29,19) (20,3) (25,11) (5,15) (6,28) (16,1) (21,16) (1,28) (20,21) (22,13) (33,7) (12,11) (16,11) (4,1) (19,32) (3,27) (17,9) (2,15) (7,10) (26,30) (32,9) (26,12) (14,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1787", "image": "data/cycle/graph_visual/hard/graph1787.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (18,25) (25,8) (20,13) (31,15) (22,17) (4,19) (18,31) (1,14) (24,10) (32,0) (25,4) (2,31) (11,5) (6,13) (23,21) (16,22) (9,27) (21,28) (26,0) (20,32) (29,5) (9,8) (1,30) (27,1) (0,1) (7,20) (29,22) (11,21) (20,28) (12,18) (2,0) (3,11) (21,10) (21,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1386", "image": "data/cycle/graph_visual/hard/graph1386.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (16,9) (7,16) (11,12) (27,9) (1,25) (10,28) (22,8) (11,16) (16,15) (28,5) (19,8) (20,18) (24,10) (23,13) (9,28) (24,3) (3,21) (6,17) (1,2) (0,21) (8,25) (3,26) (1,0) (14,3) (6,12) (4,18) (10,13) (8,26) (4,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1764", "image": "data/cycle/graph_visual/hard/graph1764.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,2) (3,24) (12,4) (16,2) (30,3) (29,0) (13,22) (6,9) (24,14) (5,8) (11,5) (15,30) (19,32) (11,9) (2,14) (22,20) (17,24) (0,1) (2,0) (25,16) (10,19) (27,20) (5,32) (12,32) (3,0) (26,32) (31,27) (12,27) (25,21) (24,18) (1,5) (28,0) (5,14) (19,7) (14,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph235", "image": "data/cycle/graph_visual/hard/graph235.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (24,22) (3,8) (26,5) (9,25) (2,4) (21,9) (5,24) (23,14) (9,10) (16,17) (25,24) (17,11) (23,1) (27,8) (18,12) (12,17) (0,12) (13,3) (15,19) (11,8) (7,16) (2,20) (6,7) (2,0) (4,15) (1,7) (3,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1516", "image": "data/cycle/graph_visual/hard/graph1516.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,2) (30,1) (16,21) (22,1) (10,26) (7,29) (22,19) (20,26) (13,0) (0,2) (24,29) (14,17) (15,20) (4,9) (10,25) (17,28) (13,28) (14,16) (9,27) (14,12) (7,2) (6,20) (6,8) (17,23) (19,15) (0,1) (18,14) (13,27) (3,9) (3,0) (8,14) (11,7) (5,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph500", "image": "data/cycle/graph_visual/hard/graph500.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,29) (21,7) (12,28) (1,15) (18,10) (6,23) (15,9) (10,22) (28,11) (12,20) (13,30) (19,2) (14,7) (4,14) (17,5) (1,6) (14,19) (28,6) (12,24) (23,29) (25,15) (28,27) (15,16) (25,17) (17,14) (8,9) (3,4) (29,26) (23,18) (30,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1579", "image": "data/cycle/graph_visual/hard/graph1579.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,23) (11,23) (29,25) (22,17) (28,7) (5,1) (8,4) (27,3) (28,8) (1,24) (27,0) (5,30) (27,11) (21,0) (14,6) (28,23) (23,19) (13,15) (10,16) (18,16) (23,14) (29,22) (29,4) (26,5) (20,14) (6,9) (0,1) (15,29) (22,12) (16,11) (2,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph155", "image": "data/cycle/graph_visual/hard/graph155.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (26,20) (5,6) (14,10) (9,4) (14,0) (4,2) (8,14) (3,5) (20,22) (25,19) (19,23) (25,18) (14,3) (2,17) (21,16) (14,9) (7,24) (17,25) (24,5) (1,17) (20,15) (13,6) (11,16) (22,25) (16,15) (18,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1360", "image": "data/cycle/graph_visual/hard/graph1360.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,14) (11,18) (9,23) (1,27) (14,11) (14,12) (0,7) (11,5) (27,15) (26,20) (15,16) (3,8) (1,21) (2,28) (19,13) (17,1) (5,4) (17,12) (23,25) (20,0) (0,1) (28,8) (24,13) (10,16) (2,7) (4,22) (6,1) (25,5) (26,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph957", "image": "data/cycle/graph_visual/hard/graph957.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (14,27) (5,25) (20,19) (28,32) (18,33) (22,21) (33,12) (34,15) (3,20) (10,2) (4,31) (0,4) (25,6) (32,21) (3,1) (8,1) (27,7) (23,9) (29,34) (30,25) (11,14) (5,24) (28,34) (7,33) (18,8) (17,4) (9,13) (4,29) (2,1) (30,29) (21,14) (2,16) (26,23) (30,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1473", "image": "data/cycle/graph_visual/hard/graph1473.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (22,24) (13,22) (19,16) (21,23) (9,11) (23,6) (3,0) (2,1) (21,19) (0,4) (5,11) (12,28) (26,22) (19,4) (4,20) (25,22) (0,20) (17,11) (2,25) (14,7) (15,17) (7,25) (23,9) (29,14) (10,7) (19,3) (0,22) (1,0) (12,4) (27,10) (22,18) (2,0) (5,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1272", "image": "data/cycle/graph_visual/hard/graph1272.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,5) (17,10) (3,14) (20,16) (8,9) (5,4) (1,25) (0,1) (8,4) (23,1) (17,19) (0,2) (22,19) (0,4) (22,14) (14,16) (10,0) (6,19) (27,11) (13,23) (24,2) (7,11) (23,14) (21,15) (22,5) (0,18) (27,13) (21,19) (26,12) (10,2) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph49", "image": "data/cycle/graph_visual/hard/graph49.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (23,25) (13,5) (14,6) (11,3) (2,24) (0,14) (18,21) (8,15) (22,8) (9,24) (10,2) (7,1) (20,11) (8,24) (13,21) (10,21) (15,16) (18,4) (15,23) (12,16) (21,17) (22,19) (21,14) (22,3) (23,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph165", "image": "data/cycle/graph_visual/hard/graph165.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,21) (9,10) (26,22) (2,26) (23,11) (0,10) (10,6) (9,21) (16,12) (18,5) (20,24) (15,26) (17,0) (19,24) (25,23) (14,3) (7,11) (17,8) (26,21) (13,17) (19,0) (7,9) (4,14) (4,5) (12,15) (1,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1164", "image": "data/cycle/graph_visual/hard/graph1164.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (9,20) (10,8) (23,25) (3,14) (0,14) (5,9) (14,12) (16,2) (9,6) (26,2) (1,0) (19,1) (21,11) (4,26) (7,21) (18,6) (24,20) (4,0) (4,21) (26,9) (22,2) (7,1) (15,8) (2,0) (15,2) (2,13) (23,12) (23,19) (0,3) (21,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph792", "image": "data/cycle/graph_visual/hard/graph792.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,22) (17,20) (8,18) (28,11) (13,26) (0,7) (7,28) (29,10) (13,9) (16,1) (24,17) (20,14) (28,16) (15,26) (25,4) (7,31) (3,18) (32,31) (27,20) (24,28) (21,9) (4,32) (5,2) (6,29) (22,18) (12,8) (1,8) (31,2) (6,5) (6,19) (24,23) (25,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1700", "image": "data/cycle/graph_visual/hard/graph1700.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (22,21) (7,21) (30,5) (27,12) (1,28) (31,15) (8,26) (4,13) (19,9) (32,1) (16,1) (7,2) (23,25) (0,8) (0,31) (2,17) (6,19) (3,30) (0,23) (28,10) (21,5) (13,9) (18,12) (24,3) (29,18) (0,1) (20,6) (31,2) (11,4) (20,32) (28,12) (15,14) (7,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph674", "image": "data/cycle/graph_visual/hard/graph674.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,2) (6,12) (24,22) (15,11) (23,11) (18,29) (6,4) (25,14) (26,21) (23,28) (29,30) (11,26) (9,31) (27,11) (21,25) (16,12) (5,19) (12,1) (19,24) (30,17) (9,18) (2,9) (20,0) (8,27) (12,9) (7,16) (13,3) (22,27) (13,6) (15,0) (3,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1151", "image": "data/cycle/graph_visual/hard/graph1151.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (18,8) (14,26) (1,0) (0,23) (6,19) (22,24) (4,26) (16,22) (3,10) (8,2) (2,6) (25,9) (26,0) (25,14) (16,6) (12,8) (15,24) (20,16) (19,7) (17,6) (21,1) (16,5) (19,1) (10,0) (26,11) (13,4) (11,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph543", "image": "data/cycle/graph_visual/hard/graph543.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,0) (29,25) (2,17) (24,26) (1,22) (22,2) (14,29) (4,19) (22,9) (20,3) (28,14) (5,13) (30,0) (4,25) (22,21) (26,8) (7,12) (0,24) (21,16) (23,20) (23,9) (27,14) (23,27) (24,18) (15,6) (12,6) (5,21) (5,6) (18,10) (5,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1972", "image": "data/cycle/graph_visual/hard/graph1972.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,2) (20,21) (1,7) (27,7) (1,0) (28,1) (18,33) (34,3) (0,30) (6,10) (16,2) (0,5) (10,30) (12,33) (16,13) (16,31) (11,32) (22,19) (17,24) (28,23) (25,17) (9,14) (0,25) (29,15) (5,32) (12,1) (0,3) (23,19) (34,29) (14,25) (4,15) (28,10) (26,24) (0,2) (11,22) (0,4) (21,23) (15,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1505", "image": "data/cycle/graph_visual/hard/graph1505.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,8) (25,9) (0,26) (16,22) (13,4) (6,16) (4,11) (7,19) (16,11) (0,25) (29,28) (5,16) (21,16) (8,12) (29,26) (15,26) (14,26) (4,24) (2,0) (8,20) (6,2) (19,6) (24,17) (10,3) (23,1) (1,19) (0,10) (0,1) (24,14) (30,11) (27,22) (18,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph256", "image": "data/cycle/graph_visual/hard/graph256.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (4,19) (2,6) (0,1) (25,1) (7,27) (23,13) (24,3) (11,7) (18,21) (22,11) (10,14) (8,11) (21,11) (3,10) (7,5) (17,0) (27,4) (12,8) (5,16) (12,26) (7,23) (14,22) (1,15) (20,22) (9,16) (6,0) (8,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1362", "image": "data/cycle/graph_visual/hard/graph1362.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (16,13) (2,4) (3,14) (24,10) (2,0) (12,14) (21,27) (27,28) (14,9) (17,25) (23,25) (27,1) (28,25) (6,5) (5,26) (16,15) (2,17) (20,15) (1,0) (24,16) (17,7) (18,22) (25,19) (14,0) (20,19) (9,4) (14,11) (18,6) (5,3) (8,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph492", "image": "data/cycle/graph_visual/hard/graph492.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,23) (13,0) (16,4) (20,6) (6,8) (19,22) (16,14) (14,11) (10,26) (29,22) (9,3) (12,14) (18,16) (7,27) (17,21) (2,28) (1,9) (13,26) (24,10) (14,17) (14,8) (25,20) (28,13) (7,2) (15,19) (5,27) (15,20) (7,9) (17,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph839", "image": "data/cycle/graph_visual/hard/graph839.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,1) (11,18) (20,11) (17,13) (2,15) (31,0) (10,28) (7,8) (29,33) (12,13) (29,4) (20,30) (26,3) (11,24) (14,28) (23,5) (21,19) (19,12) (24,8) (27,14) (32,22) (9,22) (25,9) (6,5) (2,1) (19,26) (3,5) (30,12) (30,29) (10,2) (22,24) (16,3) (31,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1132", "image": "data/cycle/graph_visual/hard/graph1132.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,5) (21,13) (10,0) (13,14) (11,0) (26,13) (12,16) (0,17) (9,20) (0,1) (10,21) (10,25) (14,5) (2,0) (0,3) (3,7) (24,15) (18,21) (22,4) (5,19) (22,16) (1,12) (19,4) (7,24) (23,4) (6,10) (22,3) (14,20) (6,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1470", "image": "data/cycle/graph_visual/hard/graph1470.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (11,9) (27,2) (2,26) (12,16) (27,7) (24,5) (14,4) (6,15) (18,1) (29,22) (20,22) (4,11) (13,1) (27,3) (8,14) (21,6) (13,4) (12,1) (0,15) (5,9) (25,20) (2,10) (1,0) (25,15) (9,17) (20,19) (28,6) (1,26) (17,25) (23,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph343", "image": "data/cycle/graph_visual/hard/graph343.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,15) (9,21) (2,14) (26,0) (26,14) (21,24) (16,10) (16,0) (23,24) (6,28) (6,18) (22,11) (4,1) (1,12) (14,25) (16,28) (19,4) (5,28) (27,23) (23,4) (11,8) (17,21) (9,7) (3,18) (20,1) (28,8) (6,20) (7,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph668", "image": "data/cycle/graph_visual/hard/graph668.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,21) (16,29) (18,8) (15,0) (18,1) (2,25) (12,15) (2,26) (30,6) (2,31) (29,11) (24,30) (2,9) (0,5) (2,3) (29,18) (4,31) (14,8) (20,7) (27,12) (19,9) (21,14) (16,20) (25,22) (12,10) (8,27) (18,31) (6,0) (28,9) (13,31) (17,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1987", "image": "data/cycle/graph_visual/hard/graph1987.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (20,6) (28,31) (28,8) (28,14) (33,14) (21,0) (19,27) (25,6) (26,1) (32,0) (24,18) (13,24) (16,1) (27,1) (3,4) (6,12) (15,31) (7,5) (11,13) (20,1) (17,14) (4,16) (1,0) (7,31) (23,17) (24,10) (0,24) (28,22) (13,27) (29,1) (1,33) (30,34) (8,2) (9,30) (31,34)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1995", "image": "data/cycle/graph_visual/hard/graph1995.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (25,0) (18,30) (12,6) (3,0) (34,16) (23,15) (24,11) (12,34) (4,5) (26,11) (2,16) (18,22) (1,17) (33,4) (10,12) (14,13) (12,27) (9,32) (20,3) (14,12) (17,0) (7,19) (0,4) (1,31) (24,29) (7,20) (12,5) (21,11) (21,20) (32,28) (31,16) (2,0) (0,1) (5,7) (32,30) (15,9) (8,15) (30,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1904", "image": "data/cycle/graph_visual/hard/graph1904.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (32,27) (30,20) (8,23) (23,1) (0,2) (15,16) (22,4) (18,14) (3,19) (5,27) (7,24) (0,13) (28,12) (11,17) (32,7) (31,6) (8,21) (13,29) (20,13) (2,4) (34,19) (15,9) (24,8) (6,16) (29,11) (30,19) (0,1) (1,28) (33,18) (29,33) (4,23) (25,10) (26,29) (10,26) (33,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph202", "image": "data/cycle/graph_visual/hard/graph202.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,6) (1,16) (23,11) (26,24) (24,22) (14,3) (19,0) (5,18) (4,21) (27,4) (11,7) (15,26) (15,12) (16,12) (2,26) (23,26) (14,21) (19,25) (20,14) (10,9) (9,7) (13,17) (5,4) (17,8) (0,10) (17,0) (9,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph607", "image": "data/cycle/graph_visual/hard/graph607.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (12,15) (11,24) (0,13) (4,8) (26,28) (0,29) (3,14) (5,22) (10,3) (30,13) (24,20) (7,16) (13,31) (0,8) (7,23) (29,1) (15,6) (28,8) (27,8) (16,2) (17,11) (30,18) (19,15) (23,26) (25,17) (22,13) (21,6) (4,10) (10,24) (0,15) (9,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph392", "image": "data/cycle/graph_visual/hard/graph392.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (11,16) (14,28) (9,5) (22,15) (11,4) (26,7) (24,18) (4,23) (12,16) (0,27) (28,10) (8,14) (12,13) (2,3) (24,1) (15,28) (25,0) (6,8) (17,26) (0,3) (20,2) (2,22) (18,9) (21,0) (19,7) (13,9) (19,14) (23,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph501", "image": "data/cycle/graph_visual/hard/graph501.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (7,30) (21,15) (2,7) (3,18) (1,5) (15,16) (13,12) (2,10) (9,1) (20,25) (26,16) (13,1) (18,0) (4,30) (15,17) (29,23) (27,13) (22,26) (5,25) (19,18) (1,11) (26,14) (30,28) (6,14) (23,11) (20,8) (15,10) (27,4) (8,24) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph93", "image": "data/cycle/graph_visual/hard/graph93.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,10) (24,15) (9,19) (4,7) (12,0) (2,19) (17,2) (12,20) (4,24) (22,17) (21,16) (1,12) (23,13) (15,6) (18,8) (19,25) (21,22) (7,5) (6,3) (6,13) (12,16) (2,14) (11,7) (8,23) (19,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1489", "image": "data/cycle/graph_visual/hard/graph1489.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,26) (10,29) (9,19) (13,18) (15,29) (20,16) (7,5) (25,6) (16,0) (11,27) (20,13) (21,2) (10,3) (0,2) (11,17) (7,8) (4,1) (22,0) (28,8) (24,5) (25,23) (20,23) (3,0) (17,8) (29,12) (28,9) (17,2) (14,25) (1,0) (2,18) (13,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph992", "image": "data/cycle/graph_visual/hard/graph992.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (31,8) (22,3) (1,20) (18,5) (31,23) (29,19) (32,25) (11,25) (17,6) (23,27) (32,16) (27,33) (10,19) (12,24) (26,18) (18,30) (34,12) (21,13) (29,30) (20,0) (0,7) (0,13) (14,24) (3,11) (28,5) (32,4) (2,1) (30,8) (6,15) (6,26) (5,25) (13,23) (4,9) (27,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1254", "image": "data/cycle/graph_visual/hard/graph1254.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,2) (9,1) (0,6) (18,21) (2,12) (5,26) (15,14) (1,8) (9,18) (16,27) (18,3) (24,4) (25,3) (0,10) (18,22) (19,8) (26,23) (9,11) (1,15) (17,24) (27,24) (0,1) (27,6) (21,23) (26,27) (26,7) (13,3) (20,12) (20,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph293", "image": "data/cycle/graph_visual/hard/graph293.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (6,5) (23,20) (11,6) (6,13) (19,22) (21,5) (14,0) (3,12) (15,21) (16,2) (20,27) (27,14) (5,12) (4,18) (26,23) (21,9) (5,10) (26,7) (18,8) (22,1) (25,4) (24,17) (22,24) (9,23) (24,0) (2,22) (14,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1973", "image": "data/cycle/graph_visual/hard/graph1973.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (34,32) (7,6) (33,13) (18,19) (1,13) (31,11) (1,0) (12,10) (22,4) (29,23) (15,30) (20,9) (14,33) (6,16) (3,27) (25,8) (5,21) (24,32) (23,5) (15,0) (5,9) (28,34) (14,3) (12,17) (23,18) (25,26) (30,17) (19,2) (18,25) (1,16) (16,17) (6,11) (4,1) (10,19) (21,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph930", "image": "data/cycle/graph_visual/hard/graph930.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (24,2) (34,13) (13,17) (23,5) (3,15) (11,19) (14,26) (21,25) (8,16) (7,8) (29,1) (24,4) (10,31) (13,18) (28,30) (6,24) (32,20) (32,4) (17,12) (10,15) (7,3) (21,2) (6,18) (27,10) (11,0) (8,32) (28,27) (23,9) (26,5) (29,22) (21,0) (29,10) (5,17) (14,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1417", "image": "data/cycle/graph_visual/hard/graph1417.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,2) (21,29) (7,9) (8,1) (13,11) (16,25) (18,24) (26,9) (24,11) (4,14) (23,2) (14,23) (22,5) (1,0) (10,7) (15,14) (12,22) (28,20) (0,3) (19,5) (6,10) (23,12) (25,3) (14,8) (29,26) (17,3) (20,6) (13,16) (17,27) (21,1) (0,4) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph395", "image": "data/cycle/graph_visual/hard/graph395.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (26,13) (17,2) (8,17) (28,9) (23,20) (2,18) (5,22) (20,13) (26,15) (27,8) (11,25) (7,8) (1,0) (3,10) (19,2) (14,9) (21,0) (13,18) (25,6) (12,15) (4,1) (16,20) (5,7) (11,17) (12,28) (0,16) (25,10) (24,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1983", "image": "data/cycle/graph_visual/hard/graph1983.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,9) (23,34) (6,11) (26,2) (17,30) (27,1) (7,17) (22,27) (29,10) (12,27) (1,0) (8,5) (26,29) (3,0) (34,25) (4,23) (32,29) (31,0) (30,19) (4,17) (1,28) (22,33) (19,11) (19,5) (0,27) (13,2) (4,0) (15,31) (8,16) (19,20) (23,18) (0,2) (21,27) (10,16) (14,1) (22,13) (3,34) (24,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph491", "image": "data/cycle/graph_visual/hard/graph491.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (16,15) (14,26) (13,27) (10,15) (14,6) (28,16) (20,25) (12,13) (5,1) (3,18) (18,21) (25,5) (11,23) (23,7) (4,19) (6,0) (0,18) (20,8) (4,27) (10,2) (17,15) (8,26) (15,22) (26,24) (19,29) (13,1) (2,7) (1,9) (11,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph972", "image": "data/cycle/graph_visual/hard/graph972.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,27) (27,12) (7,19) (3,8) (13,29) (32,11) (14,13) (4,8) (15,6) (16,12) (23,31) (31,10) (8,10) (28,9) (14,24) (4,1) (21,18) (9,30) (5,34) (10,19) (32,26) (31,32) (21,33) (21,6) (18,3) (30,27) (6,22) (20,9) (13,1) (2,8) (0,20) (15,17) (34,17) (25,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1290", "image": "data/cycle/graph_visual/hard/graph1290.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,2) (9,11) (9,5) (1,13) (27,25) (23,2) (25,17) (6,21) (1,18) (17,9) (1,12) (16,12) (25,15) (4,14) (19,20) (20,6) (10,2) (0,15) (4,11) (0,1) (8,14) (22,5) (7,27) (3,27) (13,4) (6,15) (6,26) (1,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1227", "image": "data/cycle/graph_visual/hard/graph1227.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (15,6) (22,25) (3,10) (27,20) (2,0) (23,5) (18,7) (0,1) (15,12) (3,16) (24,17) (0,4) (12,3) (11,26) (19,26) (23,8) (17,3) (11,12) (0,3) (21,25) (4,5) (18,5) (11,2) (4,14) (20,3) (18,1) (2,13) (19,21) (9,11) (27,0) (1,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1613", "image": "data/cycle/graph_visual/hard/graph1613.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (4,0) (0,3) (13,12) (3,8) (14,28) (23,25) (7,5) (8,14) (0,30) (12,29) (15,13) (26,13) (21,30) (0,1) (28,21) (27,5) (25,21) (9,2) (18,7) (31,13) (10,25) (19,14) (23,15) (11,9) (1,7) (8,17) (7,6) (22,9) (2,0) (3,2) (25,1) (26,24) (2,16) (20,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1321", "image": "data/cycle/graph_visual/hard/graph1321.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (24,3) (18,21) (3,18) (5,26) (26,2) (11,25) (20,21) (1,0) (23,25) (13,0) (25,14) (2,18) (16,25) (8,13) (25,8) (26,27) (18,12) (21,19) (18,6) (20,10) (4,16) (15,16) (17,7) (28,1) (17,28) (17,9) (1,10) (24,22) (5,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1296", "image": "data/cycle/graph_visual/hard/graph1296.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,21) (15,20) (26,19) (20,1) (19,4) (5,2) (8,23) (23,12) (22,16) (2,19) (26,10) (25,9) (7,26) (14,27) (17,16) (0,1) (16,25) (14,21) (21,6) (19,25) (11,14) (12,9) (13,14) (3,21) (20,11) (3,24) (13,23) (18,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph261", "image": "data/cycle/graph_visual/hard/graph261.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,12) (7,11) (8,4) (13,23) (23,1) (17,19) (0,10) (22,14) (4,5) (6,19) (12,5) (8,9) (20,16) (2,10) (2,24) (22,5) (1,25) (10,17) (16,14) (23,14) (22,19) (3,14) (18,0) (21,19) (27,13) (27,11) (15,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1794", "image": "data/cycle/graph_visual/hard/graph1794.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (14,10) (25,30) (5,3) (31,15) (16,31) (1,20) (28,8) (2,30) (9,4) (12,7) (24,6) (2,0) (15,17) (29,21) (26,11) (2,21) (28,16) (5,23) (0,9) (22,4) (10,15) (24,27) (6,32) (11,19) (19,22) (3,0) (3,29) (9,18) (1,12) (0,1) (5,31) (6,29) (31,7) (13,22) (26,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1598", "image": "data/cycle/graph_visual/hard/graph1598.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (26,6) (0,16) (29,15) (30,26) (17,20) (18,3) (8,0) (2,8) (2,0) (21,16) (10,11) (6,13) (5,25) (0,1) (4,17) (21,20) (30,25) (22,30) (30,14) (28,27) (19,7) (0,26) (19,24) (10,6) (9,3) (23,17) (27,8) (7,12) (7,4) (5,15) (15,9) (25,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph444", "image": "data/cycle/graph_visual/hard/graph444.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (2,6) (0,17) (20,3) (0,1) (24,17) (19,16) (21,23) (3,9) (16,7) (27,2) (28,23) (0,10) (0,19) (26,18) (8,12) (5,20) (7,8) (13,1) (13,18) (23,11) (7,28) (7,14) (21,3) (22,29) (4,15) (25,2) (6,17) (4,23) (6,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph582", "image": "data/cycle/graph_visual/hard/graph582.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,10) (17,10) (28,20) (0,15) (12,5) (14,3) (11,7) (14,16) (23,30) (24,2) (14,28) (5,4) (29,23) (9,8) (30,14) (0,10) (22,5) (25,19) (12,27) (19,21) (27,11) (30,22) (16,18) (21,13) (6,19) (19,22) (23,1) (26,1) (29,17) (8,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph488", "image": "data/cycle/graph_visual/hard/graph488.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (12,29) (16,20) (0,1) (9,19) (6,25) (23,20) (9,28) (18,2) (26,13) (27,11) (17,2) (25,14) (10,3) (4,1) (10,29) (2,21) (18,13) (8,28) (15,29) (20,13) (7,8) (7,5) (24,5) (11,17) (15,26) (23,25) (17,8) (0,16) (0,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1634", "image": "data/cycle/graph_visual/hard/graph1634.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (21,20) (28,6) (26,28) (13,1) (7,5) (28,23) (18,4) (22,16) (14,15) (22,12) (29,12) (14,17) (27,25) (21,26) (24,10) (22,8) (5,31) (31,30) (14,10) (0,1) (30,26) (3,22) (1,2) (18,5) (0,4) (14,26) (19,27) (6,2) (12,27) (19,17) (25,9) (11,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1358", "image": "data/cycle/graph_visual/hard/graph1358.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (18,14) (12,6) (12,28) (23,19) (25,11) (27,25) (1,18) (21,4) (7,6) (6,15) (15,26) (25,6) (0,1) (12,5) (9,5) (5,2) (23,17) (20,14) (26,14) (0,2) (16,25) (8,7) (8,22) (19,26) (3,21) (10,14) (3,0) (14,21) (24,11) (13,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1241", "image": "data/cycle/graph_visual/hard/graph1241.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (14,16) (22,10) (13,23) (20,7) (21,26) (21,3) (17,8) (12,9) (17,27) (4,25) (19,22) (17,11) (5,13) (24,16) (15,20) (0,3) (1,10) (15,3) (18,6) (25,27) (0,2) (6,7) (25,9) (2,4) (17,0) (0,1) (4,5) (24,22) (6,24) (17,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1555", "image": "data/cycle/graph_visual/hard/graph1555.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (14,23) (15,8) (21,18) (14,28) (8,29) (27,24) (26,1) (3,17) (4,5) (13,17) (19,29) (30,12) (22,23) (9,7) (22,17) (0,2) (7,5) (10,18) (8,12) (10,20) (0,7) (11,21) (2,16) (7,26) (16,20) (1,0) (6,26) (12,11) (27,30) (17,16) (25,12) (17,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph241", "image": "data/cycle/graph_visual/hard/graph241.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (21,23) (8,12) (2,23) (3,21) (2,25) (6,17) (19,0) (2,6) (7,8) (4,15) (1,13) (1,0) (27,6) (4,23) (20,3) (17,22) (24,18) (3,9) (11,23) (18,13) (16,7) (16,19) (17,0) (7,14) (20,5) (0,10) (7,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1307", "image": "data/cycle/graph_visual/hard/graph1307.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (4,28) (10,6) (8,17) (14,3) (18,5) (5,4) (11,23) (1,0) (10,26) (26,15) (15,12) (19,25) (7,11) (27,23) (0,2) (9,21) (10,9) (16,1) (13,17) (26,2) (4,21) (12,16) (7,9) (28,0) (24,22) (14,21) (19,0) (26,24) (17,0) (14,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph929", "image": "data/cycle/graph_visual/hard/graph929.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,16) (13,16) (23,19) (29,18) (21,24) (21,9) (14,18) (25,19) (20,0) (26,12) (23,2) (34,5) (29,33) (26,5) (28,10) (15,14) (1,29) (28,14) (27,1) (17,15) (31,1) (30,4) (1,9) (14,19) (18,0) (16,26) (14,8) (3,30) (18,6) (7,26) (22,19) (11,0) (23,16) (32,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph648", "image": "data/cycle/graph_visual/hard/graph648.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,27) (13,31) (5,20) (10,2) (28,6) (5,0) (13,17) (25,3) (11,21) (10,15) (5,25) (31,15) (12,23) (23,13) (19,24) (24,22) (18,24) (1,11) (16,13) (28,5) (28,22) (29,7) (21,30) (4,29) (24,23) (27,29) (14,12) (19,26) (24,11) (29,8) (16,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph233", "image": "data/cycle/graph_visual/hard/graph233.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,1) (21,3) (11,13) (20,1) (5,23) (15,13) (3,5) (20,6) (26,21) (24,9) (22,21) (13,17) (16,19) (18,19) (12,8) (15,27) (19,8) (9,1) (6,8) (24,4) (25,14) (15,3) (5,14) (3,2) (10,14) (0,2) (7,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1381", "image": "data/cycle/graph_visual/hard/graph1381.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (6,20) (7,9) (14,8) (3,17) (0,5) (1,21) (26,28) (3,2) (20,21) (14,23) (13,11) (13,16) (6,10) (2,23) (16,25) (3,25) (12,23) (4,0) (18,24) (5,22) (3,0) (26,9) (22,12) (8,1) (5,19) (0,2) (14,4) (27,17) (7,10) (1,0) (15,14) (24,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1099", "image": "data/cycle/graph_visual/hard/graph1099.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,17) (2,19) (12,24) (15,23) (7,25) (19,1) (7,8) (24,5) (21,14) (22,4) (0,4) (18,23) (3,0) (9,22) (14,9) (0,1) (24,3) (0,5) (13,8) (2,0) (23,12) (6,20) (20,14) (2,21) (21,12) (16,8) (16,10) (8,3) (7,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1369", "image": "data/cycle/graph_visual/hard/graph1369.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (24,5) (13,10) (12,2) (8,28) (18,28) (1,8) (9,22) (20,12) (23,15) (26,21) (9,4) (12,25) (24,3) (28,7) (9,27) (19,3) (1,13) (25,19) (1,0) (26,6) (18,11) (15,17) (16,14) (15,11) (24,4) (16,4) (25,8) (27,0) (16,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1007", "image": "data/cycle/graph_visual/hard/graph1007.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,7) (3,20) (8,20) (5,17) (2,20) (9,2) (9,13) (12,16) (16,23) (9,14) (18,19) (24,21) (1,5) (21,20) (22,10) (11,17) (16,19) (8,6) (0,18) (14,15) (20,5) (25,13) (21,10) (15,16) (0,1) (7,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph479", "image": "data/cycle/graph_visual/hard/graph479.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (2,23) (24,29) (16,1) (26,16) (17,7) (5,11) (9,10) (9,13) (28,4) (14,0) (12,22) (21,28) (3,8) (0,19) (11,8) (3,27) (24,4) (18,6) (24,0) (13,2) (25,18) (0,20) (15,26) (19,11) (16,18) (28,7) (11,12) (10,3) (4,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph950", "image": "data/cycle/graph_visual/hard/graph950.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (31,0) (11,25) (5,18) (22,15) (2,20) (21,31) (18,29) (30,4) (30,14) (25,13) (34,18) (10,3) (7,2) (32,4) (11,9) (7,24) (22,23) (23,25) (13,30) (6,10) (17,7) (5,33) (9,16) (4,3) (18,28) (26,14) (7,4) (6,5) (10,27) (22,1) (5,12) (8,7) (10,19) (13,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph441", "image": "data/cycle/graph_visual/hard/graph441.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (24,13) (27,17) (9,11) (22,6) (5,12) (18,26) (1,9) (25,21) (22,3) (25,0) (12,13) (16,13) (22,20) (19,14) (24,28) (8,4) (24,7) (28,17) (10,21) (14,3) (15,23) (19,15) (14,4) (2,1) (27,19) (18,11) (11,19) (0,16) (5,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph333", "image": "data/cycle/graph_visual/hard/graph333.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,8) (4,24) (17,27) (0,6) (1,15) (24,19) (3,13) (5,26) (15,16) (12,2) (9,12) (13,22) (1,9) (1,8) (6,26) (14,20) (7,26) (3,27) (9,18) (18,3) (26,23) (27,25) (0,10) (27,11) (21,18) (24,18) (23,21) (28,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph842", "image": "data/cycle/graph_visual/hard/graph842.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (20,27) (7,31) (5,32) (26,9) (4,21) (19,6) (27,22) (13,15) (21,30) (17,32) (8,18) (20,13) (0,24) (22,6) (28,33) (14,22) (9,19) (29,4) (16,32) (2,16) (12,30) (6,31) (19,11) (30,13) (23,8) (25,10) (16,33) (6,8) (18,24) (25,16) (1,26) (3,2) (30,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1688", "image": "data/cycle/graph_visual/hard/graph1688.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (4,25) (0,3) (14,28) (28,17) (25,22) (29,13) (13,6) (15,20) (23,31) (20,7) (10,2) (2,0) (28,12) (9,19) (9,12) (0,4) (4,16) (19,13) (9,20) (18,9) (26,27) (23,16) (27,11) (26,21) (26,8) (18,26) (24,6) (1,6) (4,3) (29,10) (22,5) (6,30) (24,4) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1596", "image": "data/cycle/graph_visual/hard/graph1596.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (21,27) (2,0) (7,25) (8,9) (23,30) (25,19) (29,10) (7,12) (23,3) (1,0) (24,29) (8,27) (13,6) (14,16) (27,26) (9,18) (11,23) (25,28) (22,25) (4,29) (5,14) (20,17) (22,2) (5,15) (3,17) (13,14) (16,4) (11,22) (1,9) (26,15) (2,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph688", "image": "data/cycle/graph_visual/hard/graph688.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,14) (12,10) (30,22) (5,17) (9,7) (4,13) (7,25) (26,2) (10,19) (11,10) (30,6) (30,11) (4,28) (8,6) (26,0) (21,15) (14,29) (23,26) (14,31) (16,3) (4,27) (10,1) (24,10) (21,26) (20,10) (1,18) (17,2) (27,23) (17,10) (3,2) (29,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph494", "image": "data/cycle/graph_visual/hard/graph494.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,2) (24,27) (9,26) (6,19) (20,13) (21,18) (8,9) (12,25) (1,18) (27,0) (17,25) (8,19) (20,12) (27,16) (28,6) (29,16) (27,23) (13,5) (23,15) (10,2) (11,2) (26,11) (27,3) (5,14) (21,5) (4,1) (21,22) (23,25) (1,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph448", "image": "data/cycle/graph_visual/hard/graph448.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,18) (13,8) (28,24) (24,29) (8,20) (18,29) (16,24) (25,11) (17,0) (2,10) (21,29) (27,18) (24,3) (29,22) (11,20) (10,27) (27,19) (1,23) (25,23) (9,13) (25,22) (23,6) (4,12) (7,10) (16,17) (9,4) (8,26) (4,5) (15,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph506", "image": "data/cycle/graph_visual/hard/graph506.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,17) (22,20) (30,18) (14,13) (22,2) (23,21) (0,11) (16,19) (27,16) (10,23) (4,24) (9,26) (13,26) (1,25) (8,10) (12,25) (26,23) (26,7) (3,26) (23,24) (27,28) (3,16) (2,17) (29,28) (5,0) (0,18) (3,12) (9,20) (0,14) (15,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1111", "image": "data/cycle/graph_visual/hard/graph1111.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,17) (13,5) (14,23) (8,4) (16,17) (24,22) (1,21) (6,3) (13,25) (24,23) (16,7) (3,0) (23,1) (0,4) (25,8) (7,19) (1,20) (10,24) (14,4) (1,0) (16,12) (26,9) (18,21) (1,15) (20,17) (2,0) (2,11) (9,19) (3,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1263", "image": "data/cycle/graph_visual/hard/graph1263.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,4) (9,23) (22,10) (24,7) (5,21) (16,22) (17,14) (13,3) (8,22) (6,13) (3,0) (11,14) (18,11) (1,0) (2,3) (23,12) (20,0) (13,4) (24,27) (26,8) (19,10) (1,20) (2,0) (1,19) (11,10) (21,25) (19,23) (24,15) (11,2) (5,18) (9,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph231", "image": "data/cycle/graph_visual/hard/graph231.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (2,5) (25,17) (1,3) (14,26) (15,27) (22,26) (27,9) (26,17) (16,10) (13,23) (4,1) (27,25) (21,0) (25,3) (21,14) (25,12) (7,11) (11,25) (10,17) (13,20) (19,17) (14,18) (19,2) (24,16) (6,5) (18,13) (10,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1259", "image": "data/cycle/graph_visual/hard/graph1259.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (25,8) (4,0) (12,27) (0,2) (24,11) (5,21) (7,8) (16,20) (13,18) (10,3) (17,8) (5,0) (19,0) (14,9) (17,2) (25,10) (2,18) (0,1) (5,7) (6,25) (0,16) (23,20) (13,20) (12,15) (15,26) (2,9) (4,1) (11,17) (0,3) (13,26) (23,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph764", "image": "data/cycle/graph_visual/hard/graph764.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,19) (16,32) (9,30) (19,21) (6,16) (10,2) (13,23) (23,4) (29,27) (14,25) (15,0) (20,17) (12,29) (11,4) (27,15) (7,27) (22,10) (17,21) (24,23) (26,3) (9,28) (18,2) (23,32) (6,30) (22,20) (9,1) (5,14) (0,24) (6,8) (31,1) (5,31) (26,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1612", "image": "data/cycle/graph_visual/hard/graph1612.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (20,29) (22,1) (2,10) (18,1) (15,1) (28,6) (20,4) (3,17) (1,6) (12,3) (7,0) (9,30) (16,14) (25,10) (19,23) (23,8) (16,0) (8,22) (2,22) (27,28) (5,16) (13,12) (9,31) (9,15) (12,5) (24,26) (9,11) (0,2) (0,1) (27,20) (12,9) (24,12) (29,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph54", "image": "data/cycle/graph_visual/hard/graph54.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (16,25) (21,17) (16,8) (3,22) (5,24) (21,8) (0,3) (18,22) (2,13) (24,10) (23,13) (14,11) (12,7) (1,16) (4,25) (20,10) (19,17) (13,8) (5,9) (7,0) (15,22) (11,9) (20,25) (12,23) (6,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1943", "image": "data/cycle/graph_visual/hard/graph1943.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (26,16) (22,20) (11,22) (14,18) (13,33) (2,0) (9,16) (25,10) (26,33) (4,6) (23,17) (16,21) (4,30) (1,26) (12,31) (12,7) (25,20) (3,7) (19,1) (32,5) (6,17) (19,20) (27,6) (6,18) (28,12) (12,8) (29,24) (29,32) (24,4) (15,9) (34,7) (0,3) (34,27) (4,0) (1,6) (33,2) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1212", "image": "data/cycle/graph_visual/hard/graph1212.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (21,17) (19,4) (0,1) (11,23) (6,14) (27,15) (8,22) (8,16) (26,23) (16,14) (26,10) (4,17) (0,9) (2,23) (12,21) (1,7) (19,11) (24,25) (13,10) (24,22) (20,15) (18,6) (16,0) (17,24) (9,3) (24,5) (15,1) (27,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1853", "image": "data/cycle/graph_visual/hard/graph1853.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,30) (0,2) (11,9) (3,13) (19,30) (21,25) (0,1) (13,28) (32,4) (1,31) (24,0) (27,33) (28,9) (33,7) (21,30) (12,4) (26,23) (5,27) (22,14) (17,29) (15,24) (5,25) (14,32) (1,3) (12,29) (3,32) (21,10) (10,23) (5,14) (20,17) (23,18) (17,6) (9,0) (16,0) (22,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph857", "image": "data/cycle/graph_visual/hard/graph857.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (30,22) (17,19) (6,31) (17,4) (3,13) (6,26) (5,16) (16,20) (18,1) (18,4) (4,29) (0,23) (32,19) (22,15) (11,21) (2,0) (25,6) (10,14) (2,33) (27,28) (22,27) (24,7) (1,8) (29,27) (13,0) (25,32) (24,23) (9,12) (16,27) (12,25) (1,11) (14,16) (0,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph978", "image": "data/cycle/graph_visual/hard/graph978.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (21,14) (11,33) (29,1) (20,7) (27,34) (7,34) (17,24) (3,13) (10,24) (9,12) (30,5) (26,23) (29,17) (22,8) (32,18) (13,26) (9,0) (12,22) (25,6) (13,25) (4,11) (3,16) (29,25) (9,11) (19,13) (31,16) (23,22) (19,14) (7,28) (5,29) (10,7) (15,27) (32,21) (2,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph975", "image": "data/cycle/graph_visual/hard/graph975.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (19,20) (21,16) (1,19) (3,7) (0,2) (16,26) (30,4) (1,6) (29,24) (11,22) (23,17) (12,31) (2,33) (25,20) (12,7) (15,9) (12,8) (4,24) (16,9) (1,26) (32,5) (33,13) (18,14) (12,28) (7,34) (18,6) (6,27) (10,25) (6,17) (20,22) (29,32) (4,6) (26,33) (27,34)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1070", "image": "data/cycle/graph_visual/hard/graph1070.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (13,18) (11,25) (25,12) (1,0) (5,7) (17,25) (0,21) (17,10) (14,20) (6,1) (25,4) (9,10) (2,5) (18,14) (14,24) (25,3) (2,19) (13,19) (3,1) (23,17) (10,16) (8,11) (22,16) (17,15) (13,21) (4,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph882", "image": "data/cycle/graph_visual/hard/graph882.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (9,6) (1,17) (21,10) (28,13) (14,20) (16,11) (21,0) (17,26) (23,7) (4,12) (27,26) (7,15) (9,3) (20,27) (5,19) (16,32) (0,17) (18,2) (24,23) (22,12) (11,5) (1,19) (28,20) (2,33) (4,31) (18,30) (31,25) (6,17) (32,29) (24,5) (12,8) (12,30) (22,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph0", "image": "data/cycle/graph_visual/hard/graph0.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (11,0) (10,13) (4,23) (3,22) (18,21) (0,10) (6,2) (24,15) (20,9) (0,17) (14,13) (1,12) (8,5) (16,22) (20,14) (19,5) (4,19) (25,21) (24,7) (22,4) (21,10) (12,16) (5,14) (6,10) (3,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph700", "image": "data/cycle/graph_visual/hard/graph700.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,23) (6,12) (19,12) (20,27) (31,29) (7,30) (31,4) (18,16) (31,11) (30,21) (2,10) (11,0) (15,0) (9,32) (14,11) (9,3) (1,23) (5,30) (8,25) (22,19) (8,7) (6,24) (1,19) (28,32) (2,27) (10,16) (15,22) (22,20) (5,26) (5,31) (18,13) (17,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph452", "image": "data/cycle/graph_visual/hard/graph452.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (17,2) (6,25) (12,29) (5,24) (13,20) (25,14) (18,2) (19,9) (20,16) (0,22) (7,8) (13,18) (4,1) (9,28) (23,20) (10,3) (17,11) (7,5) (15,29) (27,11) (26,15) (25,23) (29,10) (8,17) (1,0) (8,28) (21,2) (13,26) (0,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1504", "image": "data/cycle/graph_visual/hard/graph1504.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,6) (29,28) (13,14) (0,1) (23,21) (2,0) (2,17) (25,1) (2,22) (26,7) (24,4) (30,18) (5,0) (10,8) (16,27) (26,13) (23,10) (3,26) (9,20) (20,22) (26,9) (18,0) (23,24) (27,28) (3,16) (16,19) (24,15) (23,26) (0,11) (25,12) (3,12) (0,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1804", "image": "data/cycle/graph_visual/hard/graph1804.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (27,29) (15,7) (9,22) (21,10) (5,11) (26,21) (0,3) (30,5) (4,0) (6,12) (1,0) (25,4) (4,21) (14,0) (24,12) (30,8) (9,18) (4,5) (28,33) (2,17) (15,14) (20,13) (22,20) (0,32) (16,5) (21,14) (1,31) (3,23) (28,12) (2,0) (23,22) (17,27) (6,27) (20,14) (17,21) (31,27) (19,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1747", "image": "data/cycle/graph_visual/hard/graph1747.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (21,9) (31,29) (25,1) (24,19) (0,17) (1,29) (9,30) (1,9) (5,18) (2,0) (26,6) (3,30) (21,22) (23,16) (23,2) (14,18) (4,30) (8,28) (12,16) (20,19) (16,27) (26,11) (14,7) (14,15) (0,18) (19,14) (1,0) (0,10) (32,16) (23,19) (26,14) (28,1) (13,15) (18,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1803", "image": "data/cycle/graph_visual/hard/graph1803.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (24,16) (11,24) (0,3) (6,1) (25,0) (18,26) (16,9) (23,22) (0,20) (32,10) (29,7) (30,22) (0,2) (2,32) (14,15) (27,33) (0,6) (27,20) (26,14) (30,16) (22,3) (13,25) (21,12) (1,0) (23,2) (1,19) (4,27) (4,5) (15,12) (31,28) (33,15) (21,8) (22,21) (28,15) (32,29) (17,2) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph363", "image": "data/cycle/graph_visual/hard/graph363.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,12) (12,1) (19,16) (12,22) (28,16) (5,26) (7,25) (15,19) (14,0) (6,8) (2,5) (26,18) (19,9) (8,1) (13,0) (10,25) (4,20) (6,21) (2,0) (24,16) (19,26) (0,7) (17,3) (20,17) (23,14) (4,2) (11,9) (27,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1870", "image": "data/cycle/graph_visual/hard/graph1870.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (17,1) (8,21) (15,17) (10,29) (15,28) (2,1) (3,14) (19,3) (27,30) (32,2) (20,5) (13,31) (5,4) (27,23) (6,2) (4,18) (13,6) (16,11) (27,14) (16,30) (0,28) (31,23) (18,9) (2,21) (12,25) (26,8) (28,7) (4,19) (0,2) (14,10) (1,0) (12,18) (21,33) (24,5) (22,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1898", "image": "data/cycle/graph_visual/hard/graph1898.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (7,23) (23,4) (20,10) (20,3) (30,5) (0,1) (21,4) (18,16) (20,17) (3,31) (17,27) (0,10) (32,18) (19,25) (14,1) (13,18) (24,26) (31,26) (32,9) (11,33) (15,30) (13,4) (15,7) (7,20) (19,33) (14,28) (8,11) (3,28) (19,22) (2,17) (6,33) (27,29) (30,12) (33,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph120", "image": "data/cycle/graph_visual/hard/graph120.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (7,25) (13,23) (23,1) (24,4) (21,19) (19,16) (24,21) (13,20) (14,4) (21,3) (18,15) (6,26) (1,15) (5,20) (5,16) (17,11) (0,23) (8,6) (7,23) (9,13) (12,1) (13,22) (19,10) (6,2) (24,17) (22,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph762", "image": "data/cycle/graph_visual/hard/graph762.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (15,26) (28,11) (27,20) (31,2) (18,3) (8,18) (24,23) (6,29) (5,2) (21,9) (17,20) (4,25) (7,31) (18,22) (32,31) (28,7) (28,24) (28,16) (14,20) (10,29) (9,13) (13,26) (16,1) (30,22) (5,6) (15,25) (1,8) (12,8) (7,0) (19,6) (24,17) (32,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1872", "image": "data/cycle/graph_visual/hard/graph1872.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (12,6) (18,22) (29,18) (0,21) (17,30) (15,12) (12,31) (11,15) (23,30) (12,32) (11,14) (33,20) (16,26) (23,32) (28,3) (9,31) (31,13) (21,4) (24,16) (2,7) (20,7) (15,5) (19,16) (16,0) (28,11) (12,25) (33,21) (1,0) (27,7) (19,13) (8,31) (29,10) (11,1) (10,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph680", "image": "data/cycle/graph_visual/hard/graph680.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,16) (2,28) (22,19) (21,11) (8,14) (5,27) (12,2) (10,21) (1,0) (5,12) (10,24) (1,15) (6,7) (16,19) (1,13) (20,19) (31,6) (18,31) (4,5) (3,14) (5,19) (5,6) (20,26) (23,2) (29,9) (29,5) (11,7) (19,8) (23,25) (24,17) (31,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1659", "image": "data/cycle/graph_visual/hard/graph1659.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (5,12) (5,0) (0,1) (3,30) (7,10) (8,31) (17,12) (2,16) (13,18) (15,1) (25,28) (1,26) (24,12) (1,5) (6,2) (21,9) (25,7) (18,8) (4,11) (0,30) (4,0) (5,27) (3,0) (0,2) (22,26) (19,13) (12,14) (25,13) (20,17) (23,28) (29,1) (29,25) (16,14) (11,6) (5,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph457", "image": "data/cycle/graph_visual/hard/graph457.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (4,27) (16,21) (14,15) (6,18) (2,10) (13,22) (0,24) (0,12) (28,29) (18,24) (2,19) (0,27) (20,15) (25,13) (3,7) (6,26) (23,17) (1,29) (8,20) (22,7) (19,11) (8,18) (10,20) (5,17) (6,1) (3,11) (9,16) (9,24) (29,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1769", "image": "data/cycle/graph_visual/hard/graph1769.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (3,32) (15,0) (11,24) (9,8) (27,32) (23,10) (0,22) (32,4) (13,3) (23,16) (1,3) (24,23) (6,17) (27,5) (30,2) (20,14) (9,28) (30,1) (7,22) (29,21) (0,9) (30,18) (31,14) (25,21) (13,26) (28,12) (1,0) (10,21) (12,4) (25,5) (17,19) (29,17) (14,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1540", "image": "data/cycle/graph_visual/hard/graph1540.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,17) (9,18) (17,23) (30,22) (19,12) (5,2) (1,19) (17,0) (12,18) (21,13) (8,10) (11,10) (13,20) (14,7) (15,23) (0,3) (0,21) (25,28) (13,2) (11,4) (1,0) (24,3) (30,8) (16,14) (29,30) (26,8) (15,25) (16,12) (0,29) (1,25) (27,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1359", "image": "data/cycle/graph_visual/hard/graph1359.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,4) (17,27) (10,6) (23,12) (20,6) (25,3) (3,2) (23,2) (1,0) (12,22) (16,25) (21,1) (21,20) (3,17) (13,16) (24,11) (9,26) (7,10) (8,1) (11,13) (5,0) (14,8) (14,15) (28,26) (5,22) (24,18) (2,0) (23,14) (0,3) (9,7) (0,4) (5,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph338", "image": "data/cycle/graph_visual/hard/graph338.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,21) (26,3) (14,21) (16,24) (23,13) (10,23) (4,28) (12,9) (21,0) (26,15) (8,26) (21,3) (4,14) (1,22) (11,20) (20,17) (1,20) (23,12) (9,25) (2,19) (25,16) (14,11) (25,19) (18,16) (2,6) (5,19) (14,13) (19,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph578", "image": "data/cycle/graph_visual/hard/graph578.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (22,4) (24,25) (13,7) (3,16) (24,20) (24,29) (22,16) (26,19) (13,15) (15,8) (6,23) (27,23) (28,11) (29,12) (17,5) (14,17) (10,21) (30,2) (3,25) (30,3) (18,7) (8,23) (18,19) (23,0) (10,14) (26,9) (5,11) (1,14) (17,20) (21,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1134", "image": "data/cycle/graph_visual/hard/graph1134.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (7,16) (3,4) (3,0) (21,9) (13,0) (16,6) (22,16) (24,25) (8,23) (18,2) (5,20) (12,16) (3,14) (13,11) (26,17) (1,8) (14,5) (15,2) (11,17) (6,14) (9,18) (18,19) (8,13) (15,10) (15,12) (1,0) (24,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1456", "image": "data/cycle/graph_visual/hard/graph1456.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,10) (26,27) (18,2) (0,1) (19,21) (16,25) (13,8) (18,6) (8,25) (16,4) (18,21) (13,0) (29,1) (15,5) (3,18) (15,16) (17,28) (14,25) (21,20) (2,26) (24,22) (25,23) (20,10) (12,18) (3,24) (28,1) (5,26) (7,17) (9,17) (25,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph629", "image": "data/cycle/graph_visual/hard/graph629.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,9) (22,21) (31,16) (15,5) (13,27) (8,17) (0,24) (16,20) (19,7) (27,4) (6,17) (8,29) (4,26) (2,11) (19,5) (18,7) (20,11) (0,7) (16,14) (4,1) (23,30) (25,18) (30,13) (9,3) (31,12) (26,9) (4,28) (1,21) (26,10) (2,19) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph630", "image": "data/cycle/graph_visual/hard/graph630.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (26,0) (21,14) (15,24) (6,9) (27,5) (8,24) (16,15) (19,11) (18,17) (3,12) (15,21) (28,19) (25,9) (4,25) (21,5) (29,1) (14,23) (13,26) (21,29) (31,22) (7,29) (28,20) (31,6) (18,19) (3,0) (3,30) (26,24) (10,12) (4,1) (23,2) (19,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1537", "image": "data/cycle/graph_visual/hard/graph1537.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,0) (20,29) (20,30) (26,2) (29,12) (1,0) (25,8) (6,19) (16,7) (1,28) (13,27) (14,4) (8,27) (0,15) (10,17) (6,20) (25,4) (24,3) (23,18) (23,16) (11,25) (15,21) (5,17) (0,24) (2,0) (22,4) (16,19) (17,30) (6,25) (20,2) (0,3) (9,23) (18,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1933", "image": "data/cycle/graph_visual/hard/graph1933.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (24,17) (11,31) (7,20) (23,2) (24,8) (27,15) (27,9) (0,3) (14,4) (0,2) (32,33) (10,33) (14,32) (12,30) (22,6) (8,29) (1,10) (16,8) (19,23) (25,34) (18,13) (33,23) (32,30) (25,21) (16,26) (0,5) (18,1) (28,9) (31,6) (0,4) (5,32) (24,9) (24,20) (27,11) (0,1) (34,14) (23,27) (1,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1568", "image": "data/cycle/graph_visual/hard/graph1568.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,30) (16,6) (10,3) (26,15) (26,14) (20,8) (29,28) (8,2) (12,8) (21,16) (22,16) (11,16) (6,18) (13,4) (29,26) (16,5) (0,26) (11,4) (10,0) (17,24) (27,22) (0,1) (1,23) (6,2) (19,7) (6,19) (9,25) (1,19) (0,25) (14,24) (4,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1981", "image": "data/cycle/graph_visual/hard/graph1981.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (18,11) (32,13) (31,30) (8,5) (14,17) (7,29) (3,6) (34,17) (18,1) (24,22) (26,4) (15,28) (15,25) (26,31) (0,2) (0,32) (20,31) (17,21) (25,22) (13,33) (19,23) (34,10) (27,24) (10,25) (3,1) (23,4) (7,32) (15,12) (18,33) (27,16) (3,0) (0,1) (21,2) (11,31) (9,11) (5,0) (20,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph249", "image": "data/cycle/graph_visual/hard/graph249.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (15,12) (20,13) (15,19) (4,11) (22,6) (26,25) (2,19) (15,17) (6,7) (27,20) (22,15) (18,3) (15,11) (1,7) (0,18) (17,5) (8,17) (24,17) (19,10) (14,18) (8,21) (2,16) (4,9) (0,26) (20,12) (17,26) (7,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph633", "image": "data/cycle/graph_visual/hard/graph633.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,9) (15,11) (31,9) (16,12) (19,5) (6,4) (29,30) (17,30) (26,11) (8,27) (0,20) (15,0) (25,21) (22,24) (12,6) (7,16) (10,2) (1,12) (14,25) (18,9) (23,28) (13,6) (21,26) (11,23) (19,24) (3,13) (22,27) (23,3) (29,18) (27,11) (12,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph660", "image": "data/cycle/graph_visual/hard/graph660.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,15) (26,16) (24,13) (22,31) (23,31) (4,2) (25,0) (28,0) (20,1) (7,23) (11,3) (22,15) (10,19) (14,12) (9,1) (4,18) (14,21) (18,5) (26,1) (17,16) (20,5) (22,6) (23,14) (22,17) (9,19) (23,28) (21,8) (24,29) (8,11) (27,4) (14,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph649", "image": "data/cycle/graph_visual/hard/graph649.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (29,7) (22,8) (12,22) (18,10) (4,23) (19,20) (14,16) (21,20) (5,25) (9,11) (31,25) (2,7) (15,26) (6,4) (19,1) (26,1) (2,0) (29,24) (3,12) (12,7) (16,9) (25,27) (17,6) (17,18) (24,4) (13,6) (16,20) (12,28) (27,6) (30,26) (1,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1391", "image": "data/cycle/graph_visual/hard/graph1391.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (11,27) (22,5) (19,17) (10,2) (12,27) (0,1) (16,14) (23,14) (6,19) (28,21) (14,3) (23,1) (10,0) (1,26) (9,8) (28,13) (21,15) (23,13) (2,25) (0,18) (12,5) (17,10) (4,5) (20,16) (11,7) (4,8) (19,24) (22,19) (22,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph550", "image": "data/cycle/graph_visual/hard/graph550.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (9,28) (1,0) (7,5) (27,23) (20,16) (8,17) (29,14) (13,20) (17,2) (26,15) (12,29) (16,0) (9,21) (13,18) (0,24) (19,25) (8,7) (5,25) (3,10) (25,10) (29,8) (11,17) (13,26) (30,6) (1,4) (28,11) (20,23) (15,30) (22,2) (2,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1510", "image": "data/cycle/graph_visual/hard/graph1510.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (30,13) (11,5) (21,28) (4,26) (24,30) (8,11) (17,7) (13,2) (30,23) (3,10) (12,22) (0,19) (11,12) (2,0) (16,18) (25,30) (3,4) (28,9) (19,11) (29,18) (9,10) (6,18) (8,3) (16,26) (1,0) (14,0) (0,20) (2,27) (1,16) (24,0) (28,7) (26,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1220", "image": "data/cycle/graph_visual/hard/graph1220.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (18,0) (6,7) (2,16) (9,4) (0,1) (18,14) (19,2) (18,3) (17,26) (17,15) (19,15) (26,0) (26,25) (7,23) (8,17) (15,22) (17,5) (21,8) (13,20) (15,12) (11,4) (20,27) (19,10) (6,22) (17,24) (15,11) (7,1) (20,12) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph163", "image": "data/cycle/graph_visual/hard/graph163.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,17) (13,5) (14,12) (7,1) (4,24) (12,25) (15,13) (24,2) (9,4) (15,11) (4,16) (18,11) (21,9) (3,24) (19,3) (8,1) (26,17) (20,26) (19,25) (0,12) (9,23) (16,6) (25,8) (6,18) (10,16) (22,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph140", "image": "data/cycle/graph_visual/hard/graph140.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (25,20) (2,7) (8,20) (1,4) (25,16) (15,16) (7,23) (13,1) (2,10) (13,26) (6,0) (21,26) (15,10) (18,3) (14,6) (5,24) (14,26) (1,11) (12,15) (19,15) (23,11) (22,8) (18,0) (17,18) (13,9) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1247", "image": "data/cycle/graph_visual/hard/graph1247.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (13,20) (12,3) (1,0) (6,19) (11,19) (2,1) (9,15) (7,16) (5,16) (23,24) (11,12) (23,20) (21,12) (20,3) (25,5) (0,27) (27,23) (18,26) (0,8) (22,0) (9,13) (15,10) (16,19) (11,1) (12,26) (10,17) (14,7) (18,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1871", "image": "data/cycle/graph_visual/hard/graph1871.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (8,25) (23,20) (20,13) (28,20) (1,27) (28,21) (25,4) (18,32) (10,26) (11,3) (5,11) (29,0) (31,1) (19,4) (22,29) (31,15) (23,33) (18,12) (20,7) (0,4) (9,8) (5,30) (14,1) (0,32) (10,21) (0,2) (22,16) (27,9) (6,13) (0,1) (2,31) (22,17) (21,11) (24,21) (18,21) (3,0) (18,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1195", "image": "data/cycle/graph_visual/hard/graph1195.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (3,21) (6,8) (21,25) (0,2) (13,7) (3,5) (20,21) (13,17) (15,19) (16,19) (6,20) (0,1) (12,8) (4,0) (14,10) (3,0) (19,1) (5,14) (18,8) (1,9) (13,15) (1,5) (13,11) (22,5) (0,5) (4,24) (3,2) (24,14) (26,3) (9,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph902", "image": "data/cycle/graph_visual/hard/graph902.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (15,11) (19,13) (32,12) (1,11) (18,22) (30,10) (12,31) (13,31) (11,29) (33,20) (10,15) (8,31) (7,20) (16,0) (16,24) (30,17) (29,18) (4,21) (16,27) (11,14) (12,6) (34,25) (28,7) (28,3) (7,2) (16,19) (9,31) (25,21) (33,23) (12,26) (5,15) (21,0) (23,32) (15,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1249", "image": "data/cycle/graph_visual/hard/graph1249.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,26) (25,3) (23,21) (18,3) (18,9) (20,12) (15,1) (10,0) (18,22) (27,16) (8,19) (11,9) (26,23) (24,4) (3,13) (3,0) (0,2) (27,26) (2,12) (1,9) (15,14) (0,4) (24,17) (6,0) (24,27) (18,21) (1,8) (1,0) (27,6) (26,5) (20,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph861", "image": "data/cycle/graph_visual/hard/graph861.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (28,14) (13,32) (13,33) (28,5) (25,10) (7,1) (19,14) (15,13) (16,2) (7,6) (5,7) (8,20) (17,8) (25,21) (23,25) (21,31) (18,7) (12,30) (13,12) (8,3) (26,13) (1,25) (33,24) (29,21) (23,15) (9,22) (0,4) (30,0) (3,2) (14,8) (27,26) (9,2) (9,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1626", "image": "data/cycle/graph_visual/hard/graph1626.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,21) (8,7) (18,6) (0,1) (29,21) (15,1) (31,30) (27,12) (23,19) (3,14) (0,2) (1,23) (16,13) (9,11) (25,23) (21,8) (26,21) (10,4) (5,10) (3,28) (17,16) (10,21) (18,9) (5,20) (17,23) (22,0) (0,6) (4,30) (24,0) (1,3) (20,15) (6,31) (27,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1482", "image": "data/cycle/graph_visual/hard/graph1482.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,8) (1,0) (2,0) (20,1) (5,3) (19,8) (13,7) (13,17) (5,1) (20,6) (4,24) (2,3) (21,3) (28,22) (9,1) (5,25) (10,14) (9,26) (15,3) (15,29) (18,19) (6,23) (11,13) (3,0) (5,14) (0,4) (8,12) (24,21) (15,13) (27,14) (16,19) (28,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph875", "image": "data/cycle/graph_visual/hard/graph875.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (11,10) (23,32) (10,16) (12,10) (28,27) (16,5) (12,14) (33,4) (25,10) (21,20) (4,19) (1,7) (29,22) (13,2) (13,8) (20,10) (9,17) (31,29) (0,18) (3,24) (20,13) (5,15) (11,6) (2,23) (28,0) (31,19) (33,1) (31,26) (4,21) (5,30) (7,24) (18,9) (19,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph955", "image": "data/cycle/graph_visual/hard/graph955.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,10) (28,21) (21,20) (20,8) (16,4) (27,5) (2,12) (7,6) (6,4) (19,28) (20,26) (25,31) (30,18) (12,24) (13,15) (17,8) (6,5) (14,26) (11,10) (22,26) (0,9) (5,25) (32,13) (21,27) (12,34) (12,5) (9,20) (29,33) (30,31) (33,6) (1,26) (16,3) (15,2) (23,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1130", "image": "data/cycle/graph_visual/hard/graph1130.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,8) (4,21) (11,22) (3,25) (0,5) (8,0) (2,15) (12,24) (23,21) (17,4) (1,16) (25,6) (3,0) (26,7) (4,0) (8,15) (18,5) (23,13) (9,2) (11,10) (6,23) (0,2) (19,18) (0,1) (15,18) (24,20) (26,13) (25,15) (0,24) (10,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph273", "image": "data/cycle/graph_visual/hard/graph273.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,6) (24,20) (13,7) (15,8) (12,3) (4,23) (13,15) (27,19) (2,22) (7,18) (5,11) (25,24) (23,8) (21,22) (17,5) (17,20) (17,14) (3,19) (14,1) (21,10) (9,16) (23,11) (25,27) (24,26) (0,23) (14,10) (18,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1231", "image": "data/cycle/graph_visual/hard/graph1231.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (17,16) (26,19) (26,7) (11,20) (2,5) (26,10) (9,12) (8,23) (14,27) (1,0) (9,25) (21,14) (12,23) (18,1) (2,19) (3,24) (3,21) (16,22) (25,16) (20,15) (21,0) (13,23) (1,20) (14,11) (19,25) (13,14) (19,4) (21,6) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1835", "image": "data/cycle/graph_visual/hard/graph1835.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (6,1) (6,27) (17,23) (1,26) (22,11) (10,25) (15,9) (17,6) (21,16) (5,0) (3,0) (14,18) (13,33) (4,30) (19,1) (26,32) (19,20) (26,16) (2,0) (22,20) (4,24) (7,12) (16,9) (31,12) (4,0) (1,0) (18,6) (7,3) (24,29) (12,28) (4,6) (8,12) (33,27) (25,20) (33,2) (29,7) (32,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph135", "image": "data/cycle/graph_visual/hard/graph135.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (7,11) (13,23) (8,11) (3,23) (21,18) (7,21) (25,1) (22,11) (22,4) (3,10) (9,16) (16,5) (20,11) (8,24) (5,7) (14,22) (25,12) (19,4) (0,6) (1,15) (26,7) (0,17) (2,6) (12,8) (0,1) (14,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph170", "image": "data/cycle/graph_visual/hard/graph170.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,23) (20,17) (11,10) (8,2) (5,15) (6,10) (20,21) (0,8) (5,25) (19,7) (17,4) (13,6) (4,7) (24,15) (16,21) (26,6) (3,9) (7,12) (0,26) (18,17) (0,16) (25,1) (26,25) (22,19) (3,14) (15,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1805", "image": "data/cycle/graph_visual/hard/graph1805.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (24,12) (29,8) (0,26) (2,0) (25,14) (13,33) (9,28) (14,23) (10,33) (20,4) (29,11) (6,14) (14,19) (0,3) (2,16) (12,30) (21,17) (21,16) (15,28) (31,23) (8,22) (2,26) (22,23) (1,18) (28,33) (18,27) (5,32) (14,32) (27,10) (28,25) (0,1) (8,7) (3,18) (7,30) (4,29) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph719", "image": "data/cycle/graph_visual/hard/graph719.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,19) (1,4) (23,27) (14,17) (27,1) (13,22) (11,16) (19,28) (12,11) (21,16) (16,1) (7,30) (10,7) (24,3) (26,29) (18,20) (21,20) (17,3) (25,19) (0,8) (20,3) (25,11) (7,3) (9,32) (22,11) (31,9) (26,12) (6,28) (11,8) (2,15) (15,5) (14,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph622", "image": "data/cycle/graph_visual/hard/graph622.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,24) (0,20) (14,16) (12,22) (8,26) (20,3) (5,12) (30,8) (12,1) (9,14) (24,9) (6,2) (24,0) (29,14) (7,26) (10,0) (7,19) (14,6) (28,25) (14,13) (22,10) (18,27) (4,27) (31,14) (21,4) (30,23) (11,29) (22,7) (29,17) (30,27) (28,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1507", "image": "data/cycle/graph_visual/hard/graph1507.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (14,9) (8,11) (5,7) (21,26) (12,5) (12,25) (4,8) (15,1) (23,29) (0,20) (2,26) (19,8) (2,6) (29,27) (15,7) (17,22) (23,2) (20,29) (26,15) (13,30) (30,18) (7,28) (26,24) (10,17) (11,26) (10,8) (18,20) (22,3) (9,6) (16,2) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1969", "image": "data/cycle/graph_visual/hard/graph1969.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (6,30) (21,9) (20,14) (28,11) (16,28) (33,1) (10,29) (4,25) (15,26) (13,26) (32,27) (31,4) (8,12) (2,0) (7,0) (7,31) (8,4) (20,29) (18,3) (18,8) (6,19) (23,24) (9,13) (31,2) (7,28) (17,20) (2,5) (28,24) (8,34) (18,22) (32,22) (1,0) (5,6) (1,16) (17,24) (3,0) (25,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph255", "image": "data/cycle/graph_visual/hard/graph255.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,15) (18,19) (21,9) (25,24) (16,12) (2,15) (5,14) (2,18) (17,27) (15,10) (6,16) (13,0) (13,11) (8,1) (16,22) (27,24) (4,3) (8,13) (23,8) (18,9) (14,6) (20,5) (0,3) (7,16) (14,3) (0,26) (11,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1802", "image": "data/cycle/graph_visual/hard/graph1802.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (17,9) (21,1) (9,26) (15,5) (20,33) (4,29) (11,2) (2,0) (20,11) (17,8) (27,13) (4,26) (31,13) (5,19) (9,3) (32,16) (4,27) (31,12) (0,25) (4,1) (0,3) (24,30) (0,1) (30,8) (7,19) (17,6) (23,21) (18,28) (19,2) (16,14) (22,16) (0,7) (3,2) (7,18) (20,22) (10,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph624", "image": "data/cycle/graph_visual/hard/graph624.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (24,20) (28,9) (1,3) (2,23) (29,8) (9,27) (27,23) (31,6) (13,27) (6,22) (10,1) (30,7) (31,25) (12,18) (24,9) (18,24) (25,21) (16,8) (30,11) (11,27) (14,23) (19,1) (14,4) (5,20) (15,14) (24,8) (10,23) (2,0) (15,17) (16,26) (25,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1966", "image": "data/cycle/graph_visual/hard/graph1966.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (6,33) (27,23) (21,10) (10,11) (26,23) (10,15) (1,20) (19,3) (34,9) (31,29) (9,14) (10,28) (30,7) (33,5) (29,4) (10,17) (4,27) (22,10) (11,33) (14,32) (3,2) (9,7) (0,26) (6,12) (1,0) (2,17) (1,10) (26,2) (4,16) (21,18) (25,30) (8,17) (11,14) (30,13) (26,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph427", "image": "data/cycle/graph_visual/hard/graph427.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (2,16) (19,1) (14,3) (29,5) (27,29) (9,6) (25,20) (9,20) (6,22) (11,8) (28,27) (21,18) (14,2) (9,26) (29,10) (26,23) (23,19) (27,21) (4,9) (14,0) (15,8) (24,2) (21,7) (12,15) (2,26) (7,1) (2,17) (21,13) (23,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph125", "image": "data/cycle/graph_visual/hard/graph125.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,4) (23,11) (2,7) (2,10) (16,25) (25,20) (15,19) (6,14) (6,0) (26,14) (21,26) (12,15) (1,11) (1,13) (3,18) (5,1) (8,22) (0,18) (26,13) (8,20) (7,23) (13,9) (5,24) (15,16) (10,15) (17,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1050", "image": "data/cycle/graph_visual/hard/graph1050.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (14,20) (18,0) (11,9) (10,3) (25,12) (5,0) (18,16) (23,24) (4,0) (8,11) (11,0) (3,0) (24,17) (7,10) (23,8) (6,4) (15,14) (2,0) (22,1) (6,25) (3,21) (7,25) (15,21) (19,17) (20,2) (1,13) (0,1) (5,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1577", "image": "data/cycle/graph_visual/hard/graph1577.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (26,7) (13,30) (19,2) (24,30) (23,16) (4,8) (12,17) (3,11) (5,3) (26,0) (30,17) (18,26) (15,27) (20,29) (14,24) (23,19) (6,23) (11,15) (8,11) (25,14) (3,0) (0,1) (20,1) (5,28) (10,22) (9,25) (0,2) (21,20) (1,28) (12,7) (22,29) (7,27) (16,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph130", "image": "data/cycle/graph_visual/hard/graph130.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,9) (23,25) (11,16) (17,21) (24,6) (11,26) (18,1) (8,19) (11,2) (13,20) (14,23) (5,13) (18,21) (26,7) (19,6) (20,12) (4,2) (23,16) (21,5) (5,10) (15,25) (12,25) (3,2) (0,1) (22,9) (1,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph185", "image": "data/cycle/graph_visual/hard/graph185.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,15) (23,0) (26,25) (26,6) (24,25) (24,23) (5,11) (24,20) (7,18) (1,14) (10,21) (15,13) (11,22) (17,14) (23,4) (9,16) (10,14) (22,2) (12,3) (20,17) (5,17) (3,19) (8,23) (13,7) (18,16) (21,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph903", "image": "data/cycle/graph_visual/hard/graph903.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (16,24) (21,5) (30,20) (32,33) (14,7) (31,23) (12,4) (12,26) (26,13) (25,2) (8,5) (0,17) (5,30) (20,25) (13,24) (12,28) (11,21) (10,15) (3,24) (34,0) (14,8) (11,6) (9,13) (29,11) (15,16) (18,33) (27,31) (29,9) (5,22) (5,33) (2,17) (34,19) (1,25) (23,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph580", "image": "data/cycle/graph_visual/hard/graph580.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (12,24) (18,17) (11,21) (29,16) (13,11) (22,8) (14,13) (30,5) (25,29) (20,12) (7,26) (19,1) (16,30) (27,9) (4,17) (11,15) (17,24) (0,17) (22,26) (0,11) (28,6) (1,12) (27,30) (23,30) (5,7) (30,10) (12,3) (19,28) (12,7) (2,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph475", "image": "data/cycle/graph_visual/hard/graph475.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (19,18) (18,11) (25,12) (27,15) (7,6) (28,27) (0,6) (21,23) (29,16) (10,3) (17,27) (26,4) (22,7) (24,14) (24,13) (17,7) (12,17) (28,8) (11,20) (21,18) (5,3) (9,6) (22,1) (7,24) (27,26) (21,24) (29,19) (2,19) (14,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph910", "image": "data/cycle/graph_visual/hard/graph910.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (14,0) (31,22) (1,18) (24,7) (6,28) (18,4) (1,8) (15,16) (25,13) (16,20) (14,10) (29,4) (11,24) (17,4) (29,27) (0,23) (11,1) (21,22) (0,20) (2,12) (9,12) (3,13) (0,2) (26,23) (19,32) (32,25) (22,27) (25,6) (19,17) (6,33) (27,16) (5,16) (30,27) (12,34)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph79", "image": "data/cycle/graph_visual/hard/graph79.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (21,20) (13,8) (17,9) (20,10) (3,23) (25,1) (15,16) (16,4) (3,18) (5,15) (6,18) (2,18) (22,25) (0,13) (24,16) (25,14) (21,17) (19,24) (10,1) (7,17) (11,25) (2,5) (25,8) (18,21) (18,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph368", "image": "data/cycle/graph_visual/hard/graph368.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,24) (28,3) (12,7) (5,3) (10,22) (19,20) (14,24) (26,13) (15,27) (14,22) (18,23) (25,5) (9,25) (17,3) (26,11) (19,2) (16,21) (11,8) (1,28) (17,12) (27,7) (11,15) (23,6) (0,16) (8,4) (20,1) (26,0) (23,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph354", "image": "data/cycle/graph_visual/hard/graph354.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,7) (1,20) (16,0) (18,3) (15,20) (19,4) (14,26) (9,21) (6,18) (21,24) (11,22) (23,4) (7,9) (6,20) (17,21) (4,1) (5,28) (28,8) (25,14) (1,12) (28,6) (16,28) (2,14) (16,10) (26,0) (8,11) (27,23) (23,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph197", "image": "data/cycle/graph_visual/hard/graph197.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (12,17) (23,5) (2,7) (3,8) (1,6) (4,5) (14,12) (13,22) (26,2) (15,10) (26,13) (16,9) (18,1) (13,16) (25,21) (19,4) (0,14) (1,17) (11,14) (24,20) (25,1) (0,20) (23,8) (15,11) (7,0) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph675", "image": "data/cycle/graph_visual/hard/graph675.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (1,11) (24,6) (16,13) (14,9) (7,1) (4,17) (10,25) (27,26) (25,19) (11,15) (22,28) (20,0) (8,12) (5,24) (13,2) (29,27) (22,14) (6,25) (12,0) (0,31) (16,3) (23,21) (6,30) (0,23) (1,18) (16,20) (16,27) (29,4) (4,18) (27,22) (19,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1010", "image": "data/cycle/graph_visual/hard/graph1010.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,5) (0,13) (25,9) (7,21) (0,1) (25,6) (13,23) (15,10) (10,4) (15,18) (20,10) (3,0) (2,24) (20,17) (18,21) (1,23) (14,18) (14,13) (6,13) (4,3) (16,8) (2,3) (24,11) (21,8) (2,0) (5,22) (4,12) (19,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph398", "image": "data/cycle/graph_visual/hard/graph398.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,11) (18,25) (8,11) (23,11) (26,8) (28,7) (21,22) (27,12) (21,19) (2,6) (7,5) (1,28) (7,24) (0,17) (13,23) (3,25) (5,16) (0,6) (4,27) (3,10) (8,12) (20,4) (9,16) (10,14) (15,1) (22,14) (1,0) (22,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1316", "image": "data/cycle/graph_visual/hard/graph1316.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (26,4) (8,4) (16,7) (13,21) (22,11) (19,6) (0,1) (4,19) (17,4) (7,13) (22,6) (4,24) (17,9) (12,5) (6,27) (3,1) (7,2) (18,20) (5,15) (6,0) (23,3) (2,0) (13,0) (28,2) (25,12) (14,24) (26,5) (19,10) (0,4) (14,20) (0,3) (6,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1095", "image": "data/cycle/graph_visual/hard/graph1095.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (2,0) (0,1) (0,4) (5,16) (8,2) (12,7) (11,10) (24,17) (11,20) (7,5) (12,3) (18,16) (11,0) (13,11) (19,24) (25,4) (15,12) (17,6) (23,7) (17,21) (8,22) (18,0) (1,19) (13,9) (12,1) (12,22) (17,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1383", "image": "data/cycle/graph_visual/hard/graph1383.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,9) (13,12) (17,25) (1,17) (10,25) (9,6) (9,27) (3,0) (21,0) (24,2) (15,7) (20,24) (8,6) (2,10) (7,9) (11,3) (21,28) (15,14) (2,0) (18,9) (4,14) (12,5) (16,7) (27,26) (7,10) (1,11) (0,1) (13,26) (26,22) (4,0) (14,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph420", "image": "data/cycle/graph_visual/hard/graph420.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (21,25) (21,10) (24,7) (12,13) (1,2) (18,11) (27,17) (11,19) (6,22) (28,24) (22,3) (18,26) (29,5) (15,23) (9,11) (16,0) (20,22) (3,14) (9,1) (4,14) (17,28) (8,4) (16,13) (5,12) (27,19) (0,25) (19,14) (13,24) (19,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1113", "image": "data/cycle/graph_visual/hard/graph1113.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (5,3) (24,20) (26,6) (0,1) (21,6) (4,2) (11,21) (13,14) (17,10) (2,0) (8,22) (20,17) (22,23) (19,7) (24,19) (12,9) (2,13) (1,15) (25,24) (20,4) (6,0) (25,18) (20,3) (6,14) (26,22) (12,0) (8,15) (25,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1629", "image": "data/cycle/graph_visual/hard/graph1629.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,3) (4,19) (25,4) (25,8) (20,28) (0,2) (9,27) (1,14) (13,20) (11,21) (20,7) (9,8) (1,29) (22,29) (21,18) (15,31) (18,12) (18,25) (11,5) (2,31) (17,22) (0,4) (0,1) (24,10) (5,0) (31,20) (27,1) (28,21) (0,26) (21,23) (13,6) (16,22) (10,21) (30,18) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1251", "image": "data/cycle/graph_visual/hard/graph1251.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,6) (0,11) (22,23) (5,22) (21,27) (18,25) (0,4) (25,9) (20,11) (17,20) (19,8) (0,16) (2,0) (1,6) (23,12) (24,0) (0,5) (21,8) (7,12) (1,0) (21,9) (2,11) (3,0) (26,5) (12,10) (2,26) (3,27) (0,13) (14,6) (15,18) (8,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1799", "image": "data/cycle/graph_visual/hard/graph1799.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,24) (24,17) (5,24) (4,13) (10,20) (9,28) (18,27) (15,0) (1,15) (9,26) (3,7) (16,3) (6,7) (23,4) (17,22) (28,25) (20,29) (21,18) (1,8) (10,16) (7,1) (2,31) (24,19) (10,14) (23,30) (0,1) (9,32) (6,9) (8,30) (12,14) (21,11) (13,18) (27,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1067", "image": "data/cycle/graph_visual/hard/graph1067.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,19) (20,14) (22,16) (8,5) (3,7) (11,0) (10,0) (22,3) (7,24) (12,1) (6,2) (21,10) (4,22) (20,9) (4,23) (10,13) (0,2) (18,21) (1,0) (17,0) (0,3) (12,16) (24,15) (14,5) (13,14) (10,6) (19,5) (21,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1595", "image": "data/cycle/graph_visual/hard/graph1595.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,28) (15,3) (9,27) (15,13) (20,6) (2,0) (8,12) (24,4) (11,13) (5,14) (17,19) (13,7) (21,29) (9,1) (30,15) (6,24) (26,5) (0,4) (21,25) (21,3) (29,8) (14,10) (18,13) (3,0) (22,19) (14,28) (5,1) (1,20) (5,3) (2,3) (8,19) (0,1) (30,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph136", "image": "data/cycle/graph_visual/hard/graph136.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (21,0) (7,11) (14,19) (6,5) (10,17) (2,5) (10,16) (17,24) (3,25) (9,25) (17,25) (14,26) (11,25) (22,26) (4,1) (18,14) (13,15) (2,19) (20,26) (12,17) (25,14) (3,1) (10,8) (21,13) (18,13) (23,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph691", "image": "data/cycle/graph_visual/hard/graph691.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (16,6) (6,31) (2,4) (1,0) (27,7) (24,7) (8,18) (0,13) (8,23) (4,23) (8,24) (29,28) (12,28) (19,30) (27,5) (17,11) (3,19) (1,23) (29,13) (29,25) (30,20) (16,15) (19,31) (18,14) (29,11) (9,15) (10,26) (20,13) (22,10) (4,21) (26,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph836", "image": "data/cycle/graph_visual/hard/graph836.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (6,5) (0,31) (21,13) (11,25) (25,13) (6,10) (7,24) (4,30) (28,18) (4,3) (2,7) (14,26) (8,7) (21,18) (11,9) (12,5) (5,33) (25,23) (18,29) (2,20) (32,5) (30,14) (4,31) (10,19) (10,27) (10,3) (9,16) (22,1) (4,7) (22,23) (30,13) (15,22) (7,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1746", "image": "data/cycle/graph_visual/hard/graph1746.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (31,30) (11,22) (0,15) (4,15) (2,24) (2,22) (0,21) (26,7) (28,20) (30,10) (18,26) (0,27) (10,28) (6,30) (11,19) (12,26) (2,13) (1,0) (2,7) (24,23) (26,31) (17,14) (28,25) (32,3) (8,16) (32,24) (5,3) (14,29) (9,23) (8,10) (4,10) (31,17) (1,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1691", "image": "data/cycle/graph_visual/hard/graph1691.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,4) (7,28) (19,21) (22,3) (23,4) (20,7) (1,14) (11,6) (13,4) (17,25) (7,23) (0,10) (30,18) (27,15) (16,26) (4,12) (5,30) (31,17) (0,1) (18,11) (19,31) (28,10) (3,0) (18,13) (26,20) (2,0) (19,14) (27,24) (3,20) (17,2) (9,30) (17,15) (29,3) (20,8) (15,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph566", "image": "data/cycle/graph_visual/hard/graph566.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (30,28) (1,19) (7,1) (14,2) (21,13) (8,11) (15,12) (21,27) (20,9) (27,30) (12,23) (29,27) (9,26) (26,23) (14,3) (6,9) (10,29) (6,22) (19,23) (21,18) (0,14) (16,2) (9,4) (2,17) (8,15) (29,5) (7,21) (26,2) (2,24) (25,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1967", "image": "data/cycle/graph_visual/hard/graph1967.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (9,16) (13,30) (4,32) (3,10) (31,0) (5,33) (18,28) (2,7) (13,25) (27,10) (13,21) (7,17) (21,31) (30,14) (2,0) (26,14) (1,22) (4,7) (11,9) (2,20) (19,10) (22,23) (7,24) (23,25) (18,5) (7,8) (5,12) (10,6) (4,3) (18,29) (18,34) (0,1) (3,0) (11,25) (6,5) (15,22) (4,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph326", "image": "data/cycle/graph_visual/hard/graph326.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,23) (11,7) (27,12) (28,7) (15,1) (11,23) (21,22) (5,16) (8,26) (17,0) (4,20) (9,16) (2,6) (25,18) (10,3) (11,8) (11,22) (7,5) (27,4) (24,7) (14,22) (3,25) (10,14) (21,19) (0,6) (1,0) (28,1) (12,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph385", "image": "data/cycle/graph_visual/hard/graph385.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,3) (11,17) (0,16) (15,16) (26,2) (15,27) (28,7) (7,10) (24,0) (13,9) (3,0) (6,2) (18,16) (1,18) (5,20) (24,28) (5,11) (15,26) (19,5) (5,21) (8,23) (22,0) (28,9) (27,5) (21,14) (8,20) (12,14) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph834", "image": "data/cycle/graph_visual/hard/graph834.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (20,32) (10,25) (14,3) (21,13) (7,29) (5,27) (20,0) (8,18) (26,18) (17,3) (24,26) (25,3) (7,9) (2,13) (6,16) (4,28) (25,32) (3,27) (4,15) (19,7) (23,6) (2,8) (33,19) (3,11) (30,14) (2,14) (5,22) (23,27) (26,9) (12,4) (3,31) (9,1) (15,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1294", "image": "data/cycle/graph_visual/hard/graph1294.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,21) (0,2) (19,25) (4,15) (9,17) (17,18) (0,4) (1,6) (14,16) (13,7) (8,18) (17,4) (0,22) (23,2) (27,12) (0,26) (26,20) (20,7) (11,18) (16,18) (24,10) (3,2) (25,2) (0,1) (26,1) (25,1) (5,12) (10,20) (27,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1387", "image": "data/cycle/graph_visual/hard/graph1387.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (9,28) (0,3) (7,12) (1,26) (0,2) (0,1) (1,18) (16,21) (11,19) (20,3) (25,28) (17,24) (16,22) (2,5) (22,8) (23,10) (9,4) (3,10) (4,6) (27,15) (25,24) (22,28) (1,16) (17,0) (14,23) (0,19) (2,6) (15,11) (0,13) (15,7) (26,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1101", "image": "data/cycle/graph_visual/hard/graph1101.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (25,15) (5,21) (23,1) (25,17) (6,15) (6,24) (20,25) (6,18) (11,9) (0,1) (2,22) (2,7) (3,14) (12,10) (20,16) (26,20) (26,2) (1,12) (4,11) (13,4) (5,9) (4,8) (14,1) (0,15) (19,6) (1,13) (9,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1244", "image": "data/cycle/graph_visual/hard/graph1244.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,2) (6,1) (4,3) (26,16) (21,15) (9,6) (27,19) (24,27) (17,15) (12,10) (16,12) (11,2) (23,13) (2,8) (9,2) (4,23) (12,22) (5,9) (23,14) (23,10) (11,23) (17,24) (21,20) (12,25) (1,0) (0,3) (17,13) (18,5) (7,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1656", "image": "data/cycle/graph_visual/hard/graph1656.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,2) (23,5) (1,0) (26,3) (3,16) (24,11) (10,28) (31,0) (22,9) (25,9) (29,22) (10,2) (24,8) (5,6) (31,20) (11,20) (13,12) (30,1) (12,30) (4,29) (17,13) (21,19) (1,29) (2,1) (24,22) (12,19) (3,5) (11,18) (27,14) (7,8) (28,14) (19,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph254", "image": "data/cycle/graph_visual/hard/graph254.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,5) (9,2) (21,20) (25,16) (27,13) (19,16) (15,8) (20,5) (1,5) (4,7) (21,26) (18,17) (14,9) (10,21) (12,20) (23,19) (15,16) (7,26) (11,8) (6,26) (14,15) (2,20) (0,18) (24,10) (20,3) (17,16) (13,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph424", "image": "data/cycle/graph_visual/hard/graph424.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (4,27) (0,21) (10,16) (0,27) (5,26) (13,15) (28,23) (1,23) (5,11) (18,16) (28,8) (22,12) (11,23) (14,23) (4,8) (7,28) (1,29) (27,3) (6,14) (14,20) (6,9) (17,22) (29,22) (19,2) (11,16) (25,29) (23,19) (1,24) (15,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1278", "image": "data/cycle/graph_visual/hard/graph1278.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (9,8) (1,4) (21,18) (11,2) (16,25) (1,19) (17,21) (14,5) (20,13) (25,12) (15,23) (18,1) (20,12) (23,27) (6,26) (2,7) (0,3) (13,5) (25,23) (0,27) (0,2) (3,27) (0,1) (22,27) (5,21) (6,19) (26,11) (0,4) (2,10) (19,8) (24,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph702", "image": "data/cycle/graph_visual/hard/graph702.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,20) (20,27) (8,6) (14,7) (25,32) (18,32) (24,21) (6,17) (9,21) (22,12) (13,28) (4,29) (17,26) (1,19) (16,11) (31,24) (2,9) (5,23) (4,12) (17,0) (12,30) (22,13) (15,0) (5,19) (7,23) (3,12) (5,11) (31,16) (20,10) (26,27) (1,17) (30,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph8", "image": "data/cycle/graph_visual/hard/graph8.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (22,21) (16,14) (20,14) (23,5) (8,9) (23,11) (5,15) (12,14) (10,7) (19,15) (7,25) (0,2) (8,25) (5,25) (17,18) (9,1) (16,4) (22,2) (24,2) (22,11) (13,9) (25,4) (3,17) (6,13) (3,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph106", "image": "data/cycle/graph_visual/hard/graph106.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (21,15) (6,19) (21,24) (6,20) (14,26) (11,22) (1,10) (7,9) (7,12) (14,2) (17,6) (16,0) (1,20) (16,23) (3,18) (26,19) (8,11) (14,24) (21,9) (23,8) (4,1) (13,20) (16,5) (18,4) (0,25) (4,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph808", "image": "data/cycle/graph_visual/hard/graph808.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (11,24) (22,21) (17,2) (12,21) (1,6) (33,27) (23,22) (6,0) (7,29) (26,14) (15,14) (18,26) (15,12) (2,32) (29,32) (20,27) (24,16) (30,22) (1,19) (10,32) (3,22) (25,0) (23,2) (21,8) (28,15) (5,4) (28,31) (13,25) (4,27) (9,16) (20,0) (16,30) (33,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1944", "image": "data/cycle/graph_visual/hard/graph1944.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (33,1) (21,4) (3,24) (13,2) (10,25) (13,20) (13,8) (9,18) (6,11) (31,26) (10,20) (28,27) (19,28) (29,22) (18,0) (34,32) (29,31) (5,16) (34,4) (7,24) (2,23) (10,11) (30,5) (19,4) (23,33) (28,0) (31,19) (9,17) (16,10) (12,14) (10,12) (7,1) (5,15) (1,0) (21,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1580", "image": "data/cycle/graph_visual/hard/graph1580.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,15) (10,2) (27,5) (28,7) (5,21) (23,0) (3,27) (15,29) (1,29) (0,16) (14,13) (4,0) (22,5) (9,14) (5,6) (5,20) (11,18) (28,9) (20,8) (1,0) (8,26) (24,30) (0,3) (2,26) (4,18) (16,15) (7,12) (0,24) (21,17) (11,5) (19,16) (30,25) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1104", "image": "data/cycle/graph_visual/hard/graph1104.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,1) (5,17) (2,16) (23,17) (19,2) (12,15) (24,26) (4,11) (0,26) (20,8) (19,15) (14,18) (25,17) (18,3) (19,10) (4,9) (17,15) (21,7) (6,22) (8,17) (7,6) (7,1) (0,18) (11,15) (20,13) (22,15) (26,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1076", "image": "data/cycle/graph_visual/hard/graph1076.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,4) (22,15) (24,21) (7,4) (13,3) (3,5) (0,4) (24,16) (4,19) (0,1) (23,17) (15,0) (18,4) (0,3) (12,8) (7,17) (17,3) (12,4) (4,1) (1,22) (11,1) (23,25) (21,10) (6,24) (0,2) (23,20) (7,14) (1,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1828", "image": "data/cycle/graph_visual/hard/graph1828.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (8,16) (19,18) (29,10) (10,16) (22,28) (29,31) (23,27) (5,19) (4,17) (17,21) (19,9) (22,32) (1,0) (23,4) (11,27) (5,8) (20,27) (26,29) (12,1) (2,13) (30,17) (27,0) (7,6) (30,19) (26,2) (27,1) (27,33) (1,24) (0,2) (23,15) (13,22) (31,14) (7,17) (3,0) (3,11) (25,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph796", "image": "data/cycle/graph_visual/hard/graph796.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (17,23) (23,24) (1,7) (15,28) (5,10) (5,30) (32,30) (23,29) (17,21) (9,25) (19,16) (8,28) (26,6) (0,13) (29,1) (22,4) (3,11) (12,19) (18,13) (20,19) (6,7) (32,4) (16,31) (27,4) (13,7) (3,4) (6,27) (24,2) (22,14) (11,8) (18,31) (9,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1317", "image": "data/cycle/graph_visual/hard/graph1317.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,14) (0,2) (4,27) (1,12) (23,4) (10,12) (9,17) (2,10) (22,15) (24,20) (16,9) (12,27) (24,25) (28,23) (18,0) (5,6) (18,11) (12,8) (22,18) (0,26) (4,14) (21,7) (23,19) (21,26) (7,3) (0,1) (5,28) (7,24) (28,13) (8,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1156", "image": "data/cycle/graph_visual/hard/graph1156.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (17,0) (7,11) (23,13) (7,5) (25,1) (24,8) (22,14) (11,22) (2,0) (21,7) (3,23) (5,16) (12,25) (2,6) (26,7) (3,10) (0,3) (19,4) (0,6) (4,22) (15,1) (1,0) (11,20) (11,8) (12,8) (18,21) (14,10) (9,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph223", "image": "data/cycle/graph_visual/hard/graph223.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,27) (26,23) (24,17) (21,18) (25,3) (20,13) (1,8) (21,23) (8,19) (13,3) (22,18) (15,1) (3,18) (9,11) (24,27) (10,0) (20,12) (27,16) (18,9) (0,6) (24,4) (5,26) (7,26) (1,9) (6,27) (12,2) (14,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph503", "image": "data/cycle/graph_visual/hard/graph503.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (8,18) (4,1) (12,24) (28,10) (0,11) (4,23) (15,26) (14,3) (26,2) (27,22) (12,8) (20,23) (19,24) (11,28) (15,16) (9,26) (22,17) (26,7) (3,28) (29,22) (29,3) (21,10) (2,24) (16,30) (17,13) (20,17) (0,8) (28,6) (6,5) (25,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1893", "image": "data/cycle/graph_visual/hard/graph1893.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (4,13) (6,33) (23,4) (26,24) (4,21) (18,16) (30,5) (15,7) (7,20) (33,19) (10,20) (15,30) (12,30) (8,11) (13,18) (18,32) (14,1) (14,28) (0,10) (9,32) (31,3) (20,3) (33,20) (22,19) (29,27) (0,1) (20,17) (27,17) (3,28) (33,11) (17,2) (31,26) (19,25) (7,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph793", "image": "data/cycle/graph_visual/hard/graph793.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,27) (20,27) (26,28) (8,29) (20,7) (24,8) (18,3) (16,22) (9,12) (10,14) (16,5) (31,14) (18,13) (30,27) (11,19) (4,21) (32,7) (23,31) (17,0) (8,16) (17,9) (1,18) (4,13) (11,6) (25,0) (8,11) (16,2) (15,14) (27,28) (5,9) (27,1) (14,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph266", "image": "data/cycle/graph_visual/hard/graph266.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,15) (26,23) (14,20) (14,3) (17,8) (21,14) (0,19) (16,12) (10,9) (19,25) (16,1) (7,11) (7,9) (4,21) (5,18) (10,6) (11,23) (24,26) (9,21) (15,12) (10,0) (17,13) (4,27) (2,26) (24,22) (0,17) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1508", "image": "data/cycle/graph_visual/hard/graph1508.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,1) (14,0) (0,1) (7,4) (12,2) (30,8) (6,16) (11,5) (4,19) (3,7) (25,14) (6,18) (22,12) (28,6) (29,18) (25,7) (12,9) (13,22) (0,2) (26,28) (4,10) (3,0) (6,11) (15,27) (0,20) (15,2) (23,20) (12,14) (15,30) (16,21) (1,17) (12,26) (15,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph895", "image": "data/cycle/graph_visual/hard/graph895.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (25,4) (17,21) (33,28) (16,5) (31,1) (10,21) (27,31) (8,30) (20,13) (6,19) (24,12) (21,4) (7,15) (15,14) (0,32) (26,21) (14,0) (27,17) (14,20) (2,17) (9,18) (20,22) (9,22) (29,27) (22,23) (27,6) (12,28) (5,11) (30,5) (6,12) (14,21) (4,5) (3,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1084", "image": "data/cycle/graph_visual/hard/graph1084.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,3) (2,18) (1,10) (18,6) (16,4) (25,14) (19,24) (13,0) (17,21) (2,5) (11,25) (21,20) (18,21) (16,15) (22,25) (13,8) (9,17) (16,24) (0,1) (25,1) (25,8) (23,3) (20,10) (17,7) (15,5) (12,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1655", "image": "data/cycle/graph_visual/hard/graph1655.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (4,0) (12,27) (30,31) (21,26) (9,25) (15,14) (14,17) (12,29) (5,7) (21,20) (14,10) (26,28) (26,11) (23,28) (27,19) (12,22) (4,18) (5,31) (19,17) (2,6) (2,1) (16,22) (18,5) (3,0) (3,22) (14,26) (26,30) (10,24) (27,25) (0,1) (13,1) (22,8) (2,0) (28,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1189", "image": "data/cycle/graph_visual/hard/graph1189.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (5,16) (1,25) (8,12) (22,11) (0,1) (20,11) (3,23) (24,8) (1,15) (14,10) (21,7) (2,6) (14,22) (0,2) (3,10) (13,23) (4,0) (11,7) (25,12) (4,19) (0,17) (21,18) (8,11) (3,0) (16,9) (6,0) (4,22) (7,5) (0,5) (26,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1078", "image": "data/cycle/graph_visual/hard/graph1078.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,13) (12,11) (19,11) (12,3) (24,12) (5,16) (6,19) (1,2) (22,5) (20,13) (1,0) (0,8) (9,15) (12,18) (0,23) (20,23) (21,0) (16,7) (10,15) (19,16) (14,7) (4,18) (10,17) (1,11) (20,3) (25,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1027", "image": "data/cycle/graph_visual/hard/graph1027.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,13) (2,4) (17,6) (11,18) (7,16) (1,5) (11,0) (0,23) (13,10) (2,0) (0,3) (7,25) (0,1) (20,12) (8,22) (25,4) (16,20) (5,16) (14,9) (9,15) (13,2) (22,16) (24,0) (19,15) (21,5) (25,15) (6,25) (13,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1452", "image": "data/cycle/graph_visual/hard/graph1452.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,27) (24,5) (22,15) (17,28) (10,9) (3,2) (3,0) (29,15) (7,19) (0,24) (22,2) (1,0) (14,28) (13,9) (19,14) (6,8) (26,0) (4,11) (23,4) (18,9) (26,20) (12,16) (23,6) (16,11) (18,25) (12,13) (1,29) (0,28) (2,21) (14,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1145", "image": "data/cycle/graph_visual/hard/graph1145.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (0,3) (24,11) (13,0) (1,23) (10,4) (25,9) (18,21) (17,20) (15,18) (2,0) (0,4) (13,6) (6,26) (2,24) (25,6) (3,19) (15,10) (3,2) (0,1) (20,10) (21,8) (23,13) (4,3) (0,5) (18,14) (8,16) (21,7) (12,4) (14,13) (22,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1279", "image": "data/cycle/graph_visual/hard/graph1279.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (17,4) (24,10) (5,12) (11,18) (8,18) (26,0) (26,1) (10,20) (0,4) (12,27) (23,2) (0,1) (25,1) (7,13) (25,2) (20,26) (0,22) (1,6) (18,16) (25,19) (16,14) (17,18) (1,21) (15,4) (9,27) (7,20) (2,3) (17,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1605", "image": "data/cycle/graph_visual/hard/graph1605.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (25,21) (23,28) (9,2) (16,7) (11,15) (6,13) (12,6) (3,23) (26,11) (4,6) (22,24) (1,12) (21,26) (9,31) (25,14) (11,23) (27,11) (3,13) (22,27) (5,19) (18,9) (12,16) (30,17) (18,29) (24,19) (29,30) (0,1) (0,15) (0,20) (9,12) (27,8) (2,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph539", "image": "data/cycle/graph_visual/hard/graph539.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,5) (24,7) (7,6) (19,18) (18,21) (26,12) (11,22) (15,24) (12,17) (24,14) (29,20) (28,8) (30,9) (4,26) (10,3) (6,10) (1,22) (19,30) (19,2) (0,6) (27,29) (7,23) (14,13) (27,16) (18,11) (17,27) (27,28) (21,25) (17,7) (24,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1604", "image": "data/cycle/graph_visual/hard/graph1604.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (22,29) (10,21) (2,31) (22,17) (25,18) (6,13) (18,21) (3,11) (9,8) (28,21) (0,5) (1,27) (19,4) (1,0) (9,27) (29,1) (21,23) (4,25) (12,18) (21,11) (18,30) (28,20) (5,11) (13,20) (0,26) (31,20) (22,16) (20,7) (1,14) (31,15) (25,8) (10,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph104", "image": "data/cycle/graph_visual/hard/graph104.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (9,18) (6,13) (23,25) (7,15) (23,26) (15,17) (16,2) (9,3) (15,0) (24,20) (10,0) (1,19) (8,5) (2,19) (25,21) (13,9) (1,20) (3,0) (14,10) (8,4) (12,2) (22,3) (25,8) (11,8) (4,2) (23,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph328", "image": "data/cycle/graph_visual/hard/graph328.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (11,20) (24,3) (16,24) (25,23) (14,4) (22,25) (27,21) (1,23) (12,10) (4,9) (18,22) (11,3) (17,0) (26,8) (11,28) (1,17) (4,6) (25,27) (8,13) (23,7) (20,8) (18,24) (18,15) (19,16) (5,24) (10,27) (9,13) (10,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1057", "image": "data/cycle/graph_visual/hard/graph1057.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (10,24) (25,15) (23,20) (3,25) (12,8) (6,24) (14,1) (15,8) (15,2) (24,9) (24,19) (13,23) (0,8) (0,2) (1,0) (25,13) (21,4) (17,18) (7,2) (15,18) (18,5) (11,10) (0,22) (23,6) (4,16) (11,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph134", "image": "data/cycle/graph_visual/hard/graph134.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (16,23) (26,17) (26,4) (20,12) (22,8) (5,16) (0,25) (11,0) (22,5) (13,10) (15,9) (25,6) (18,11) (16,21) (19,6) (13,3) (9,14) (13,2) (0,24) (5,1) (25,7) (20,15) (4,2) (13,18) (7,16) (25,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1591", "image": "data/cycle/graph_visual/hard/graph1591.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (4,2) (13,2) (26,16) (4,25) (16,7) (0,1) (18,13) (0,27) (0,28) (4,0) (15,9) (12,20) (23,5) (0,3) (24,25) (9,14) (22,8) (21,30) (0,11) (13,10) (15,20) (5,16) (24,30) (26,17) (11,29) (25,7) (18,29) (6,19) (16,22) (25,15) (0,2) (1,5) (6,25) (13,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph627", "image": "data/cycle/graph_visual/hard/graph627.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (18,4) (8,11) (8,21) (0,28) (14,23) (1,26) (24,29) (24,13) (9,1) (25,0) (27,4) (28,23) (16,26) (21,14) (29,14) (22,6) (17,22) (16,17) (19,10) (9,19) (2,4) (20,1) (30,15) (3,11) (20,5) (23,31) (23,7) (22,31) (18,5) (22,15) (14,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph446", "image": "data/cycle/graph_visual/hard/graph446.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (28,18) (18,14) (20,29) (12,18) (9,13) (25,14) (18,10) (16,20) (21,1) (27,26) (8,15) (2,17) (11,22) (21,20) (0,6) (28,15) (8,11) (26,9) (23,4) (6,15) (1,4) (9,8) (17,23) (3,22) (25,24) (11,2) (2,5) (21,7) (19,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1184", "image": "data/cycle/graph_visual/hard/graph1184.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (12,24) (9,10) (0,1) (12,14) (16,22) (6,7) (10,14) (10,20) (19,0) (3,5) (1,15) (2,22) (25,5) (17,25) (8,10) (25,6) (11,2) (0,16) (11,15) (17,4) (23,11) (0,20) (9,13) (22,18) (10,5) (21,15) (26,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph867", "image": "data/cycle/graph_visual/hard/graph867.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (33,20) (3,2) (16,22) (17,6) (4,1) (18,7) (23,21) (9,3) (12,31) (30,8) (7,0) (14,16) (2,11) (22,20) (18,28) (0,25) (19,5) (17,8) (29,4) (24,30) (4,26) (19,2) (32,16) (26,10) (17,9) (1,21) (20,11) (26,9) (4,27) (31,13) (19,7) (13,27) (5,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1724", "image": "data/cycle/graph_visual/hard/graph1724.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,21) (21,32) (11,20) (2,7) (12,25) (12,6) (26,16) (12,15) (18,29) (9,31) (19,16) (10,28) (4,0) (19,13) (1,0) (12,31) (7,27) (23,29) (16,0) (15,5) (1,11) (18,22) (12,30) (30,17) (3,0) (10,15) (13,31) (32,23) (2,0) (7,20) (15,11) (31,8) (11,14) (3,28) (21,4) (16,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph598", "image": "data/cycle/graph_visual/hard/graph598.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,30) (7,23) (7,16) (6,0) (9,28) (11,24) (25,0) (5,13) (12,19) (26,2) (15,20) (13,15) (22,11) (15,26) (22,29) (4,2) (7,17) (19,11) (21,4) (22,18) (19,26) (5,14) (8,14) (27,22) (4,1) (9,5) (11,10) (23,15) (6,3) (3,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1015", "image": "data/cycle/graph_visual/hard/graph1015.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,5) (9,2) (3,20) (21,24) (5,17) (14,9) (8,6) (21,20) (14,15) (13,9) (1,0) (23,16) (13,25) (20,2) (8,20) (10,22) (10,21) (18,0) (16,15) (2,0) (16,12) (19,18) (4,7) (17,11) (19,16) (1,5) (7,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph973", "image": "data/cycle/graph_visual/hard/graph973.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (8,34) (25,34) (31,16) (11,31) (6,7) (6,27) (28,15) (33,32) (4,3) (17,21) (20,19) (24,2) (8,29) (14,22) (13,7) (13,0) (32,18) (22,4) (17,23) (19,16) (3,11) (7,1) (18,13) (9,2) (23,29) (9,26) (34,27) (4,1) (28,6) (23,24) (5,10) (12,19) (30,33) (5,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1707", "image": "data/cycle/graph_visual/hard/graph1707.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (18,30) (28,24) (0,27) (3,5) (26,2) (1,9) (27,28) (7,32) (21,3) (10,7) (9,22) (0,3) (23,10) (15,27) (21,6) (5,11) (15,17) (25,23) (9,7) (0,2) (8,1) (12,30) (16,19) (7,14) (32,13) (4,29) (24,8) (20,28) (21,16) (6,29) (22,31) (12,11) (30,2) (0,1) (0,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1166", "image": "data/cycle/graph_visual/hard/graph1166.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,9) (7,0) (25,4) (17,21) (0,2) (6,9) (13,2) (26,12) (10,25) (14,11) (13,23) (7,12) (16,25) (4,0) (22,18) (8,21) (24,23) (1,16) (17,19) (8,13) (5,9) (10,20) (0,3) (16,8) (20,26) (22,3) (5,24) (22,15) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph938", "image": "data/cycle/graph_visual/hard/graph938.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (18,4) (17,19) (24,11) (25,6) (33,6) (25,32) (8,1) (14,0) (1,11) (27,16) (13,25) (6,28) (5,16) (13,3) (29,27) (26,23) (19,32) (22,31) (12,34) (7,24) (4,17) (16,20) (27,30) (15,16) (4,29) (0,2) (18,1) (9,12) (21,22) (14,10) (23,0) (2,12) (0,20) (22,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1210", "image": "data/cycle/graph_visual/hard/graph1210.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,7) (23,8) (8,1) (24,27) (22,16) (1,0) (12,15) (11,13) (25,24) (6,16) (11,17) (2,18) (0,2) (16,12) (0,13) (26,0) (5,20) (0,4) (10,15) (4,3) (18,9) (21,9) (19,18) (14,3) (6,14) (0,3) (5,14) (13,8) (2,15) (27,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1897", "image": "data/cycle/graph_visual/hard/graph1897.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (13,22) (32,11) (32,17) (14,17) (2,7) (30,11) (4,6) (33,31) (8,20) (13,21) (11,5) (26,19) (1,26) (0,1) (24,12) (12,0) (28,8) (18,29) (6,26) (26,20) (29,15) (9,25) (4,15) (23,10) (9,13) (8,10) (28,14) (27,1) (33,0) (12,8) (7,14) (8,16) (25,12) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph669", "image": "data/cycle/graph_visual/hard/graph669.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (9,18) (28,3) (22,0) (18,6) (1,3) (0,6) (10,4) (19,23) (21,8) (7,8) (26,21) (20,5) (31,6) (31,30) (4,30) (23,25) (21,10) (2,21) (16,13) (1,15) (17,23) (1,23) (11,9) (3,14) (24,0) (16,17) (12,27) (5,10) (20,15) (21,29) (31,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1594", "image": "data/cycle/graph_visual/hard/graph1594.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (4,24) (8,2) (29,26) (6,18) (19,6) (26,15) (9,25) (30,11) (16,21) (0,25) (16,11) (8,12) (13,4) (20,8) (28,29) (6,16) (10,3) (19,7) (22,16) (19,1) (24,17) (26,0) (2,6) (26,14) (4,11) (27,22) (0,1) (14,24) (1,23) (16,5) (0,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1849", "image": "data/cycle/graph_visual/hard/graph1849.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (4,0) (30,21) (10,2) (27,24) (30,17) (26,9) (30,15) (0,1) (1,17) (25,28) (2,0) (12,20) (8,28) (0,3) (0,32) (12,30) (23,6) (22,25) (16,14) (24,31) (14,9) (7,30) (25,27) (0,13) (11,4) (33,23) (1,19) (23,8) (29,14) (3,15) (10,4) (16,18) (33,9) (30,24) (2,19) (5,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1467", "image": "data/cycle/graph_visual/hard/graph1467.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,17) (27,16) (16,14) (16,24) (5,13) (2,4) (17,11) (9,25) (1,0) (26,21) (10,22) (13,23) (10,1) (29,16) (6,7) (17,28) (6,18) (3,15) (17,0) (21,3) (9,12) (5,4) (15,20) (3,0) (4,25) (19,22) (24,22) (27,17) (24,6) (2,0) (20,7) (27,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph234", "image": "data/cycle/graph_visual/hard/graph234.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (27,7) (21,18) (22,24) (20,1) (16,7) (26,19) (11,2) (21,1) (15,1) (5,13) (24,10) (3,10) (25,13) (11,17) (8,25) (16,17) (6,3) (8,4) (14,4) (27,9) (20,17) (2,0) (1,23) (19,9) (16,12) (24,23) (14,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1561", "image": "data/cycle/graph_visual/hard/graph1561.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (12,1) (28,1) (7,4) (25,22) (4,10) (11,21) (23,17) (0,15) (8,24) (4,0) (0,1) (30,18) (3,19) (6,13) (7,17) (13,16) (1,4) (15,4) (4,24) (2,0) (4,26) (3,17) (30,6) (23,27) (23,14) (1,21) (22,24) (3,0) (21,29) (5,3) (12,9) (14,16) (20,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1785", "image": "data/cycle/graph_visual/hard/graph1785.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (5,21) (22,13) (31,10) (27,5) (24,0) (11,24) (19,21) (28,2) (30,28) (12,13) (17,26) (24,2) (0,2) (6,16) (31,23) (25,28) (1,8) (19,7) (14,28) (6,9) (3,12) (18,26) (30,8) (32,0) (17,16) (3,31) (24,20) (29,9) (17,23) (21,18) (0,17) (1,0) (14,15) (4,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1413", "image": "data/cycle/graph_visual/hard/graph1413.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (16,22) (3,0) (25,18) (22,2) (5,3) (10,20) (25,12) (0,1) (27,0) (2,11) (9,10) (11,15) (2,0) (0,28) (2,20) (8,29) (9,17) (28,16) (1,15) (5,26) (12,14) (6,7) (10,13) (10,14) (24,11) (6,25) (0,21) (19,22) (5,10) (20,29) (4,17) (15,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1602", "image": "data/cycle/graph_visual/hard/graph1602.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (3,28) (2,0) (23,25) (0,3) (9,18) (8,7) (26,21) (4,10) (1,3) (5,20) (6,0) (31,27) (29,21) (19,23) (6,18) (14,3) (0,22) (10,5) (10,21) (17,16) (12,27) (16,13) (21,2) (1,0) (30,4) (15,20) (11,9) (23,1) (0,4) (15,1) (24,0) (6,31) (17,23) (31,30) (21,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1843", "image": "data/cycle/graph_visual/hard/graph1843.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (23,17) (29,24) (1,6) (16,26) (16,21) (28,12) (1,0) (4,30) (8,12) (4,6) (22,11) (27,33) (22,20) (33,13) (2,33) (19,1) (7,29) (20,25) (7,12) (27,6) (6,17) (14,18) (12,31) (3,7) (6,18) (32,5) (0,2) (10,25) (26,32) (1,26) (20,19) (4,24) (9,15) (9,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1442", "image": "data/cycle/graph_visual/hard/graph1442.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (4,9) (11,4) (1,0) (17,27) (22,6) (22,15) (19,0) (20,14) (6,7) (2,0) (29,20) (28,26) (12,20) (1,7) (17,15) (15,23) (10,29) (18,3) (17,5) (26,21) (17,8) (17,26) (12,15) (2,19) (2,18) (8,24) (29,0) (16,18) (15,13) (19,11) (7,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1361", "image": "data/cycle/graph_visual/hard/graph1361.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,20) (27,20) (1,7) (6,22) (17,24) (6,7) (27,28) (10,19) (8,21) (3,18) (11,15) (14,18) (15,19) (11,4) (9,4) (17,5) (2,19) (8,17) (23,7) (12,15) (0,1) (12,20) (0,26) (15,22) (18,0) (25,26) (15,17) (2,16) (17,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph428", "image": "data/cycle/graph_visual/hard/graph428.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,4) (15,22) (2,3) (6,24) (21,20) (14,20) (6,0) (29,3) (24,14) (12,5) (1,3) (13,22) (9,4) (16,5) (8,23) (6,19) (23,6) (26,5) (7,17) (13,0) (2,7) (7,13) (19,4) (28,6) (26,4) (19,11) (25,4) (17,10) (27,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph497", "image": "data/cycle/graph_visual/hard/graph497.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,3) (18,3) (27,28) (27,3) (18,9) (27,19) (12,27) (14,9) (23,26) (1,15) (18,21) (25,18) (26,10) (21,23) (0,11) (24,4) (20,16) (6,29) (20,24) (5,29) (22,8) (2,12) (1,8) (0,6) (29,26) (15,17) (9,1) (26,7) (13,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1768", "image": "data/cycle/graph_visual/hard/graph1768.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (10,29) (0,1) (27,28) (3,16) (15,25) (31,30) (32,18) (26,22) (0,17) (27,11) (26,1) (4,14) (26,24) (6,32) (21,7) (16,23) (11,9) (11,3) (1,7) (12,19) (31,27) (12,5) (28,20) (25,1) (18,22) (12,16) (8,30) (0,2) (7,2) (31,4) (17,32) (19,13) (22,29) (5,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph225", "image": "data/cycle/graph_visual/hard/graph225.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,24) (0,14) (7,21) (0,25) (27,10) (17,9) (10,23) (5,6) (9,15) (22,13) (26,21) (11,18) (12,27) (18,0) (18,20) (14,4) (12,8) (8,16) (23,17) (1,12) (7,3) (5,12) (23,4) (24,7) (24,19) (2,10) (26,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1427", "image": "data/cycle/graph_visual/hard/graph1427.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,28) (19,5) (10,3) (2,21) (14,28) (5,25) (20,15) (12,7) (1,3) (8,6) (13,15) (6,26) (28,22) (16,10) (23,8) (27,29) (9,14) (17,20) (27,5) (21,24) (24,25) (14,4) (5,0) (10,11) (7,6) (9,15) (15,18) (16,21) (2,0) (3,22) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1683", "image": "data/cycle/graph_visual/hard/graph1683.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (7,31) (15,27) (13,29) (22,24) (5,8) (11,18) (17,21) (9,11) (7,28) (15,25) (18,1) (26,4) (23,19) (6,3) (21,2) (5,0) (1,3) (10,0) (17,14) (0,1) (25,22) (4,17) (18,13) (31,0) (30,20) (11,31) (12,15) (16,27) (25,10) (23,31) (24,26) (20,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph976", "image": "data/cycle/graph_visual/hard/graph976.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,18) (24,9) (13,26) (23,25) (32,12) (16,2) (7,5) (29,26) (14,20) (9,11) (34,14) (30,0) (34,19) (7,6) (34,13) (5,30) (4,0) (21,33) (27,28) (13,12) (3,2) (7,1) (8,3) (21,31) (8,17) (1,25) (25,21) (28,33) (9,2) (10,25) (15,23) (8,14) (13,15) (8,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1336", "image": "data/cycle/graph_visual/hard/graph1336.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,2) (7,23) (24,15) (11,10) (7,13) (24,21) (25,4) (0,2) (0,15) (11,3) (7,6) (3,26) (12,28) (22,10) (27,26) (27,1) (9,20) (0,1) (8,5) (2,6) (4,11) (16,15) (17,20) (21,17) (28,2) (18,10) (17,2) (8,11) (7,10) (22,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph215", "image": "data/cycle/graph_visual/hard/graph215.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (21,11) (17,20) (6,14) (22,23) (18,25) (22,26) (3,20) (27,6) (2,4) (22,8) (24,19) (25,24) (27,2) (5,3) (26,13) (19,7) (9,12) (25,16) (15,8) (17,10) (12,0) (6,21) (1,15) (14,13) (20,24) (0,6) (4,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1006", "image": "data/cycle/graph_visual/hard/graph1006.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (3,0) (22,3) (18,12) (14,8) (24,17) (4,0) (22,5) (9,24) (15,5) (13,16) (1,21) (10,6) (6,20) (13,11) (3,17) (1,0) (2,23) (0,2) (23,14) (16,25) (1,8) (7,14) (21,20) (23,12) (19,11) (14,4) (2,3) (25,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1778", "image": "data/cycle/graph_visual/hard/graph1778.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,11) (16,28) (7,12) (31,18) (0,2) (0,31) (15,22) (8,6) (29,4) (1,0) (25,6) (30,13) (18,19) (19,11) (0,26) (24,23) (2,11) (13,27) (12,10) (20,16) (1,12) (17,18) (5,13) (26,21) (25,14) (18,22) (9,2) (6,3) (28,4) (28,24) (2,30) (19,8) (28,12) (23,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph937", "image": "data/cycle/graph_visual/hard/graph937.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (11,29) (0,34) (24,13) (20,25) (16,24) (1,25) (20,30) (11,21) (33,32) (0,17) (25,2) (10,15) (18,33) (5,8) (28,12) (5,33) (2,17) (8,14) (24,3) (16,15) (29,9) (13,9) (6,11) (19,34) (27,31) (14,7) (21,5) (31,23) (30,5) (12,4) (12,26) (13,26) (22,5) (23,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1116", "image": "data/cycle/graph_visual/hard/graph1116.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,23) (2,5) (8,20) (26,6) (16,14) (0,2) (19,21) (25,24) (25,11) (25,6) (26,14) (21,4) (14,17) (5,0) (18,1) (22,11) (14,10) (1,0) (5,9) (0,3) (19,26) (23,13) (5,12) (21,3) (14,18) (6,15) (7,6) (0,4) (25,12) (8,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph748", "image": "data/cycle/graph_visual/hard/graph748.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (8,10) (12,26) (3,5) (3,32) (0,15) (17,14) (0,27) (20,28) (14,29) (8,16) (7,2) (24,2) (25,28) (10,28) (17,1) (11,19) (30,10) (10,4) (22,11) (0,21) (26,31) (24,23) (9,23) (7,26) (30,6) (2,22) (31,17) (2,13) (15,4) (32,24) (30,31) (18,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph115", "image": "data/cycle/graph_visual/hard/graph115.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,20) (8,17) (3,10) (10,25) (0,1) (23,11) (24,8) (5,7) (19,5) (21,23) (25,6) (2,18) (25,15) (22,20) (2,17) (20,16) (0,14) (13,26) (16,0) (18,13) (11,17) (9,2) (12,9) (26,15) (4,1) (7,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1087", "image": "data/cycle/graph_visual/hard/graph1087.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (16,6) (12,1) (13,3) (3,22) (0,5) (7,9) (25,16) (6,0) (0,2) (1,9) (18,20) (1,8) (23,6) (2,12) (18,3) (21,23) (19,24) (20,10) (21,18) (18,9) (17,13) (15,11) (24,4) (15,8) (25,19) (14,24) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph678", "image": "data/cycle/graph_visual/hard/graph678.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (21,10) (19,20) (23,2) (5,29) (26,20) (6,5) (0,1) (3,14) (16,30) (5,19) (6,7) (19,16) (18,31) (6,31) (7,11) (15,1) (5,27) (24,17) (29,9) (22,19) (12,2) (31,0) (28,2) (10,24) (13,1) (14,8) (12,5) (4,5) (8,19) (25,23) (21,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1238", "image": "data/cycle/graph_visual/hard/graph1238.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (11,15) (2,10) (15,3) (2,0) (27,0) (19,24) (4,1) (15,0) (17,14) (26,23) (13,19) (27,5) (3,6) (0,1) (3,8) (24,16) (6,22) (13,12) (25,7) (8,2) (21,25) (14,15) (0,24) (9,24) (18,4) (12,20) (12,25) (0,3) (20,18) (24,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1783", "image": "data/cycle/graph_visual/hard/graph1783.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (10,1) (7,32) (1,0) (0,4) (22,15) (3,7) (13,6) (1,20) (12,13) (25,11) (20,9) (24,5) (2,14) (5,16) (17,25) (10,3) (1,2) (8,32) (16,21) (23,4) (15,30) (29,28) (0,2) (32,22) (22,21) (10,18) (31,20) (19,26) (27,30) (20,28) (23,20) (0,26) (21,6) (30,0) (0,3) (17,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph897", "image": "data/cycle/graph_visual/hard/graph897.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (21,28) (30,14) (23,2) (5,33) (7,26) (2,24) (0,28) (5,24) (15,0) (30,9) (7,2) (18,8) (1,17) (8,10) (10,30) (3,32) (15,4) (17,31) (11,20) (27,28) (11,22) (26,13) (26,31) (29,10) (3,6) (31,32) (19,26) (17,14) (22,0) (2,16) (25,24) (23,12) (4,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph161", "image": "data/cycle/graph_visual/hard/graph161.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (12,20) (9,14) (25,15) (0,11) (13,3) (16,7) (13,10) (6,25) (9,15) (0,25) (11,18) (13,18) (19,6) (1,5) (2,13) (8,22) (7,25) (21,16) (16,5) (26,17) (20,15) (0,24) (16,23) (2,4) (4,26) (5,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1941", "image": "data/cycle/graph_visual/hard/graph1941.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (29,9) (19,6) (16,25) (32,5) (30,21) (28,30) (32,17) (2,16) (19,11) (1,0) (31,4) (26,34) (22,27) (20,13) (14,22) (20,27) (10,25) (26,1) (30,13) (34,16) (18,24) (7,31) (33,28) (8,23) (3,2) (8,6) (4,21) (24,0) (13,15) (30,12) (6,22) (19,9) (8,18) (33,16) (32,6) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph537", "image": "data/cycle/graph_visual/hard/graph537.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (15,6) (18,28) (4,1) (15,8) (9,13) (21,20) (16,20) (11,22) (30,29) (4,23) (11,8) (5,2) (18,12) (9,8) (21,1) (28,19) (28,15) (2,11) (22,3) (2,17) (6,0) (18,10) (24,25) (25,14) (17,23) (30,20) (27,26) (7,21) (9,26) (18,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1326", "image": "data/cycle/graph_visual/hard/graph1326.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,6) (3,0) (20,2) (7,26) (1,0) (1,24) (14,28) (11,16) (8,14) (6,23) (19,7) (22,15) (12,13) (26,17) (9,13) (22,2) (24,18) (11,4) (27,0) (28,10) (14,19) (4,23) (9,18) (15,28) (12,16) (0,25) (2,3) (5,9) (0,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph362", "image": "data/cycle/graph_visual/hard/graph362.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (21,6) (27,7) (4,13) (23,5) (6,22) (20,25) (27,3) (6,27) (11,4) (11,9) (9,17) (28,20) (24,2) (18,1) (15,0) (14,4) (1,13) (2,26) (17,25) (26,1) (8,14) (12,16) (2,10) (6,15) (20,19) (5,9) (15,25) (1,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph356", "image": "data/cycle/graph_visual/hard/graph356.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (12,14) (20,24) (6,9) (28,4) (14,3) (27,4) (21,11) (23,12) (23,25) (6,18) (27,21) (26,27) (9,26) (19,1) (7,21) (5,9) (21,17) (19,23) (26,2) (14,0) (15,2) (16,2) (15,8) (9,20) (13,2) (2,22) (1,7) (8,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1235", "image": "data/cycle/graph_visual/hard/graph1235.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,20) (3,0) (17,15) (11,14) (8,22) (7,5) (1,0) (16,18) (13,11) (13,10) (2,8) (17,22) (0,5) (19,26) (7,12) (11,21) (11,0) (7,25) (18,0) (1,19) (26,23) (9,27) (3,12) (12,1) (5,16) (24,17) (4,27) (12,24) (2,0) (0,4) (6,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1829", "image": "data/cycle/graph_visual/hard/graph1829.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (25,28) (21,33) (5,21) (23,32) (0,1) (1,8) (7,19) (17,26) (0,3) (9,6) (33,0) (28,31) (9,30) (6,16) (24,2) (24,20) (14,15) (28,2) (24,0) (19,21) (17,23) (18,29) (11,24) (13,22) (17,0) (27,5) (28,4) (14,28) (3,12) (17,16) (2,0) (31,10) (12,13) (3,31) (30,8) (0,4) (26,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph716", "image": "data/cycle/graph_visual/hard/graph716.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (21,4) (30,13) (6,19) (8,18) (22,14) (2,3) (23,8) (25,10) (32,16) (30,12) (9,26) (24,0) (20,13) (4,29) (19,11) (5,32) (19,9) (6,8) (6,31) (7,31) (32,17) (1,26) (20,27) (25,16) (28,30) (16,2) (30,21) (24,18) (6,22) (13,15) (22,27) (16,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1955", "image": "data/cycle/graph_visual/hard/graph1955.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,22) (25,10) (0,24) (12,30) (0,26) (8,32) (14,18) (17,31) (2,21) (33,12) (2,31) (13,34) (26,7) (0,3) (3,30) (11,32) (34,12) (21,19) (20,2) (6,22) (0,1) (12,16) (10,29) (23,22) (3,9) (32,17) (15,4) (13,8) (11,25) (18,25) (12,27) (4,31) (28,34) (23,0) (5,2) (19,24) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1341", "image": "data/cycle/graph_visual/hard/graph1341.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (20,18) (13,23) (14,5) (0,9) (0,19) (22,15) (7,8) (6,4) (12,14) (26,2) (1,0) (0,3) (8,1) (7,4) (28,25) (24,11) (10,1) (2,0) (11,25) (5,19) (3,16) (3,23) (22,28) (21,17) (20,28) (2,7) (23,21) (10,19) (27,28) (17,5) (13,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1404", "image": "data/cycle/graph_visual/hard/graph1404.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,0) (8,25) (5,8) (26,20) (28,23) (6,13) (9,18) (4,2) (10,14) (3,9) (25,28) (4,8) (2,12) (23,29) (19,2) (0,10) (1,28) (17,15) (2,16) (11,8) (25,21) (27,19) (20,1) (2,0) (15,0) (9,13) (1,0) (22,3) (7,15) (27,9) (23,24) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1496", "image": "data/cycle/graph_visual/hard/graph1496.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,2) (21,25) (15,0) (9,24) (14,15) (19,13) (6,23) (25,28) (0,22) (20,18) (4,18) (0,1) (4,1) (20,12) (2,10) (28,24) (15,11) (17,14) (27,26) (0,24) (24,19) (6,3) (5,27) (16,24) (3,15) (13,12) (2,0) (3,8) (7,25) (29,22) (26,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1230", "image": "data/cycle/graph_visual/hard/graph1230.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (3,24) (2,0) (0,27) (19,3) (24,5) (4,24) (8,25) (13,7) (2,12) (20,12) (22,9) (27,17) (14,15) (18,6) (12,25) (11,15) (9,26) (25,19) (4,9) (26,21) (6,16) (11,18) (23,15) (0,1) (16,13) (17,8) (4,16) (10,1) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph666", "image": "data/cycle/graph_visual/hard/graph666.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,28) (26,27) (10,29) (6,1) (30,6) (27,11) (4,16) (23,31) (22,5) (10,2) (4,3) (26,21) (9,12) (18,26) (14,28) (28,12) (25,22) (9,19) (13,29) (9,20) (24,4) (18,9) (0,2) (19,13) (23,16) (6,13) (26,8) (25,4) (6,24) (15,20) (20,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1044", "image": "data/cycle/graph_visual/hard/graph1044.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (6,15) (20,12) (14,2) (0,1) (9,19) (7,11) (0,12) (19,2) (16,21) (15,24) (1,12) (6,13) (2,17) (2,0) (7,4) (19,25) (8,18) (23,19) (3,6) (12,16) (13,23) (22,21) (5,7) (23,8) (5,10) (22,17) (4,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph995", "image": "data/cycle/graph_visual/hard/graph995.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (5,32) (24,17) (12,33) (16,13) (17,25) (32,11) (34,29) (2,16) (29,15) (11,22) (15,4) (28,1) (21,20) (30,10) (2,30) (0,3) (14,25) (23,19) (0,30) (19,22) (14,9) (16,31) (23,28) (27,7) (12,1) (23,21) (10,28) (18,33) (34,3) (8,15) (25,0) (24,26) (1,7) (6,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph838", "image": "data/cycle/graph_visual/hard/graph838.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (18,2) (24,14) (27,6) (10,26) (0,33) (22,29) (29,5) (7,31) (17,7) (32,8) (17,15) (30,27) (16,8) (3,25) (15,21) (25,1) (18,5) (19,33) (1,9) (3,13) (8,19) (20,0) (4,24) (1,23) (31,19) (12,16) (17,6) (4,25) (1,15) (22,4) (25,28) (13,11) (10,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph214", "image": "data/cycle/graph_visual/hard/graph214.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (24,5) (22,24) (8,27) (23,1) (16,17) (7,1) (6,7) (23,14) (20,2) (7,16) (12,0) (4,2) (17,12) (25,24) (2,0) (3,8) (9,10) (26,3) (9,21) (12,18) (17,11) (13,3) (26,5) (4,15) (19,15) (8,11) (9,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph926", "image": "data/cycle/graph_visual/hard/graph926.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (6,11) (30,5) (6,2) (21,17) (34,27) (26,23) (1,29) (4,11) (7,25) (15,34) (13,18) (5,9) (13,25) (8,27) (25,31) (12,33) (12,26) (12,17) (28,24) (9,22) (29,25) (7,10) (1,28) (14,34) (4,0) (8,18) (32,0) (13,20) (2,16) (30,3) (1,5) (5,12) (14,16) (1,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1190", "image": "data/cycle/graph_visual/hard/graph1190.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,0) (6,16) (26,11) (18,8) (2,0) (23,0) (16,20) (26,0) (21,1) (26,14) (8,2) (3,10) (24,15) (16,5) (6,17) (1,19) (25,9) (26,4) (12,8) (6,19) (16,11) (2,6) (16,22) (19,7) (25,14) (24,22) (1,0) (13,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph679", "image": "data/cycle/graph_visual/hard/graph679.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,15) (16,8) (5,4) (16,17) (30,16) (25,15) (12,4) (30,1) (10,12) (17,2) (31,6) (23,20) (22,0) (24,11) (22,28) (9,6) (27,26) (16,19) (4,13) (9,14) (8,21) (26,3) (31,15) (4,29) (3,28) (23,25) (18,7) (18,21) (14,21) (27,5) (30,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1846", "image": "data/cycle/graph_visual/hard/graph1846.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (21,30) (27,20) (19,11) (2,3) (22,14) (8,6) (28,30) (7,31) (25,10) (28,33) (5,32) (9,19) (18,8) (17,32) (27,22) (13,15) (2,0) (16,33) (9,26) (32,16) (4,29) (21,4) (0,1) (6,22) (13,30) (23,8) (0,24) (26,1) (2,16) (30,12) (13,20) (18,24) (31,6) (16,25) (19,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1355", "image": "data/cycle/graph_visual/hard/graph1355.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (3,14) (28,4) (27,23) (19,25) (11,7) (10,26) (16,12) (16,1) (21,4) (7,9) (0,19) (14,20) (26,24) (23,11) (17,13) (1,0) (5,18) (22,24) (8,17) (15,26) (14,21) (4,5) (15,12) (9,10) (6,10) (2,26) (28,0) (21,9) (0,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph994", "image": "data/cycle/graph_visual/hard/graph994.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (8,31) (4,30) (34,4) (9,23) (15,28) (6,4) (13,2) (6,8) (25,16) (8,29) (4,1) (6,11) (2,1) (19,11) (15,34) (0,12) (1,3) (28,21) (12,27) (11,12) (14,17) (30,22) (19,24) (34,33) (26,34) (34,32) (7,23) (23,17) (1,18) (27,5) (7,20) (15,20) (16,26) (3,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph78", "image": "data/cycle/graph_visual/hard/graph78.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (1,21) (23,2) (7,14) (9,24) (4,0) (12,18) (17,24) (3,22) (12,23) (5,22) (6,20) (11,13) (8,14) (17,3) (6,10) (14,23) (25,10) (15,5) (21,20) (4,14) (11,19) (1,8) (13,16) (3,2) (16,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph310", "image": "data/cycle/graph_visual/hard/graph310.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,18) (23,21) (25,24) (27,22) (2,22) (24,20) (7,13) (7,18) (8,15) (1,14) (9,16) (15,13) (24,27) (10,14) (23,0) (28,3) (16,19) (10,21) (3,25) (14,17) (3,12) (26,11) (6,26) (4,23) (20,17) (8,23) (11,5) (5,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1874", "image": "data/cycle/graph_visual/hard/graph1874.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (8,16) (2,20) (12,26) (14,28) (10,27) (14,25) (6,21) (13,23) (1,4) (14,15) (5,18) (1,0) (1,30) (24,33) (14,26) (29,32) (13,9) (11,15) (6,8) (3,7) (9,17) (0,10) (6,5) (1,12) (28,17) (1,2) (5,22) (24,5) (13,21) (7,17) (17,32) (27,21) (27,19) (31,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1760", "image": "data/cycle/graph_visual/hard/graph1760.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (16,13) (3,0) (11,1) (3,16) (6,24) (17,19) (12,0) (28,22) (29,27) (23,0) (7,1) (4,18) (4,0) (0,1) (1,18) (31,19) (21,23) (0,20) (29,4) (26,27) (2,13) (32,0) (8,12) (4,17) (16,27) (6,30) (22,27) (20,16) (25,10) (0,2) (14,22) (9,14) (25,32) (5,24) (11,15) (25,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1129", "image": "data/cycle/graph_visual/hard/graph1129.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (6,25) (13,9) (0,1) (20,10) (6,1) (7,23) (5,6) (19,24) (6,16) (19,13) (21,12) (25,22) (0,2) (15,0) (18,9) (15,6) (1,17) (9,11) (4,0) (26,15) (25,14) (0,3) (18,3) (8,23) (18,2) (14,8) (20,14) (12,11) (6,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph276", "image": "data/cycle/graph_visual/hard/graph276.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (20,24) (1,17) (8,6) (25,17) (14,22) (7,15) (2,10) (12,13) (9,18) (10,25) (5,12) (24,27) (7,10) (11,1) (9,7) (2,23) (0,27) (7,16) (9,19) (4,14) (14,15) (26,21) (3,11) (26,9) (9,6) (0,1) (13,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1819", "image": "data/cycle/graph_visual/hard/graph1819.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,31) (27,28) (9,17) (5,15) (13,20) (31,19) (11,6) (4,0) (13,2) (12,14) (0,1) (20,10) (20,21) (32,23) (3,0) (4,19) (8,13) (12,10) (22,29) (7,24) (4,21) (18,9) (25,10) (1,7) (11,10) (33,1) (5,16) (10,16) (3,24) (28,19) (0,18) (4,33) (28,0) (0,2) (31,26) (2,23) (30,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1924", "image": "data/cycle/graph_visual/hard/graph1924.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (24,20) (3,1) (14,4) (6,31) (0,2) (23,27) (2,23) (9,24) (26,16) (33,23) (24,8) (11,31) (14,32) (8,29) (1,0) (10,1) (18,13) (33,10) (25,34) (32,33) (25,21) (27,9) (5,32) (17,24) (23,19) (30,32) (27,11) (22,6) (1,18) (7,20) (9,28) (8,16) (27,15) (12,30) (34,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1440", "image": "data/cycle/graph_visual/hard/graph1440.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (23,2) (9,13) (4,24) (14,0) (19,11) (11,5) (25,18) (18,6) (27,3) (28,21) (26,15) (24,29) (0,19) (20,0) (8,3) (12,11) (11,8) (16,26) (4,26) (7,17) (1,0) (10,9) (0,2) (12,22) (3,10) (16,18) (1,16) (2,13) (7,28) (4,28) (24,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph557", "image": "data/cycle/graph_visual/hard/graph557.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (7,13) (6,24) (25,21) (30,15) (19,8) (17,19) (24,4) (6,20) (14,28) (21,3) (12,8) (10,14) (20,1) (28,23) (13,15) (13,11) (22,19) (13,18) (2,0) (3,15) (27,9) (5,3) (8,29) (30,16) (5,14) (26,5) (1,9) (3,2) (21,29) (5,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph617", "image": "data/cycle/graph_visual/hard/graph617.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (21,11) (22,16) (21,10) (25,8) (28,20) (22,29) (1,27) (18,21) (22,17) (21,28) (31,15) (27,9) (5,11) (29,1) (7,20) (19,4) (30,18) (23,21) (31,20) (20,13) (10,24) (4,25) (13,6) (5,0) (31,2) (0,26) (18,25) (11,3) (8,9) (12,18) (14,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph314", "image": "data/cycle/graph_visual/hard/graph314.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,23) (2,15) (1,11) (9,24) (0,28) (6,13) (7,0) (18,8) (19,9) (14,0) (7,20) (26,10) (15,13) (9,25) (16,21) (22,17) (10,21) (13,27) (21,4) (20,22) (9,5) (3,15) (27,26) (8,7) (14,12) (0,9) (4,23) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph584", "image": "data/cycle/graph_visual/hard/graph584.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (13,18) (13,15) (26,5) (8,12) (17,19) (28,23) (27,9) (21,25) (1,5) (19,8) (7,13) (1,20) (6,24) (2,3) (30,16) (14,5) (28,14) (19,22) (21,3) (15,30) (29,21) (24,4) (9,1) (3,15) (11,13) (8,29) (3,5) (10,14) (0,2) (6,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1165", "image": "data/cycle/graph_visual/hard/graph1165.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,14) (8,20) (17,2) (5,11) (7,6) (20,7) (10,11) (3,11) (0,15) (10,7) (24,26) (15,10) (15,13) (3,0) (25,3) (26,2) (21,22) (17,18) (12,22) (2,0) (2,16) (21,17) (23,4) (2,6) (9,7) (1,8) (4,11) (19,10) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1366", "image": "data/cycle/graph_visual/hard/graph1366.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (5,9) (20,10) (20,27) (0,3) (27,8) (22,18) (25,10) (6,9) (24,5) (28,27) (26,12) (4,0) (17,21) (0,2) (1,16) (23,13) (26,16) (7,12) (17,19) (11,9) (25,4) (1,0) (24,23) (13,2) (0,7) (0,5) (11,14) (3,22) (21,8) (15,22) (8,13) (25,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph659", "image": "data/cycle/graph_visual/hard/graph659.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,23) (18,30) (24,11) (5,7) (20,3) (31,12) (1,17) (22,18) (26,12) (0,9) (5,4) (24,27) (30,16) (28,16) (0,17) (14,13) (21,11) (19,7) (30,4) (11,25) (2,16) (12,5) (8,15) (20,7) (15,9) (1,31) (13,29) (12,14) (12,10) (12,6) (21,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1665", "image": "data/cycle/graph_visual/hard/graph1665.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (1,2) (5,24) (0,3) (23,4) (13,12) (16,21) (20,9) (0,1) (20,29) (0,2) (20,22) (6,13) (0,8) (25,17) (22,21) (11,25) (20,23) (0,30) (3,10) (28,31) (1,10) (14,2) (22,15) (19,26) (15,30) (6,21) (30,26) (20,1) (28,7) (28,27) (18,10) (17,8) (5,16) (3,7) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph274", "image": "data/cycle/graph_visual/hard/graph274.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (19,16) (26,1) (24,3) (23,9) (20,27) (25,6) (25,8) (22,2) (20,6) (10,17) (0,19) (23,18) (6,19) (16,7) (4,17) (18,1) (12,27) (15,0) (14,15) (23,16) (5,17) (20,2) (4,13) (24,8) (4,25) (25,11) (21,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1985", "image": "data/cycle/graph_visual/hard/graph1985.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,31) (27,20) (13,15) (9,19) (24,0) (22,6) (6,32) (22,27) (5,32) (30,12) (13,20) (30,21) (23,8) (1,26) (21,4) (33,28) (1,0) (14,22) (30,13) (2,3) (18,24) (28,30) (8,18) (6,8) (26,34) (16,25) (19,11) (16,2) (29,9) (19,6) (10,25) (16,33) (34,16) (17,32) (31,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1678", "image": "data/cycle/graph_visual/hard/graph1678.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (29,25) (31,8) (1,29) (14,12) (27,5) (9,5) (9,21) (18,13) (12,5) (1,15) (25,13) (2,0) (19,13) (18,8) (4,0) (16,14) (28,25) (1,5) (17,20) (0,30) (6,2) (0,1) (7,10) (12,24) (26,1) (16,2) (11,4) (12,17) (7,25) (26,22) (23,28) (6,11) (3,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1265", "image": "data/cycle/graph_visual/hard/graph1265.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (9,16) (12,17) (5,4) (26,13) (20,25) (11,16) (7,2) (22,25) (7,0) (5,11) (15,27) (0,1) (10,15) (1,19) (3,8) (1,6) (0,14) (20,0) (14,12) (23,13) (14,11) (5,24) (1,17) (26,1) (13,18) (23,8) (2,27) (4,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph246", "image": "data/cycle/graph_visual/hard/graph246.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (20,18) (3,22) (4,8) (22,26) (2,26) (2,23) (8,10) (7,15) (20,23) (16,8) (11,26) (24,12) (14,2) (6,9) (8,11) (9,13) (0,20) (7,5) (17,10) (5,12) (15,1) (19,26) (21,17) (15,26) (6,2) (27,18) (7,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1545", "image": "data/cycle/graph_visual/hard/graph1545.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (26,28) (25,14) (6,28) (17,1) (9,12) (13,22) (20,0) (15,27) (2,12) (29,18) (2,15) (4,10) (18,6) (25,7) (20,23) (0,1) (7,3) (15,24) (12,26) (21,16) (14,12) (12,22) (2,1) (8,30) (14,0) (30,15) (19,4) (16,6) (11,6) (11,5) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph62", "image": "data/cycle/graph_visual/hard/graph62.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (3,4) (21,18) (11,24) (8,16) (14,18) (23,1) (18,15) (20,17) (15,10) (22,5) (24,2) (6,13) (21,7) (4,12) (23,13) (13,14) (9,25) (0,13) (0,5) (6,25) (21,8) (3,2) (10,20) (4,10) (19,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph48", "image": "data/cycle/graph_visual/hard/graph48.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (23,11) (18,13) (19,0) (6,7) (20,5) (17,2) (23,18) (2,24) (7,14) (8,7) (16,7) (4,15) (13,1) (9,3) (0,25) (12,8) (21,3) (19,16) (20,3) (0,1) (17,22) (21,23) (4,23) (10,0) (6,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1563", "image": "data/cycle/graph_visual/hard/graph1563.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (15,10) (11,2) (9,22) (7,20) (14,20) (9,2) (11,6) (2,0) (25,11) (27,18) (0,1) (27,3) (13,17) (29,19) (7,25) (4,17) (10,29) (8,19) (12,13) (27,14) (16,29) (2,5) (16,23) (15,2) (13,30) (19,21) (3,1) (0,28) (26,12) (17,19) (11,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1671", "image": "data/cycle/graph_visual/hard/graph1671.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,14) (3,21) (27,1) (2,0) (21,11) (0,1) (1,28) (22,20) (21,29) (2,29) (27,22) (17,18) (30,6) (4,0) (18,31) (24,11) (24,5) (0,20) (24,14) (12,10) (22,18) (8,4) (4,13) (16,0) (25,19) (30,15) (9,10) (19,13) (0,3) (8,26) (28,14) (11,19) (28,15) (7,1) (9,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1533", "image": "data/cycle/graph_visual/hard/graph1533.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,12) (0,1) (8,11) (9,21) (7,13) (27,23) (2,0) (17,20) (6,21) (4,1) (29,14) (30,19) (14,2) (4,22) (30,15) (8,28) (19,6) (14,26) (16,0) (0,3) (5,28) (26,0) (24,11) (16,10) (18,21) (1,20) (23,4) (28,16) (28,23) (20,6) (18,3) (25,24) (9,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph960", "image": "data/cycle/graph_visual/hard/graph960.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (31,22) (29,25) (10,23) (21,9) (31,34) (13,14) (1,26) (18,5) (14,23) (15,22) (6,22) (8,12) (3,11) (29,20) (32,5) (28,0) (28,4) (27,0) (19,11) (7,34) (30,23) (4,18) (8,21) (17,22) (14,32) (4,2) (33,15) (1,20) (31,23) (1,9) (24,14) (19,24) (17,16) (26,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph190", "image": "data/cycle/graph_visual/hard/graph190.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (17,0) (8,14) (6,5) (22,15) (20,24) (4,18) (26,0) (23,7) (9,21) (8,23) (12,17) (24,21) (12,15) (3,10) (21,6) (22,6) (7,25) (19,12) (13,1) (20,4) (26,23) (11,23) (2,26) (13,16) (9,3) (20,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1986", "image": "data/cycle/graph_visual/hard/graph1986.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (24,27) (2,13) (29,1) (5,20) (24,34) (29,28) (32,2) (7,27) (30,14) (32,8) (18,6) (9,12) (4,34) (4,3) (12,30) (26,1) (0,28) (20,6) (1,0) (31,22) (26,17) (12,8) (17,25) (17,16) (22,23) (31,10) (29,10) (5,16) (21,31) (19,9) (1,19) (31,33) (11,29) (22,15) (19,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph138", "image": "data/cycle/graph_visual/hard/graph138.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (8,4) (25,23) (25,21) (11,8) (4,2) (1,20) (3,22) (9,13) (8,5) (26,23) (16,2) (9,18) (12,2) (14,10) (7,15) (24,20) (9,3) (19,2) (0,10) (23,9) (0,3) (25,8) (13,6) (17,15) (0,15) (19,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1565", "image": "data/cycle/graph_visual/hard/graph1565.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (29,24) (2,20) (7,8) (7,13) (23,16) (17,8) (1,19) (23,9) (14,21) (7,27) (0,3) (30,11) (8,3) (4,22) (28,30) (16,10) (18,9) (14,9) (6,20) (0,1) (5,24) (15,8) (3,29) (19,23) (12,25) (21,2) (26,12) (22,14) (28,27) (21,27) (12,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1996", "image": "data/cycle/graph_visual/hard/graph1996.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (21,27) (0,1) (34,3) (23,18) (15,31) (14,1) (19,5) (7,9) (26,29) (17,24) (19,11) (25,34) (6,11) (27,0) (12,27) (13,22) (28,1) (8,5) (19,30) (2,26) (13,2) (19,20) (4,23) (32,29) (10,29) (0,31) (22,27) (33,22) (23,34) (27,1) (17,7) (2,0) (17,4) (17,30) (8,16) (16,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1745", "image": "data/cycle/graph_visual/hard/graph1745.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,14) (27,5) (0,2) (15,24) (9,6) (32,15) (19,11) (8,24) (15,6) (9,25) (4,25) (0,3) (2,23) (18,19) (31,21) (1,0) (13,26) (14,21) (4,1) (31,22) (28,20) (14,19) (3,30) (17,18) (26,24) (5,21) (26,0) (15,16) (29,21) (1,29) (28,19) (3,12) (7,29) (12,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1614", "image": "data/cycle/graph_visual/hard/graph1614.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (20,23) (28,24) (24,8) (0,1) (28,19) (31,7) (13,7) (3,21) (27,15) (21,6) (16,18) (9,7) (1,8) (0,12) (2,25) (28,27) (16,21) (11,12) (9,22) (29,12) (5,11) (29,4) (9,1) (27,0) (30,2) (7,10) (14,15) (22,30) (10,23) (0,2) (17,30) (3,5) (26,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1615", "image": "data/cycle/graph_visual/hard/graph1615.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,19) (20,13) (5,4) (30,0) (27,26) (5,16) (15,7) (21,14) (22,20) (2,0) (17,2) (12,24) (31,1) (3,0) (9,22) (15,14) (14,20) (25,21) (14,0) (23,22) (30,8) (21,4) (27,17) (27,6) (31,6) (21,10) (1,0) (4,12) (18,9) (29,27) (28,5) (23,3) (21,17) (5,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph413", "image": "data/cycle/graph_visual/hard/graph413.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,27) (6,9) (26,27) (25,12) (18,19) (14,10) (22,7) (26,4) (24,13) (5,3) (7,6) (21,23) (20,11) (7,17) (17,27) (18,21) (12,17) (22,1) (10,3) (21,24) (24,14) (0,6) (19,29) (24,7) (29,16) (19,2) (27,28) (8,28) (11,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1461", "image": "data/cycle/graph_visual/hard/graph1461.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (27,5) (18,15) (22,28) (10,16) (28,14) (8,23) (9,14) (25,5) (3,10) (5,19) (8,6) (6,7) (21,16) (8,28) (0,2) (2,21) (15,13) (20,17) (12,7) (0,5) (20,15) (10,11) (0,1) (26,6) (3,22) (1,3) (25,24) (24,21) (9,15) (4,14) (27,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1310", "image": "data/cycle/graph_visual/hard/graph1310.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,0) (0,4) (2,19) (23,25) (10,8) (22,6) (0,28) (13,10) (0,2) (25,17) (10,5) (5,14) (16,4) (7,27) (14,27) (20,28) (27,21) (3,12) (3,14) (0,1) (11,6) (26,8) (25,16) (16,8) (3,0) (1,27) (15,3) (16,19) (9,18) (9,5) (3,11) (24,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph315", "image": "data/cycle/graph_visual/hard/graph315.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,7) (0,9) (18,8) (13,27) (8,7) (11,1) (10,26) (19,9) (7,20) (2,15) (7,11) (23,4) (4,21) (20,22) (21,10) (17,22) (24,9) (19,23) (13,15) (28,0) (0,14) (9,5) (3,15) (14,12) (25,9) (16,21) (6,13) (26,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph963", "image": "data/cycle/graph_visual/hard/graph963.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (34,17) (24,11) (2,28) (28,14) (19,7) (32,9) (23,0) (16,17) (9,6) (21,29) (8,1) (25,28) (23,17) (0,24) (12,13) (28,33) (19,21) (31,10) (18,30) (8,30) (26,18) (12,3) (14,15) (20,24) (21,33) (31,3) (28,4) (16,6) (17,26) (27,5) (31,34) (2,24) (13,22) (5,34)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph252", "image": "data/cycle/graph_visual/hard/graph252.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (15,3) (16,4) (16,8) (11,3) (8,25) (16,24) (27,0) (13,10) (14,23) (5,10) (1,27) (25,17) (12,3) (8,10) (9,18) (20,27) (7,27) (19,0) (6,11) (6,21) (16,19) (9,5) (2,19) (14,3) (5,14) (26,14) (25,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph565", "image": "data/cycle/graph_visual/hard/graph565.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (16,2) (15,17) (6,13) (0,15) (15,7) (26,23) (9,13) (25,21) (9,18) (0,10) (3,22) (30,3) (27,9) (8,5) (8,25) (8,4) (8,11) (20,27) (2,12) (2,19) (23,28) (1,28) (28,25) (19,29) (14,10) (24,9) (23,30) (3,0) (20,1) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1739", "image": "data/cycle/graph_visual/hard/graph1739.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (18,2) (6,30) (25,26) (31,5) (23,32) (26,3) (19,30) (4,11) (17,21) (30,9) (14,5) (7,27) (27,15) (25,14) (6,16) (23,4) (20,22) (15,0) (24,0) (12,29) (20,17) (6,8) (24,23) (16,32) (9,1) (21,19) (0,1) (27,29) (10,22) (28,9) (13,23) (10,2) (31,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph405", "image": "data/cycle/graph_visual/hard/graph405.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (16,2) (2,20) (22,6) (14,11) (20,12) (7,12) (10,17) (3,18) (9,5) (28,7) (9,22) (29,0) (10,16) (26,4) (19,27) (25,13) (21,22) (26,21) (14,4) (6,19) (1,3) (25,12) (21,23) (29,8) (24,10) (13,21) (4,3) (15,14) (8,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph361", "image": "data/cycle/graph_visual/hard/graph361.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (22,19) (9,3) (7,2) (8,6) (10,23) (28,2) (20,6) (14,12) (13,25) (8,14) (16,4) (9,7) (27,5) (17,21) (14,16) (28,22) (20,24) (28,13) (18,16) (15,19) (0,13) (26,7) (1,9) (11,14) (10,26) (17,14) (27,17) (15,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph806", "image": "data/cycle/graph_visual/hard/graph806.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (12,9) (10,31) (8,12) (1,19) (29,10) (0,28) (32,31) (7,27) (24,27) (22,31) (29,24) (18,6) (22,15) (6,20) (3,19) (9,19) (1,29) (2,32) (30,14) (28,12) (16,5) (17,25) (11,29) (3,4) (1,26) (22,23) (4,33) (8,30) (13,2) (17,26) (20,5) (31,21) (16,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph90", "image": "data/cycle/graph_visual/hard/graph90.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (10,24) (9,10) (25,9) (17,18) (8,21) (10,13) (16,9) (21,0) (4,18) (1,2) (16,5) (3,20) (16,11) (8,3) (19,4) (13,22) (25,1) (23,8) (7,3) (14,16) (6,12) (24,3) (6,15) (12,11) (8,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph178", "image": "data/cycle/graph_visual/hard/graph178.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,6) (8,23) (3,18) (5,6) (15,0) (4,6) (6,1) (16,6) (17,1) (18,2) (14,20) (13,9) (11,9) (20,10) (25,14) (25,22) (23,7) (21,12) (6,25) (13,19) (26,15) (14,8) (24,19) (9,18) (0,3) (11,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1798", "image": "data/cycle/graph_visual/hard/graph1798.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (1,3) (2,1) (31,28) (23,9) (16,20) (14,27) (18,8) (10,2) (1,0) (0,4) (9,17) (2,13) (5,25) (5,20) (25,6) (17,28) (26,29) (4,15) (12,9) (23,24) (3,19) (21,32) (14,21) (30,22) (14,11) (4,29) (25,30) (1,8) (7,27) (4,30) (7,29) (18,21) (9,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1658", "image": "data/cycle/graph_visual/hard/graph1658.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (29,27) (6,7) (10,29) (17,30) (8,5) (0,27) (27,20) (30,19) (19,9) (5,19) (27,11) (29,26) (0,1) (3,11) (31,14) (7,17) (27,1) (19,18) (21,17) (23,15) (2,13) (26,2) (17,4) (2,0) (12,1) (22,28) (22,25) (8,16) (16,10) (0,24) (31,4) (23,1) (13,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph14", "image": "data/cycle/graph_visual/hard/graph14.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (16,22) (2,11) (16,11) (9,2) (13,0) (25,17) (3,1) (1,0) (19,10) (12,23) (7,25) (14,20) (24,11) (15,10) (11,6) (7,20) (4,17) (12,13) (9,21) (15,2) (17,19) (8,19) (5,2) (18,19) (3,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph784", "image": "data/cycle/graph_visual/hard/graph784.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (21,16) (11,8) (11,16) (10,7) (7,3) (28,6) (29,26) (22,13) (19,28) (24,3) (17,14) (3,20) (27,23) (19,32) (14,5) (25,19) (12,11) (5,15) (26,12) (17,3) (20,21) (32,9) (4,1) (20,18) (2,15) (1,27) (30,7) (16,1) (11,22) (8,0) (31,9) (11,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph380", "image": "data/cycle/graph_visual/hard/graph380.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (26,19) (5,2) (28,12) (26,15) (3,21) (27,25) (6,12) (21,14) (5,12) (18,14) (4,21) (8,22) (11,25) (14,20) (13,27) (25,6) (7,8) (2,0) (26,14) (17,23) (15,6) (14,10) (1,18) (19,23) (25,16) (6,7) (9,5) (24,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph869", "image": "data/cycle/graph_visual/hard/graph869.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (6,1) (6,0) (5,4) (26,14) (25,13) (32,2) (12,21) (33,27) (29,32) (27,4) (30,16) (24,16) (24,11) (23,22) (12,15) (25,0) (21,22) (28,15) (20,27) (16,9) (30,22) (2,17) (32,10) (7,29) (15,14) (18,26) (22,3) (19,1) (31,28) (21,8) (33,15) (20,0) (23,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1126", "image": "data/cycle/graph_visual/hard/graph1126.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,21) (4,18) (14,6) (22,3) (22,19) (23,15) (21,11) (24,2) (11,3) (26,23) (14,0) (24,9) (24,8) (21,14) (16,15) (1,7) (2,0) (23,1) (17,21) (1,0) (15,8) (16,12) (20,26) (2,10) (22,10) (3,0) (8,25) (13,5) (21,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1485", "image": "data/cycle/graph_visual/hard/graph1485.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,4) (11,2) (2,0) (12,19) (13,15) (22,18) (0,6) (7,16) (22,11) (15,23) (14,5) (4,21) (8,14) (10,11) (22,28) (7,23) (11,19) (0,24) (26,15) (26,29) (3,6) (4,2) (5,13) (3,23) (25,22) (19,26) (7,17) (27,9) (1,0) (9,5) (20,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1306", "image": "data/cycle/graph_visual/hard/graph1306.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,7) (13,18) (0,10) (6,28) (19,16) (17,6) (11,23) (20,3) (2,24) (7,16) (1,0) (0,19) (1,13) (3,21) (21,23) (2,0) (22,28) (17,23) (20,5) (27,7) (9,3) (26,2) (17,0) (12,8) (2,6) (25,18) (4,15) (14,7) (4,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph647", "image": "data/cycle/graph_visual/hard/graph647.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (25,2) (21,5) (26,12) (9,29) (21,11) (31,19) (3,24) (11,28) (6,11) (23,24) (14,7) (16,15) (4,12) (30,5) (18,5) (20,25) (14,8) (5,8) (13,24) (31,0) (20,30) (13,9) (23,27) (26,13) (29,5) (17,0) (16,24) (15,10) (2,17) (12,22) (1,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph683", "image": "data/cycle/graph_visual/hard/graph683.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (28,26) (0,8) (22,13) (13,31) (17,11) (3,14) (0,13) (16,2) (15,6) (7,16) (10,24) (24,11) (10,3) (15,19) (17,25) (30,18) (9,1) (30,13) (4,8) (26,23) (8,27) (7,23) (6,21) (15,12) (5,22) (24,20) (10,4) (0,15) (29,0) (1,29) (8,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1356", "image": "data/cycle/graph_visual/hard/graph1356.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,24) (8,6) (15,20) (11,8) (4,15) (0,4) (7,16) (0,12) (5,26) (10,7) (23,18) (25,1) (1,0) (23,24) (26,3) (9,22) (9,13) (17,12) (0,2) (21,2) (4,2) (8,3) (3,0) (24,5) (1,7) (9,25) (16,17) (14,3) (11,17) (19,12) (28,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph59", "image": "data/cycle/graph_visual/hard/graph59.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (14,12) (22,13) (21,25) (17,1) (0,20) (16,13) (13,5) (3,8) (7,2) (4,5) (11,14) (17,12) (10,15) (6,1) (18,1) (7,0) (19,4) (1,24) (23,8) (9,16) (25,2) (5,11) (14,0) (20,23) (11,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1970", "image": "data/cycle/graph_visual/hard/graph1970.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,2) (14,34) (29,1) (13,25) (4,0) (34,27) (27,8) (7,25) (11,4) (14,16) (11,6) (7,10) (1,0) (31,25) (5,1) (23,26) (22,9) (12,26) (12,5) (12,17) (8,18) (28,1) (3,0) (3,30) (0,32) (13,18) (29,25) (21,17) (12,33) (5,30) (5,9) (16,2) (20,13) (1,19) (34,15) (24,28) (2,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph370", "image": "data/cycle/graph_visual/hard/graph370.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,26) (3,25) (11,8) (6,2) (13,23) (27,4) (11,22) (12,27) (1,28) (10,14) (5,7) (20,4) (7,28) (0,6) (1,0) (18,25) (24,7) (11,23) (1,15) (3,10) (16,9) (11,7) (5,16) (21,22) (21,19) (8,12) (0,17) (14,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1449", "image": "data/cycle/graph_visual/hard/graph1449.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,1) (0,4) (15,16) (26,16) (14,0) (29,10) (17,25) (24,11) (12,14) (24,25) (27,8) (23,18) (28,25) (19,20) (18,6) (14,9) (13,14) (0,3) (27,22) (27,5) (1,27) (6,5) (9,4) (20,15) (25,19) (14,3) (2,0) (17,7) (28,29) (4,2) (3,5) (17,2) (21,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1457", "image": "data/cycle/graph_visual/hard/graph1457.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,8) (23,13) (14,11) (5,24) (19,17) (2,13) (0,24) (29,3) (16,25) (26,23) (12,7) (27,8) (9,6) (11,9) (26,12) (22,18) (21,17) (5,9) (7,0) (10,25) (8,21) (28,16) (29,27) (25,4) (22,15) (1,0) (22,3) (20,10) (16,1) (27,20) (3,0) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph433", "image": "data/cycle/graph_visual/hard/graph433.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,9) (20,9) (2,17) (14,0) (9,4) (2,14) (29,10) (21,7) (2,24) (11,8) (22,6) (29,5) (6,9) (2,16) (21,27) (12,23) (8,15) (13,21) (15,12) (1,19) (14,3) (7,1) (26,23) (21,18) (27,28) (20,25) (2,26) (27,29) (23,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1187", "image": "data/cycle/graph_visual/hard/graph1187.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,11) (1,8) (9,18) (16,22) (3,0) (0,13) (15,10) (7,16) (0,24) (9,21) (16,6) (0,5) (5,14) (0,4) (26,17) (17,11) (2,15) (24,25) (18,19) (5,20) (15,12) (14,6) (3,4) (0,1) (8,23) (3,14) (18,2) (0,2) (16,12) (13,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph935", "image": "data/cycle/graph_visual/hard/graph935.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (9,32) (5,4) (7,20) (16,2) (22,18) (24,11) (11,26) (17,0) (0,25) (5,7) (21,11) (17,1) (16,31) (18,30) (6,12) (12,34) (20,3) (32,28) (13,30) (5,12) (14,12) (31,1) (15,9) (34,16) (14,13) (29,24) (30,32) (19,7) (33,4) (10,12) (27,12) (8,15) (21,20) (23,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1771", "image": "data/cycle/graph_visual/hard/graph1771.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (6,12) (5,27) (29,31) (3,16) (6,4) (16,4) (14,26) (15,2) (20,26) (1,0) (12,24) (13,23) (17,8) (2,12) (5,32) (1,26) (13,31) (10,1) (0,9) (25,5) (15,13) (21,27) (10,11) (21,28) (28,19) (20,9) (6,5) (18,30) (26,22) (25,30) (20,8) (21,20) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1642", "image": "data/cycle/graph_visual/hard/graph1642.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,22) (12,2) (23,25) (11,1) (23,29) (28,24) (11,31) (16,27) (15,14) (2,17) (20,30) (1,0) (13,9) (4,5) (0,5) (23,5) (10,27) (7,19) (20,11) (8,16) (29,15) (26,20) (25,18) (23,19) (10,11) (27,24) (5,3) (13,10) (14,1) (2,1) (0,2) (10,6) (0,4) (21,28) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1515", "image": "data/cycle/graph_visual/hard/graph1515.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,20) (16,0) (17,2) (2,18) (1,0) (26,15) (4,0) (21,9) (8,17) (16,20) (29,8) (17,11) (13,26) (15,30) (10,25) (22,2) (3,0) (7,8) (12,29) (10,3) (11,28) (13,20) (1,4) (0,2) (25,5) (25,19) (24,0) (27,23) (28,9) (5,7) (14,29) (6,30) (18,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph735", "image": "data/cycle/graph_visual/hard/graph735.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (22,12) (5,23) (17,0) (7,23) (6,17) (20,28) (14,7) (25,32) (24,21) (19,5) (13,22) (0,15) (6,8) (12,30) (29,4) (2,9) (16,31) (18,30) (11,5) (20,27) (16,11) (13,28) (26,27) (18,32) (1,17) (17,26) (19,1) (3,12) (10,20) (9,21) (24,31) (4,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph337", "image": "data/cycle/graph_visual/hard/graph337.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (21,16) (27,17) (28,21) (5,23) (25,28) (5,24) (3,2) (19,0) (18,10) (13,22) (21,10) (9,17) (26,0) (9,11) (0,14) (25,15) (2,20) (18,23) (9,24) (26,12) (20,19) (12,15) (8,4) (6,14) (15,22) (4,27) (7,1) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph5", "image": "data/cycle/graph_visual/hard/graph5.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,11) (17,22) (10,7) (17,14) (1,2) (16,11) (23,22) (9,23) (8,5) (21,19) (0,25) (3,19) (4,12) (19,15) (20,4) (21,18) (0,20) (13,22) (22,24) (22,10) (19,4) (23,6) (11,9) (2,25) (12,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1620", "image": "data/cycle/graph_visual/hard/graph1620.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,30) (2,11) (2,3) (15,5) (4,28) (14,16) (8,29) (7,18) (17,8) (19,2) (3,0) (21,1) (26,9) (11,20) (12,31) (17,9) (4,0) (7,0) (20,16) (4,26) (13,30) (10,26) (1,4) (5,19) (16,31) (0,2) (18,25) (7,19) (27,4) (17,6) (24,0) (9,3) (22,21) (0,1) (27,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph312", "image": "data/cycle/graph_visual/hard/graph312.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (21,4) (13,4) (27,17) (7,18) (9,23) (7,20) (15,5) (24,7) (11,25) (20,23) (21,10) (22,27) (1,8) (27,6) (4,5) (28,4) (27,12) (23,6) (0,9) (14,28) (2,17) (21,19) (25,5) (20,16) (8,21) (0,13) (3,9) (26,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1990", "image": "data/cycle/graph_visual/hard/graph1990.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (9,28) (30,34) (24,17) (23,24) (1,18) (34,13) (12,19) (33,2) (25,16) (16,32) (14,8) (25,31) (29,11) (7,6) (33,21) (11,25) (0,8) (10,7) (4,32) (32,10) (1,8) (1,0) (11,9) (2,0) (23,26) (5,17) (34,3) (20,2) (21,11) (6,12) (27,17) (23,30) (31,15) (22,12) (23,6) (5,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1979", "image": "data/cycle/graph_visual/hard/graph1979.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (2,3) (10,0) (0,2) (1,29) (11,6) (7,28) (23,11) (0,1) (12,2) (3,4) (28,13) (25,27) (28,6) (11,18) (1,15) (19,9) (28,25) (30,10) (4,31) (34,5) (32,21) (33,12) (16,32) (26,2) (14,34) (29,8) (17,12) (9,5) (29,20) (0,33) (12,28) (22,30) (20,28) (24,19) (33,14) (32,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph846", "image": "data/cycle/graph_visual/hard/graph846.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (8,22) (31,23) (0,26) (15,28) (2,16) (20,4) (25,28) (8,7) (33,10) (27,10) (19,14) (27,18) (14,25) (16,21) (33,28) (21,17) (12,24) (29,11) (4,29) (9,28) (8,29) (14,32) (18,1) (14,6) (14,23) (30,7) (16,7) (2,26) (18,3) (12,30) (32,5) (23,22) (33,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph220", "image": "data/cycle/graph_visual/hard/graph220.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (4,16) (10,20) (21,17) (25,22) (21,18) (14,25) (13,0) (23,3) (2,26) (25,26) (26,5) (5,15) (18,12) (7,17) (27,1) (18,2) (11,25) (16,24) (17,9) (6,18) (24,19) (18,3) (15,16) (1,10) (13,8) (25,8) (20,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph528", "image": "data/cycle/graph_visual/hard/graph528.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,21) (16,29) (10,30) (15,11) (28,6) (8,22) (26,7) (22,26) (0,11) (8,2) (13,11) (16,30) (19,1) (27,9) (12,20) (12,3) (30,27) (28,19) (29,25) (30,5) (12,24) (17,4) (24,17) (12,7) (14,13) (0,17) (30,23) (5,7) (1,12) (17,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph144", "image": "data/cycle/graph_visual/hard/graph144.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (7,26) (8,12) (24,2) (17,20) (18,24) (16,26) (6,26) (21,20) (8,14) (0,11) (6,5) (3,11) (25,15) (19,10) (3,13) (9,17) (0,8) (1,4) (24,12) (15,16) (22,17) (22,3) (2,26) (10,23) (22,10) (4,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1680", "image": "data/cycle/graph_visual/hard/graph1680.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,9) (16,5) (10,25) (12,5) (12,24) (15,1) (28,6) (9,15) (4,20) (27,28) (31,9) (17,3) (22,1) (23,8) (1,0) (13,12) (26,24) (29,20) (2,22) (1,6) (23,19) (8,22) (1,18) (14,16) (29,21) (0,7) (27,20) (3,12) (9,12) (9,30) (16,0) (2,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1252", "image": "data/cycle/graph_visual/hard/graph1252.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (17,7) (0,7) (24,4) (20,12) (2,13) (0,19) (3,10) (1,16) (4,23) (16,26) (9,10) (26,4) (9,13) (6,18) (16,18) (21,2) (22,18) (11,5) (19,11) (27,24) (24,0) (25,3) (12,11) (1,0) (15,26) (11,8) (3,8) (0,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph671", "image": "data/cycle/graph_visual/hard/graph671.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,5) (3,28) (4,22) (26,15) (22,7) (21,19) (10,23) (29,10) (4,29) (26,4) (13,18) (14,9) (0,31) (19,13) (9,29) (5,1) (16,2) (17,21) (12,9) (14,27) (8,6) (26,30) (20,3) (25,5) (8,21) (11,4) (20,5) (16,21) (0,8) (17,25) (0,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1991", "image": "data/cycle/graph_visual/hard/graph1991.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (3,0) (9,17) (5,15) (34,32) (20,21) (10,25) (24,3) (33,23) (31,19) (13,20) (9,18) (12,14) (2,0) (19,28) (31,26) (10,12) (28,27) (4,21) (23,2) (20,10) (7,1) (29,31) (6,11) (2,13) (24,7) (16,10) (8,13) (4,34) (0,18) (29,22) (0,28) (0,1) (10,11) (1,33) (5,16) (5,30) (4,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph911", "image": "data/cycle/graph_visual/hard/graph911.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,31) (1,18) (28,30) (29,11) (16,7) (19,14) (26,0) (20,4) (4,29) (34,30) (33,10) (21,17) (27,10) (3,18) (24,12) (33,13) (32,23) (27,18) (2,26) (14,25) (8,29) (14,23) (2,16) (25,28) (22,8) (15,28) (30,12) (16,21) (32,5) (28,9) (8,7) (33,14) (14,6) (23,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1350", "image": "data/cycle/graph_visual/hard/graph1350.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (3,12) (23,4) (11,26) (15,13) (16,9) (10,14) (20,24) (0,3) (0,4) (7,18) (17,20) (2,0) (27,22) (6,26) (8,23) (16,19) (3,25) (27,24) (1,14) (18,19) (8,15) (17,14) (7,13) (22,2) (21,10) (21,23) (0,23) (24,25) (5,11) (17,5) (28,3) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph416", "image": "data/cycle/graph_visual/hard/graph416.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,15) (16,11) (14,6) (11,23) (29,1) (1,24) (4,27) (7,28) (29,25) (2,19) (22,17) (21,0) (13,15) (10,16) (20,14) (8,28) (6,9) (28,23) (29,22) (23,1) (19,23) (16,18) (27,3) (0,27) (4,8) (26,5) (12,22) (23,14) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1152", "image": "data/cycle/graph_visual/hard/graph1152.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (4,0) (16,25) (7,23) (0,1) (0,15) (12,11) (2,10) (19,1) (22,5) (5,4) (25,11) (26,19) (0,2) (20,3) (8,11) (21,19) (18,6) (17,3) (12,3) (26,20) (21,24) (1,18) (12,14) (5,18) (3,0) (4,13) (2,11) (3,15) (9,3) (23,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1752", "image": "data/cycle/graph_visual/hard/graph1752.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,5) (3,0) (16,15) (16,6) (30,20) (22,10) (29,11) (27,5) (31,29) (30,19) (26,10) (4,0) (24,7) (31,6) (20,13) (14,18) (0,1) (0,13) (25,29) (28,12) (15,9) (0,2) (8,23) (1,27) (4,2) (8,18) (32,19) (17,11) (4,23) (26,32) (29,13) (4,21) (8,24) (19,3) (28,7) (1,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph194", "image": "data/cycle/graph_visual/hard/graph194.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (2,5) (16,20) (26,25) (16,22) (3,18) (15,22) (6,2) (17,24) (11,19) (6,4) (9,7) (1,14) (23,13) (26,10) (0,19) (0,12) (9,4) (17,0) (24,25) (7,15) (15,11) (1,23) (21,10) (16,1) (8,22) (10,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1411", "image": "data/cycle/graph_visual/hard/graph1411.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (23,7) (28,12) (17,2) (16,15) (20,9) (26,28) (17,20) (2,19) (11,10) (21,17) (8,5) (15,0) (24,15) (7,13) (1,0) (11,3) (18,10) (26,3) (29,25) (3,0) (2,0) (4,27) (11,4) (27,1) (24,21) (7,6) (10,22) (14,22) (29,2) (2,6) (7,10) (11,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1133", "image": "data/cycle/graph_visual/hard/graph1133.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (16,8) (13,23) (11,17) (7,0) (25,5) (0,1) (2,1) (19,12) (18,4) (9,6) (10,21) (3,24) (19,14) (13,10) (14,5) (8,4) (2,18) (15,22) (0,19) (0,3) (21,22) (20,4) (24,6) (7,4) (26,18) (22,9) (11,2) (2,0) (10,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1689", "image": "data/cycle/graph_visual/hard/graph1689.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,11) (15,10) (21,23) (4,8) (18,13) (2,21) (21,0) (12,17) (8,16) (5,17) (14,13) (3,7) (28,27) (6,24) (29,20) (1,29) (18,6) (23,9) (0,1) (22,5) (30,10) (25,10) (8,7) (14,26) (29,28) (15,3) (26,5) (0,11) (24,2) (17,31) (4,24) (10,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1014", "image": "data/cycle/graph_visual/hard/graph1014.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (1,0) (22,0) (25,13) (14,1) (7,2) (8,12) (20,23) (23,13) (18,15) (17,18) (4,16) (24,9) (0,2) (8,15) (19,24) (4,21) (11,10) (18,5) (3,25) (8,0) (11,21) (23,6) (15,25) (24,10) (24,6) (2,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph74", "image": "data/cycle/graph_visual/hard/graph74.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (19,21) (18,21) (22,10) (7,10) (8,5) (11,16) (0,20) (9,11) (23,22) (13,22) (24,22) (12,4) (5,11) (25,0) (23,6) (4,19) (9,23) (17,22) (25,2) (3,19) (2,1) (19,15) (14,17) (7,12) (4,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph285", "image": "data/cycle/graph_visual/hard/graph285.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,9) (17,16) (3,21) (2,19) (19,25) (21,14) (13,23) (2,5) (10,26) (20,1) (23,12) (25,16) (21,6) (13,14) (19,26) (24,3) (25,9) (20,11) (18,1) (23,8) (22,16) (19,4) (11,14) (27,14) (7,26) (20,15) (0,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1270", "image": "data/cycle/graph_visual/hard/graph1270.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (4,7) (9,0) (22,13) (25,2) (16,3) (7,8) (10,26) (18,27) (5,14) (3,23) (0,2) (24,20) (0,1) (1,8) (23,21) (17,5) (15,22) (6,4) (10,19) (13,23) (5,19) (21,17) (19,0) (12,14) (11,20) (25,11) (7,2) (18,1) (22,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph146", "image": "data/cycle/graph_visual/hard/graph146.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (5,26) (12,10) (9,25) (11,0) (21,2) (22,5) (3,0) (7,6) (26,3) (20,11) (8,19) (22,23) (1,6) (25,18) (12,7) (20,17) (13,0) (11,2) (8,21) (16,0) (14,6) (15,18) (12,23) (4,8) (21,9) (0,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1834", "image": "data/cycle/graph_visual/hard/graph1834.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,15) (9,18) (6,31) (2,0) (9,11) (26,0) (21,8) (14,3) (10,5) (20,5) (21,32) (29,31) (17,23) (3,31) (18,17) (22,23) (33,16) (15,20) (30,33) (8,7) (12,27) (3,1) (1,0) (23,27) (2,21) (19,6) (21,28) (4,10) (13,16) (24,0) (0,6) (1,23) (30,4) (25,32) (21,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph387", "image": "data/cycle/graph_visual/hard/graph387.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,0) (1,22) (12,6) (3,6) (14,21) (18,24) (11,7) (15,12) (4,16) (5,13) (16,25) (2,24) (17,10) (23,5) (20,13) (11,10) (22,0) (8,4) (1,19) (2,8) (27,28) (26,3) (28,21) (10,9) (10,26) (0,25) (8,11) (10,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1875", "image": "data/cycle/graph_visual/hard/graph1875.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (7,23) (5,18) (33,31) (21,8) (1,9) (2,0) (19,9) (17,16) (21,14) (5,32) (15,32) (20,28) (8,11) (1,0) (12,14) (20,1) (29,23) (10,19) (27,4) (4,18) (31,22) (15,22) (2,4) (26,1) (17,22) (4,0) (26,16) (24,29) (25,0) (14,23) (28,0) (30,14) (6,22) (13,24) (3,11) (31,23) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph596", "image": "data/cycle/graph_visual/hard/graph596.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,18) (2,20) (17,5) (4,14) (29,12) (1,18) (2,26) (1,28) (23,16) (25,6) (11,25) (15,21) (16,7) (19,16) (30,17) (10,17) (0,19) (24,0) (25,4) (27,8) (29,20) (9,23) (27,13) (24,3) (6,20) (15,0) (25,8) (19,6) (4,22) (30,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph191", "image": "data/cycle/graph_visual/hard/graph191.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (6,24) (4,9) (4,19) (21,10) (1,11) (5,3) (23,22) (24,1) (17,3) (17,7) (17,23) (1,21) (7,4) (0,2) (0,15) (16,22) (8,12) (14,26) (7,15) (12,4) (25,21) (14,23) (1,4) (20,4) (24,18) (13,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph105", "image": "data/cycle/graph_visual/hard/graph105.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (22,11) (7,13) (20,17) (26,6) (10,14) (25,24) (25,26) (16,9) (20,24) (19,3) (15,8) (1,14) (13,15) (22,2) (18,7) (11,5) (17,5) (17,14) (23,0) (23,8) (4,23) (10,21) (19,21) (12,3) (23,24) (16,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph862", "image": "data/cycle/graph_visual/hard/graph862.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (20,22) (24,12) (21,14) (1,31) (27,31) (4,25) (21,17) (27,17) (26,21) (3,23) (12,6) (12,28) (5,16) (14,0) (32,0) (4,5) (23,22) (15,14) (30,8) (33,28) (6,27) (9,18) (9,22) (30,5) (20,13) (15,7) (17,2) (6,19) (14,20) (21,4) (5,11) (27,29) (21,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1300", "image": "data/cycle/graph_visual/hard/graph1300.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (11,15) (28,8) (4,9) (1,13) (18,28) (13,10) (26,6) (4,24) (18,11) (5,24) (4,16) (12,20) (2,12) (3,24) (9,27) (15,17) (28,7) (23,15) (16,14) (12,25) (8,1) (1,0) (27,0) (16,6) (19,25) (3,19) (22,9) (8,25) (0,2) (26,21) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph760", "image": "data/cycle/graph_visual/hard/graph760.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,7) (2,15) (19,32) (27,23) (1,4) (26,12) (11,12) (7,3) (19,28) (0,8) (8,11) (3,24) (11,22) (25,19) (20,18) (13,22) (15,5) (1,16) (9,32) (14,5) (31,9) (6,28) (26,29) (25,11) (27,1) (20,21) (17,3) (10,7) (16,21) (11,16) (17,14) (20,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph942", "image": "data/cycle/graph_visual/hard/graph942.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (33,0) (15,1) (8,19) (8,34) (25,1) (8,18) (6,27) (34,2) (7,17) (20,5) (31,7) (15,23) (17,6) (14,3) (12,13) (9,18) (19,31) (4,32) (3,25) (4,26) (27,33) (25,4) (11,1) (22,34) (13,16) (17,15) (21,0) (29,5) (16,24) (10,28) (22,30) (24,1) (25,29) (10,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph95", "image": "data/cycle/graph_visual/hard/graph95.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,24) (18,21) (1,16) (9,13) (4,23) (15,7) (2,20) (11,19) (18,16) (3,10) (25,24) (8,11) (3,22) (12,11) (24,4) (17,12) (11,5) (0,14) (18,6) (3,8) (0,19) (9,10) (16,4) (7,0) (2,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph311", "image": "data/cycle/graph_visual/hard/graph311.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (22,17) (7,4) (14,9) (13,28) (10,26) (7,26) (3,20) (15,16) (24,28) (16,19) (21,20) (14,15) (5,1) (8,11) (2,28) (16,27) (28,18) (18,0) (9,21) (25,19) (20,5) (5,23) (16,17) (6,26) (8,15) (21,10) (12,20) (20,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph462", "image": "data/cycle/graph_visual/hard/graph462.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,23) (22,28) (5,9) (17,7) (26,29) (20,15) (21,4) (11,2) (8,14) (13,15) (3,23) (12,19) (6,3) (9,27) (1,4) (24,0) (26,15) (6,0) (14,5) (23,15) (2,4) (19,26) (5,13) (19,11) (11,22) (10,11) (22,18) (16,7) (25,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1646", "image": "data/cycle/graph_visual/hard/graph1646.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (16,27) (17,24) (25,29) (16,3) (29,1) (13,25) (0,3) (23,22) (21,28) (13,19) (13,3) (27,15) (29,5) (21,14) (1,0) (7,5) (0,9) (2,29) (9,12) (26,13) (19,14) (31,10) (10,24) (22,8) (4,11) (0,2) (11,30) (7,20) (25,6) (29,17) (26,23) (11,9) (12,22) (18,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1841", "image": "data/cycle/graph_visual/hard/graph1841.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,0) (3,0) (2,32) (21,31) (20,6) (22,31) (9,12) (14,30) (3,19) (32,31) (30,8) (9,19) (20,5) (25,17) (33,4) (12,8) (11,29) (4,3) (15,22) (31,10) (1,29) (27,24) (24,29) (12,28) (17,26) (1,26) (18,6) (16,17) (1,19) (29,10) (0,1) (27,7) (0,4) (28,0) (22,23) (5,16) (13,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph907", "image": "data/cycle/graph_visual/hard/graph907.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (14,16) (31,25) (28,1) (7,10) (13,25) (26,12) (12,33) (29,25) (1,5) (34,15) (8,18) (4,11) (34,14) (4,0) (19,1) (25,7) (17,12) (23,26) (1,29) (16,2) (30,3) (11,6) (5,9) (6,2) (12,5) (34,27) (20,13) (8,27) (28,24) (21,17) (18,13) (32,0) (30,5) (22,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph75", "image": "data/cycle/graph_visual/hard/graph75.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (3,22) (0,3) (16,14) (13,20) (17,6) (0,8) (21,0) (23,15) (12,19) (13,21) (2,13) (16,12) (17,25) (17,23) (12,18) (24,15) (25,8) (5,2) (8,10) (19,1) (11,10) (1,25) (11,4) (7,14) (18,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1685", "image": "data/cycle/graph_visual/hard/graph1685.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,16) (2,4) (0,3) (31,6) (1,23) (28,12) (23,8) (1,26) (29,13) (0,2) (0,1) (4,23) (24,7) (20,13) (11,17) (19,3) (15,9) (28,29) (8,24) (27,5) (19,30) (27,7) (18,8) (6,16) (18,14) (30,20) (11,29) (25,29) (31,19) (13,0) (10,26) (21,4) (10,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph542", "image": "data/cycle/graph_visual/hard/graph542.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,16) (30,15) (26,14) (6,20) (1,12) (28,5) (4,1) (27,23) (4,23) (1,20) (24,11) (25,24) (28,8) (2,14) (9,21) (6,21) (9,7) (19,30) (16,10) (11,8) (20,17) (28,23) (0,16) (19,6) (13,7) (22,4) (14,29) (26,0) (18,21) (3,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1647", "image": "data/cycle/graph_visual/hard/graph1647.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,24) (8,7) (23,9) (4,8) (10,27) (21,0) (4,24) (29,28) (18,13) (1,0) (15,10) (14,13) (0,11) (23,21) (17,12) (7,3) (2,0) (19,11) (31,17) (21,2) (27,28) (5,26) (29,1) (26,14) (16,8) (10,25) (18,6) (17,5) (29,20) (30,10) (5,22) (15,3) (24,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1065", "image": "data/cycle/graph_visual/hard/graph1065.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (24,19) (12,7) (12,22) (0,4) (12,3) (9,13) (10,11) (11,20) (0,3) (2,8) (25,4) (24,17) (19,1) (1,0) (17,6) (11,13) (0,5) (17,14) (16,18) (2,0) (23,7) (1,12) (21,17) (0,11) (16,5) (8,22) (18,0) (5,7) (12,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph887", "image": "data/cycle/graph_visual/hard/graph887.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (9,30) (2,9) (16,33) (23,19) (25,21) (18,32) (3,2) (29,23) (22,16) (15,0) (33,27) (33,31) (0,6) (7,33) (8,30) (21,14) (13,29) (2,31) (2,29) (12,27) (20,9) (2,26) (12,15) (5,0) (20,10) (14,8) (18,1) (17,31) (25,24) (18,6) (28,32) (31,4) (12,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1581", "image": "data/cycle/graph_visual/hard/graph1581.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (5,14) (4,13) (24,14) (3,22) (20,10) (30,7) (2,0) (13,14) (0,18) (27,3) (11,20) (12,1) (21,10) (25,4) (28,8) (9,5) (23,21) (30,4) (15,16) (5,19) (10,6) (10,29) (2,6) (7,26) (19,28) (16,24) (17,22) (21,13) (12,0) (22,4) (0,1) (27,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph560", "image": "data/cycle/graph_visual/hard/graph560.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,29) (14,11) (19,6) (30,12) (19,27) (12,25) (13,25) (4,26) (10,16) (22,9) (28,7) (12,8) (3,4) (21,26) (8,24) (21,23) (16,2) (14,15) (1,3) (4,14) (20,29) (22,21) (7,12) (3,18) (20,2) (22,6) (5,9) (24,10) (17,10) (13,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1225", "image": "data/cycle/graph_visual/hard/graph1225.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,1) (17,25) (25,27) (22,27) (20,7) (7,1) (1,12) (23,2) (25,13) (27,21) (18,15) (9,3) (4,11) (2,21) (25,20) (13,0) (24,5) (15,14) (9,18) (9,6) (4,5) (26,0) (12,4) (1,0) (8,7) (10,14) (19,25) (16,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1812", "image": "data/cycle/graph_visual/hard/graph1812.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (4,16) (21,27) (1,10) (31,25) (5,6) (14,26) (5,27) (7,6) (23,13) (26,1) (30,31) (2,15) (20,8) (24,12) (33,5) (15,13) (20,21) (0,2) (30,18) (21,28) (2,12) (10,11) (0,3) (4,0) (33,29) (0,1) (16,3) (20,9) (32,13) (5,25) (26,22) (26,20) (0,9) (6,4) (12,6) (19,28) (17,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph137", "image": "data/cycle/graph_visual/hard/graph137.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (20,23) (20,7) (5,12) (5,4) (0,9) (9,23) (20,14) (17,2) (15,7) (3,9) (22,5) (17,6) (16,21) (25,11) (13,0) (1,8) (8,21) (21,25) (2,24) (4,26) (13,4) (23,6) (7,19) (18,4) (21,10) (21,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1908", "image": "data/cycle/graph_visual/hard/graph1908.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,2) (0,1) (33,5) (22,23) (9,11) (7,24) (2,0) (13,21) (28,18) (32,4) (31,21) (29,18) (23,25) (10,19) (5,12) (18,34) (27,10) (9,16) (5,18) (22,1) (26,14) (0,31) (10,3) (13,25) (4,3) (6,5) (15,22) (4,30) (0,3) (7,4) (14,30) (13,30) (10,6) (2,20) (11,25) (8,7) (7,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph526", "image": "data/cycle/graph_visual/hard/graph526.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (27,0) (12,16) (9,13) (9,18) (29,7) (17,9) (18,26) (2,3) (28,20) (2,22) (30,10) (15,30) (15,22) (0,28) (23,6) (11,4) (21,26) (25,0) (19,7) (2,24) (8,6) (28,14) (12,13) (8,14) (24,5) (3,0) (29,1) (23,4) (16,11) (14,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1774", "image": "data/cycle/graph_visual/hard/graph1774.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (2,0) (12,29) (20,23) (19,27) (30,32) (23,13) (6,14) (31,28) (31,17) (32,4) (3,6) (17,11) (32,10) (32,1) (31,16) (10,6) (27,21) (5,9) (24,4) (11,24) (15,29) (11,23) (27,9) (7,24) (1,0) (8,29) (25,3) (9,6) (2,18) (26,7) (22,25) (8,24) (1,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1506", "image": "data/cycle/graph_visual/hard/graph1506.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,28) (27,19) (25,23) (15,10) (0,24) (13,9) (28,20) (26,18) (3,20) (16,29) (12,22) (6,19) (0,2) (0,27) (5,26) (9,15) (20,13) (8,0) (3,12) (17,10) (29,12) (12,11) (3,0) (14,7) (5,16) (11,19) (28,21) (0,1) (11,1) (0,4) (2,1) (18,4) (7,16) (30,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph776", "image": "data/cycle/graph_visual/hard/graph776.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (27,30) (16,14) (8,30) (7,22) (27,4) (14,13) (21,4) (7,26) (20,0) (29,14) (11,29) (2,6) (7,19) (14,31) (28,14) (27,18) (12,22) (15,24) (30,23) (9,24) (22,10) (26,8) (1,12) (14,6) (14,32) (32,9) (17,29) (25,28) (24,0) (20,3) (10,0) (12,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph864", "image": "data/cycle/graph_visual/hard/graph864.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (22,32) (1,24) (23,4) (2,13) (1,27) (27,11) (29,26) (7,17) (17,4) (8,16) (7,6) (10,16) (1,12) (2,26) (17,30) (25,0) (23,15) (27,0) (17,21) (27,23) (27,33) (31,14) (27,20) (19,18) (28,22) (31,29) (5,8) (11,3) (10,29) (13,22) (9,19) (19,30) (5,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph570", "image": "data/cycle/graph_visual/hard/graph570.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,21) (24,25) (25,30) (4,18) (9,16) (6,26) (3,11) (24,29) (0,24) (5,26) (25,2) (1,13) (9,23) (23,15) (17,2) (12,6) (26,18) (10,13) (15,14) (17,21) (11,0) (11,8) (22,24) (27,22) (7,1) (20,1) (1,12) (28,11) (15,29) (20,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1664", "image": "data/cycle/graph_visual/hard/graph1664.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (3,23) (26,1) (27,15) (8,4) (18,4) (20,16) (19,5) (28,30) (10,14) (24,25) (9,24) (21,19) (6,12) (7,26) (4,13) (11,15) (17,23) (29,6) (3,8) (14,6) (11,28) (3,0) (16,13) (1,0) (22,13) (13,31) (21,1) (11,24) (24,8) (1,9) (0,2) (30,0) (12,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph831", "image": "data/cycle/graph_visual/hard/graph831.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (20,27) (27,31) (8,16) (26,28) (31,14) (23,32) (16,2) (17,0) (4,21) (16,22) (8,29) (18,3) (6,11) (5,16) (4,13) (14,30) (15,14) (11,8) (18,13) (9,17) (14,10) (27,1) (23,27) (7,22) (27,28) (12,9) (7,20) (1,18) (5,9) (25,0) (8,24) (22,33) (11,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph171", "image": "data/cycle/graph_visual/hard/graph171.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (17,2) (15,16) (25,19) (26,20) (18,12) (6,13) (22,25) (25,17) (24,5) (1,17) (8,14) (11,16) (3,14) (14,10) (7,24) (4,9) (15,20) (22,20) (3,5) (6,5) (0,14) (2,4) (25,18) (19,23) (14,9) (16,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1352", "image": "data/cycle/graph_visual/hard/graph1352.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,11) (21,28) (11,10) (13,5) (1,0) (21,14) (27,28) (25,16) (3,26) (20,10) (2,8) (0,2) (3,0) (27,0) (18,24) (11,8) (12,6) (10,9) (0,25) (24,2) (0,22) (16,4) (3,6) (26,10) (1,22) (17,10) (13,20) (4,8) (1,19) (23,5) (15,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph515", "image": "data/cycle/graph_visual/hard/graph515.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (4,29) (1,12) (10,29) (7,3) (26,21) (4,28) (9,19) (7,21) (24,27) (28,15) (18,0) (14,0) (13,18) (5,6) (22,16) (10,2) (23,4) (17,8) (0,26) (8,12) (17,9) (24,7) (12,27) (20,23) (11,12) (25,18) (30,23) (30,14) (5,28) (22,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph552", "image": "data/cycle/graph_visual/hard/graph552.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (27,9) (23,17) (7,2) (17,14) (26,20) (1,22) (10,26) (14,16) (9,4) (28,17) (6,8) (5,16) (14,12) (24,29) (14,8) (11,7) (0,13) (13,28) (14,18) (15,20) (16,21) (28,2) (19,15) (9,3) (10,25) (19,22) (6,20) (29,7) (13,27) (1,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1339", "image": "data/cycle/graph_visual/hard/graph1339.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (9,5) (25,10) (26,16) (8,13) (27,8) (3,0) (14,11) (23,13) (27,20) (6,9) (21,17) (23,24) (13,2) (12,26) (22,18) (11,9) (19,17) (1,16) (8,21) (25,4) (2,0) (16,25) (0,1) (3,22) (15,22) (24,5) (7,12) (20,10) (0,7) (28,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph984", "image": "data/cycle/graph_visual/hard/graph984.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (1,31) (24,29) (18,22) (9,15) (11,26) (20,21) (0,25) (5,12) (20,7) (5,4) (5,7) (12,6) (7,19) (20,3) (8,15) (34,12) (12,14) (10,12) (16,34) (17,1) (13,30) (9,32) (31,16) (28,32) (11,24) (18,30) (11,21) (32,30) (17,0) (4,33) (13,14) (27,12) (16,2) (23,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1181", "image": "data/cycle/graph_visual/hard/graph1181.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,6) (15,25) (19,2) (18,26) (12,1) (0,12) (3,6) (0,2) (4,7) (17,22) (7,11) (19,23) (20,8) (21,22) (19,18) (16,12) (12,24) (0,1) (23,8) (4,24) (0,3) (13,23) (9,19) (7,5) (10,5) (15,6) (21,16) (14,2) (17,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1468", "image": "data/cycle/graph_visual/hard/graph1468.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (20,16) (0,1) (24,27) (26,1) (4,5) (22,17) (2,16) (7,26) (0,4) (29,12) (0,3) (23,22) (0,2) (17,13) (25,12) (29,19) (23,14) (3,17) (27,14) (5,7) (17,26) (12,11) (16,17) (11,21) (8,28) (10,20) (21,18) (0,7) (7,9) (18,10) (12,8) (8,15) (26,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1806", "image": "data/cycle/graph_visual/hard/graph1806.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (21,27) (6,5) (16,8) (10,0) (17,28) (33,24) (6,21) (23,13) (0,31) (10,27) (1,4) (0,2) (18,5) (13,9) (1,0) (17,9) (14,15) (11,15) (2,1) (25,14) (12,1) (26,14) (2,20) (13,21) (6,8) (30,1) (12,26) (19,27) (22,5) (32,17) (3,7) (7,17) (0,3) (32,29) (24,5) (14,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph152", "image": "data/cycle/graph_visual/hard/graph152.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,26) (26,9) (25,10) (4,23) (4,21) (16,22) (13,15) (22,9) (3,15) (11,7) (12,14) (15,2) (23,19) (0,9) (11,1) (8,17) (14,0) (20,18) (21,13) (7,0) (6,13) (8,7) (5,9) (9,19) (20,7) (21,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph774", "image": "data/cycle/graph_visual/hard/graph774.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (12,1) (2,1) (20,2) (14,24) (26,14) (9,13) (10,0) (12,26) (11,15) (17,9) (13,21) (31,17) (22,5) (5,6) (28,17) (3,7) (5,32) (19,27) (7,17) (6,21) (1,29) (6,8) (8,16) (15,14) (5,18) (27,10) (25,32) (27,21) (1,4) (28,14) (13,23) (0,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph559", "image": "data/cycle/graph_visual/hard/graph559.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (5,4) (1,23) (12,5) (4,8) (11,27) (2,24) (11,7) (23,30) (10,17) (14,30) (16,18) (10,2) (6,19) (0,10) (29,17) (14,28) (5,22) (19,22) (22,30) (13,21) (9,8) (1,26) (15,0) (14,3) (27,12) (29,23) (21,19) (14,16) (20,28) (25,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1484", "image": "data/cycle/graph_visual/hard/graph1484.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,28) (19,11) (15,3) (3,29) (9,1) (2,27) (10,2) (3,0) (18,3) (0,10) (2,7) (17,13) (13,1) (23,2) (6,1) (16,6) (1,26) (20,1) (12,4) (26,12) (0,1) (13,25) (13,24) (16,22) (8,20) (17,14) (2,0) (4,5) (29,21) (26,18) (17,2) (18,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1668", "image": "data/cycle/graph_visual/hard/graph1668.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,20) (23,1) (31,6) (23,8) (1,0) (28,29) (4,0) (8,24) (0,2) (10,26) (27,5) (0,13) (23,4) (13,29) (21,4) (6,16) (20,13) (7,24) (2,4) (18,14) (22,10) (27,7) (28,12) (15,16) (11,17) (9,15) (31,19) (0,3) (3,19) (25,29) (19,30) (1,26) (8,18) (29,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph912", "image": "data/cycle/graph_visual/hard/graph912.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (16,26) (12,17) (21,5) (34,22) (31,4) (28,16) (12,34) (20,13) (25,12) (19,26) (5,3) (31,15) (23,5) (21,27) (0,9) (30,5) (2,6) (17,1) (23,11) (16,29) (23,26) (6,18) (8,2) (20,34) (27,31) (30,9) (28,6) (32,12) (2,12) (0,10) (16,7) (1,14) (24,6) (33,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1451", "image": "data/cycle/graph_visual/hard/graph1451.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (22,13) (27,22) (0,1) (23,13) (21,19) (0,23) (10,13) (1,14) (21,26) (29,25) (6,25) (12,17) (7,28) (3,6) (15,24) (13,20) (18,24) (8,21) (15,1) (27,6) (6,9) (4,24) (7,23) (29,2) (5,16) (19,11) (5,20) (16,19) (23,1) (4,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1914", "image": "data/cycle/graph_visual/hard/graph1914.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,21) (3,0) (6,17) (2,0) (23,0) (12,3) (22,12) (4,0) (16,33) (26,17) (7,23) (19,1) (34,18) (19,5) (13,22) (24,5) (0,17) (20,28) (14,34) (12,30) (32,31) (1,0) (18,30) (11,5) (17,1) (26,27) (20,15) (6,9) (20,27) (13,28) (12,4) (34,8) (4,32) (10,21) (29,31) (24,25) (11,16) (9,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph301", "image": "data/cycle/graph_visual/hard/graph301.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (15,18) (15,11) (19,21) (2,5) (24,13) (17,0) (13,23) (5,8) (9,20) (14,11) (25,28) (25,11) (0,23) (17,1) (4,3) (6,9) (16,21) (19,26) (13,9) (7,13) (8,17) (26,3) (11,13) (0,26) (10,27) (14,27) (8,22) (12,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1790", "image": "data/cycle/graph_visual/hard/graph1790.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (22,12) (26,12) (20,30) (0,27) (11,21) (14,8) (26,13) (28,23) (23,24) (14,7) (1,25) (5,8) (4,12) (3,24) (29,9) (2,25) (9,13) (15,10) (19,31) (0,1) (5,30) (29,11) (13,24) (32,27) (16,24) (20,25) (17,2) (2,0) (6,11) (18,5) (5,21) (16,15) (5,31) (17,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1061", "image": "data/cycle/graph_visual/hard/graph1061.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (17,5) (1,0) (9,0) (23,3) (21,23) (24,2) (16,3) (8,7) (11,25) (22,13) (14,5) (7,4) (23,13) (19,0) (2,7) (8,1) (20,11) (10,1) (12,14) (21,17) (22,25) (15,22) (19,5) (19,10) (6,4) (20,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph508", "image": "data/cycle/graph_visual/hard/graph508.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,2) (6,15) (29,14) (24,0) (0,30) (25,4) (28,14) (5,21) (23,20) (18,10) (23,27) (3,0) (6,12) (9,23) (5,13) (22,9) (1,22) (29,25) (4,19) (2,22) (24,18) (8,26) (7,12) (5,11) (24,26) (16,21) (3,20) (5,6) (14,27) (22,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph516", "image": "data/cycle/graph_visual/hard/graph516.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (27,14) (6,15) (25,29) (22,9) (21,5) (21,16) (26,8) (18,10) (6,5) (24,18) (27,23) (24,0) (6,12) (12,7) (22,1) (20,23) (17,2) (28,14) (0,3) (11,5) (29,14) (2,22) (20,3) (5,13) (26,24) (22,21) (4,19) (25,4) (9,23) (0,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1593", "image": "data/cycle/graph_visual/hard/graph1593.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,29) (14,6) (4,20) (2,4) (22,29) (24,26) (15,1) (2,27) (16,8) (23,30) (22,8) (18,25) (25,21) (6,23) (3,5) (19,7) (14,13) (1,0) (17,10) (24,25) (11,29) (20,3) (0,4) (12,21) (22,26) (24,20) (15,0) (12,9) (3,0) (20,19) (0,2) (6,28) (27,13) (6,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1645", "image": "data/cycle/graph_visual/hard/graph1645.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,1) (31,18) (7,23) (17,6) (27,20) (9,2) (4,25) (26,27) (7,14) (0,2) (5,19) (20,28) (1,0) (18,30) (5,23) (15,0) (12,22) (20,10) (29,16) (4,12) (24,21) (30,12) (3,12) (24,31) (26,17) (11,16) (22,13) (13,28) (1,17) (8,6) (3,0) (4,0) (0,17) (11,5) (21,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph245", "image": "data/cycle/graph_visual/hard/graph245.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (9,6) (2,15) (22,20) (19,1) (20,9) (2,18) (9,4) (6,17) (21,27) (0,14) (9,26) (3,14) (24,23) (15,8) (2,26) (2,14) (10,21) (11,2) (12,13) (21,16) (7,21) (8,5) (19,23) (25,27) (26,27) (7,1) (12,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph722", "image": "data/cycle/graph_visual/hard/graph722.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (24,10) (28,21) (0,26) (1,14) (8,25) (12,18) (23,21) (31,18) (0,32) (31,2) (21,18) (32,20) (18,25) (20,7) (9,27) (22,29) (4,25) (1,30) (8,9) (19,4) (21,10) (29,5) (11,5) (20,28) (22,17) (16,22) (11,21) (11,3) (13,6) (20,13) (27,1) (31,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph188", "image": "data/cycle/graph_visual/hard/graph188.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (3,0) (17,15) (7,15) (25,8) (23,25) (10,0) (21,25) (19,1) (9,13) (5,8) (20,1) (14,10) (4,8) (15,0) (23,26) (3,22) (9,23) (16,2) (2,12) (6,13) (4,2) (24,20) (9,3) (2,19) (11,8) (9,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1293", "image": "data/cycle/graph_visual/hard/graph1293.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (19,18) (4,3) (17,11) (12,15) (13,0) (6,16) (16,7) (15,10) (16,12) (23,8) (0,26) (14,3) (5,14) (15,2) (27,24) (11,13) (2,0) (6,14) (1,0) (1,8) (24,25) (2,18) (17,27) (9,18) (3,0) (16,22) (8,13) (5,20) (9,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph712", "image": "data/cycle/graph_visual/hard/graph712.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (19,28) (2,27) (23,18) (11,28) (0,29) (20,9) (5,26) (32,7) (21,4) (32,14) (18,22) (23,4) (14,4) (13,2) (13,32) (23,10) (16,24) (28,26) (27,17) (27,24) (9,3) (6,29) (12,6) (8,2) (31,23) (25,23) (5,3) (1,5) (32,0) (0,30) (18,15) (26,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph386", "image": "data/cycle/graph_visual/hard/graph386.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,13) (26,0) (8,5) (11,14) (17,0) (25,28) (11,13) (20,9) (11,25) (4,3) (1,17) (27,14) (2,5) (22,8) (23,13) (3,26) (16,21) (0,12) (10,27) (13,9) (21,19) (24,13) (15,18) (11,15) (19,26) (6,9) (0,23) (17,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1937", "image": "data/cycle/graph_visual/hard/graph1937.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (32,10) (29,19) (28,0) (19,15) (0,1) (29,5) (28,26) (33,23) (0,30) (0,3) (11,7) (0,33) (2,13) (15,25) (6,7) (12,17) (25,33) (1,4) (31,25) (28,14) (8,26) (2,10) (2,18) (0,2) (24,18) (7,3) (14,34) (17,13) (22,11) (17,21) (6,31) (20,31) (16,27) (9,10) (27,11) (4,26) (9,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph810", "image": "data/cycle/graph_visual/hard/graph810.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (12,8) (20,26) (17,32) (14,28) (21,13) (0,33) (3,8) (23,10) (26,6) (7,2) (32,11) (26,19) (1,27) (7,14) (8,28) (15,4) (8,10) (25,12) (8,16) (13,22) (9,25) (1,26) (12,0) (29,18) (11,30) (14,17) (11,5) (12,24) (13,9) (29,15) (4,6) (31,33) (20,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph400", "image": "data/cycle/graph_visual/hard/graph400.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,13) (17,9) (0,18) (9,19) (10,29) (3,7) (4,28) (0,26) (27,24) (29,23) (2,10) (21,7) (17,8) (7,24) (5,6) (12,1) (24,22) (0,14) (28,15) (12,27) (28,5) (20,23) (4,23) (21,26) (22,16) (8,12) (11,12) (18,25) (4,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1431", "image": "data/cycle/graph_visual/hard/graph1431.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (21,28) (21,8) (22,3) (28,12) (0,5) (0,3) (0,13) (23,6) (15,10) (28,1) (20,27) (28,13) (27,23) (4,16) (14,28) (13,2) (24,11) (18,15) (9,25) (28,26) (8,17) (7,21) (5,27) (0,2) (10,4) (24,10) (1,0) (3,4) (18,29) (20,19) (2,3) (18,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph173", "image": "data/cycle/graph_visual/hard/graph173.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (4,14) (4,7) (26,12) (19,11) (25,18) (21,9) (18,11) (19,15) (13,12) (22,10) (16,13) (15,22) (21,3) (22,5) (20,25) (14,19) (24,17) (1,2) (17,19) (1,9) (6,24) (13,24) (3,14) (23,0) (8,11) (16,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph122", "image": "data/cycle/graph_visual/hard/graph122.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (25,3) (11,12) (22,13) (11,16) (19,4) (8,26) (10,9) (14,16) (1,25) (24,10) (8,19) (9,26) (21,8) (16,9) (18,17) (6,12) (1,2) (6,15) (16,5) (4,18) (0,21) (8,23) (24,3) (7,3) (13,10) (3,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph29", "image": "data/cycle/graph_visual/hard/graph29.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,23) (15,19) (2,11) (1,6) (2,7) (16,22) (5,14) (12,20) (9,5) (15,17) (23,11) (18,21) (8,23) (3,4) (25,24) (12,16) (0,2) (13,23) (17,13) (21,12) (9,2) (17,24) (9,6) (10,12) (23,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1662", "image": "data/cycle/graph_visual/hard/graph1662.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,19) (9,12) (26,22) (8,12) (19,4) (26,19) (5,30) (0,3) (28,7) (21,31) (26,21) (0,26) (8,3) (9,30) (13,27) (1,15) (1,18) (8,24) (0,2) (7,4) (7,17) (18,10) (11,17) (16,20) (29,5) (20,25) (6,23) (4,0) (21,13) (11,14) (24,15) (16,23) (0,1) (26,9) (3,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1857", "image": "data/cycle/graph_visual/hard/graph1857.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (19,1) (10,29) (9,19) (29,1) (25,17) (0,1) (13,2) (31,10) (8,30) (33,4) (6,20) (29,24) (22,15) (29,11) (4,3) (24,27) (22,31) (14,30) (16,5) (17,16) (26,1) (19,3) (31,32) (17,26) (12,9) (20,5) (0,2) (22,23) (2,32) (6,18) (27,7) (28,0) (28,12) (8,12) (21,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1474", "image": "data/cycle/graph_visual/hard/graph1474.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,19) (28,12) (9,11) (0,22) (25,22) (1,0) (0,20) (20,4) (2,1) (11,17) (17,15) (24,22) (26,22) (21,23) (5,11) (19,4) (23,9) (14,29) (10,7) (21,19) (23,6) (0,3) (12,4) (14,7) (8,5) (22,13) (10,27) (25,2) (16,19) (0,2) (7,25) (18,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1780", "image": "data/cycle/graph_visual/hard/graph1780.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (12,2) (5,11) (7,23) (0,11) (20,26) (29,21) (21,16) (1,0) (27,20) (1,25) (28,15) (0,2) (3,9) (24,8) (15,9) (28,12) (25,11) (28,30) (3,21) (0,13) (17,29) (8,18) (27,8) (4,21) (10,19) (29,7) (22,14) (7,10) (0,32) (11,14) (12,14) (6,0) (26,31) (19,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph371", "image": "data/cycle/graph_visual/hard/graph371.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (4,19) (7,9) (28,8) (13,7) (5,28) (4,23) (20,1) (23,24) (21,17) (22,11) (12,1) (16,28) (15,20) (14,25) (21,24) (2,14) (6,28) (14,26) (0,26) (1,4) (18,6) (27,23) (20,6) (16,10) (11,8) (18,3) (9,21) (0,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph275", "image": "data/cycle/graph_visual/hard/graph275.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,9) (26,24) (7,18) (7,13) (19,3) (20,24) (22,2) (23,0) (24,25) (14,17) (5,11) (17,5) (27,25) (22,21) (23,4) (17,20) (23,11) (14,10) (23,8) (10,21) (12,3) (15,8) (18,16) (6,26) (13,15) (19,27) (1,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1476", "image": "data/cycle/graph_visual/hard/graph1476.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,9) (6,29) (0,1) (8,23) (13,28) (0,26) (17,12) (26,2) (7,3) (28,22) (29,26) (6,21) (25,20) (20,12) (8,16) (22,15) (4,23) (21,10) (17,0) (18,13) (1,19) (23,11) (21,24) (20,1) (28,4) (24,27) (2,0) (5,6) (15,12) (9,3) (14,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph586", "image": "data/cycle/graph_visual/hard/graph586.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,28) (19,4) (18,6) (29,18) (20,23) (16,6) (0,14) (10,4) (7,3) (17,1) (14,25) (4,7) (15,24) (14,12) (25,7) (12,2) (11,5) (2,15) (28,26) (27,15) (22,13) (9,12) (15,30) (11,6) (2,1) (26,12) (12,22) (16,21) (8,30) (20,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1623", "image": "data/cycle/graph_visual/hard/graph1623.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (0,10) (25,5) (3,5) (12,18) (2,0) (23,5) (17,1) (22,12) (9,30) (24,16) (15,31) (20,6) (16,26) (1,14) (21,27) (18,6) (2,6) (16,7) (3,0) (31,4) (16,28) (11,23) (20,13) (0,4) (0,1) (23,26) (29,27) (0,9) (26,19) (12,17) (2,8) (30,12) (31,2) (6,28) (21,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph431", "image": "data/cycle/graph_visual/hard/graph431.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (11,7) (7,17) (16,9) (2,6) (7,29) (0,6) (3,26) (28,12) (28,1) (27,4) (11,24) (11,22) (25,7) (8,12) (8,11) (21,4) (10,14) (20,21) (1,15) (8,27) (25,19) (13,23) (22,14) (22,23) (0,18) (16,5) (10,3) (0,1) (5,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1599", "image": "data/cycle/graph_visual/hard/graph1599.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (9,6) (13,23) (29,3) (10,25) (14,30) (20,10) (7,12) (26,12) (25,4) (17,21) (25,16) (18,22) (13,8) (19,22) (30,27) (11,9) (2,0) (28,0) (7,0) (0,3) (3,24) (27,20) (11,15) (8,21) (5,24) (1,0) (16,29) (17,22) (5,9) (26,23) (16,1) (13,2) (8,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1437", "image": "data/cycle/graph_visual/hard/graph1437.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,28) (26,12) (23,15) (0,2) (22,20) (29,15) (0,14) (6,16) (10,6) (3,7) (11,22) (9,4) (14,24) (7,25) (2,12) (25,15) (1,13) (15,2) (11,5) (0,1) (3,0) (18,27) (18,6) (0,20) (14,12) (1,2) (12,21) (16,19) (0,4) (8,12) (17,4) (6,28) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1088", "image": "data/cycle/graph_visual/hard/graph1088.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,16) (20,4) (4,2) (23,22) (5,14) (11,10) (7,17) (15,21) (4,1) (0,1) (19,15) (13,5) (18,22) (3,6) (0,6) (2,0) (2,11) (22,25) (8,14) (24,9) (4,0) (19,12) (15,13) (0,3) (23,7) (15,22) (0,11) (5,9) (23,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph472", "image": "data/cycle/graph_visual/hard/graph472.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (4,19) (23,6) (17,11) (24,22) (12,4) (2,25) (7,25) (19,21) (7,14) (22,0) (17,15) (22,25) (1,2) (11,9) (18,22) (14,29) (26,22) (13,22) (12,28) (5,8) (23,21) (20,0) (11,5) (4,20) (19,16) (7,10) (3,19) (10,27) (9,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1836", "image": "data/cycle/graph_visual/hard/graph1836.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (13,28) (23,14) (17,33) (32,25) (32,21) (20,0) (29,27) (1,13) (8,3) (31,10) (16,10) (31,30) (12,27) (21,18) (17,15) (4,8) (7,32) (13,14) (9,26) (10,8) (18,3) (4,27) (2,8) (12,11) (31,22) (21,6) (1,4) (9,19) (20,6) (15,6) (32,24) (1,0) (9,30) (19,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph66", "image": "data/cycle/graph_visual/hard/graph66.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (10,21) (8,12) (21,1) (21,24) (4,9) (24,16) (15,0) (3,13) (22,1) (17,7) (2,0) (23,20) (25,23) (6,24) (15,22) (19,4) (4,1) (17,3) (12,4) (18,4) (14,7) (7,4) (17,23) (11,1) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph602", "image": "data/cycle/graph_visual/hard/graph602.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,10) (8,23) (15,31) (22,28) (20,17) (29,16) (12,17) (19,23) (29,8) (15,29) (0,13) (14,31) (31,9) (11,30) (24,22) (6,0) (23,21) (16,18) (15,4) (7,29) (26,24) (2,1) (26,2) (3,27) (13,10) (19,11) (30,5) (8,27) (2,25) (26,18) (20,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1573", "image": "data/cycle/graph_visual/hard/graph1573.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (27,28) (17,14) (2,19) (4,14) (28,12) (24,12) (26,29) (5,17) (14,7) (0,3) (28,6) (29,23) (19,14) (2,0) (15,16) (13,30) (15,25) (6,23) (9,8) (0,29) (10,18) (9,15) (6,1) (0,1) (11,28) (20,12) (2,30) (25,17) (22,10) (3,4) (1,15) (21,7) (18,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1172", "image": "data/cycle/graph_visual/hard/graph1172.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (23,8) (1,0) (5,11) (13,7) (11,22) (3,12) (13,15) (26,6) (24,25) (19,3) (2,22) (5,17) (25,26) (14,10) (1,14) (2,0) (9,16) (17,20) (8,15) (21,19) (23,4) (17,14) (20,24) (7,18) (24,23) (21,10) (16,18) (0,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph625", "image": "data/cycle/graph_visual/hard/graph625.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (4,23) (5,3) (27,17) (10,23) (26,5) (31,20) (28,11) (26,13) (7,5) (3,9) (26,4) (21,9) (0,23) (28,19) (6,12) (23,18) (4,22) (0,30) (1,20) (16,24) (24,18) (15,18) (27,25) (14,4) (8,2) (28,2) (23,27) (2,13) (14,1) (0,29) (6,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph278", "image": "data/cycle/graph_visual/hard/graph278.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (17,3) (26,19) (3,20) (13,2) (14,4) (11,12) (2,11) (6,15) (25,22) (7,18) (27,0) (1,19) (26,11) (5,4) (23,8) (12,3) (3,10) (19,21) (12,15) (17,24) (16,3) (1,18) (25,21) (9,11) (27,20) (5,18) (23,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph43", "image": "data/cycle/graph_visual/hard/graph43.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (3,12) (18,22) (6,12) (5,11) (1,22) (8,5) (17,4) (21,5) (23,9) (0,22) (5,6) (19,9) (13,21) (25,20) (23,20) (16,24) (15,2) (23,14) (4,25) (10,6) (22,2) (18,7) (14,0) (14,24) (21,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph790", "image": "data/cycle/graph_visual/hard/graph790.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,29) (17,28) (14,28) (20,9) (9,12) (23,16) (24,6) (26,8) (26,18) (5,22) (31,6) (4,3) (20,15) (4,25) (18,9) (26,27) (4,24) (19,13) (20,7) (21,26) (22,25) (29,10) (23,32) (2,0) (4,16) (10,2) (30,13) (6,13) (27,11) (6,1) (9,19) (28,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph727", "image": "data/cycle/graph_visual/hard/graph727.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (9,1) (19,9) (14,16) (0,26) (22,29) (10,8) (18,7) (29,9) (2,15) (32,30) (18,14) (21,23) (17,32) (26,10) (14,1) (20,30) (31,3) (3,6) (11,9) (6,19) (15,18) (0,28) (12,9) (25,5) (4,19) (17,15) (21,2) (24,2) (13,16) (24,27) (19,8) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1821", "image": "data/cycle/graph_visual/hard/graph1821.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,4) (25,16) (17,26) (2,0) (25,29) (17,24) (21,11) (27,9) (11,9) (17,5) (7,10) (0,5) (21,31) (32,16) (10,32) (19,33) (1,0) (15,12) (8,1) (11,28) (0,3) (3,32) (30,19) (23,22) (25,11) (12,6) (4,8) (23,30) (33,2) (14,1) (18,2) (24,23) (12,20) (8,0) (13,31) (6,7) (6,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph587", "image": "data/cycle/graph_visual/hard/graph587.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,4) (18,12) (29,7) (11,14) (12,0) (21,9) (4,16) (0,17) (8,20) (25,14) (28,30) (8,15) (26,22) (5,11) (14,4) (15,24) (17,7) (11,13) (2,8) (23,11) (28,10) (20,25) (21,3) (0,21) (22,27) (10,5) (1,15) (27,19) (19,21) (16,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1950", "image": "data/cycle/graph_visual/hard/graph1950.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,12) (7,19) (27,32) (21,32) (1,5) (17,34) (3,33) (12,27) (16,28) (25,22) (30,32) (12,34) (24,14) (5,8) (22,13) (32,5) (29,0) (10,19) (26,2) (24,3) (16,2) (30,15) (9,6) (11,5) (2,14) (20,23) (9,11) (5,14) (29,14) (24,18) (19,24) (0,1) (27,20) (31,0) (25,34)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph850", "image": "data/cycle/graph_visual/hard/graph850.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (6,2) (14,16) (13,19) (22,33) (12,5) (1,29) (16,2) (0,4) (6,11) (7,25) (17,12) (9,21) (10,7) (18,8) (25,13) (12,26) (5,30) (28,24) (27,22) (8,27) (15,1) (28,1) (14,12) (30,3) (26,23) (13,18) (20,17) (25,29) (1,5) (0,32) (25,31) (4,11) (5,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1888", "image": "data/cycle/graph_visual/hard/graph1888.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (14,9) (3,33) (20,21) (2,30) (25,17) (14,25) (24,26) (15,8) (30,10) (12,1) (23,21) (2,0) (27,7) (3,0) (22,19) (15,29) (16,2) (28,1) (0,5) (0,1) (1,7) (32,12) (10,28) (11,22) (18,33) (25,0) (29,16) (13,16) (6,10) (32,5) (0,30) (0,4) (23,28) (4,15) (31,11) (19,23) (17,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1034", "image": "data/cycle/graph_visual/hard/graph1034.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,10) (8,21) (16,25) (13,23) (22,18) (14,11) (5,9) (19,17) (11,9) (16,8) (0,1) (20,25) (2,13) (7,0) (24,5) (22,15) (21,17) (3,0) (9,6) (8,13) (1,16) (4,25) (12,23) (7,12) (22,3) (24,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph521", "image": "data/cycle/graph_visual/hard/graph521.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (19,26) (27,0) (9,6) (14,30) (4,3) (26,3) (30,8) (22,19) (28,29) (5,2) (27,10) (17,0) (0,23) (13,11) (24,8) (17,25) (30,20) (12,0) (18,15) (21,9) (30,11) (26,13) (15,11) (13,7) (9,13) (14,29) (17,1) (8,5) (21,16) (13,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph645", "image": "data/cycle/graph_visual/hard/graph645.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,17) (0,7) (1,21) (16,31) (2,19) (4,28) (20,11) (25,18) (19,7) (16,20) (29,8) (27,13) (5,15) (1,4) (0,24) (5,19) (26,4) (10,26) (2,11) (2,3) (12,31) (3,9) (8,17) (9,17) (16,14) (4,27) (23,30) (30,13) (7,18) (26,9) (21,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph442", "image": "data/cycle/graph_visual/hard/graph442.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (23,21) (3,23) (8,1) (20,22) (4,9) (14,5) (23,29) (4,7) (7,8) (28,13) (21,17) (6,29) (13,29) (11,24) (29,5) (19,0) (26,2) (3,18) (22,16) (15,14) (10,19) (0,12) (7,2) (1,10) (25,28) (19,5) (17,27) (20,28) (11,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1315", "image": "data/cycle/graph_visual/hard/graph1315.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,12) (15,5) (21,19) (23,9) (8,1) (18,7) (16,20) (17,27) (7,20) (27,22) (21,4) (11,25) (17,2) (21,10) (4,28) (1,0) (14,28) (9,3) (20,23) (25,5) (13,0) (24,7) (4,13) (0,9) (6,27) (2,26) (4,5) (21,8) (23,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph219", "image": "data/cycle/graph_visual/hard/graph219.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,18) (21,10) (14,23) (4,22) (1,11) (7,15) (17,23) (3,5) (1,4) (24,6) (12,8) (0,15) (23,24) (1,21) (4,20) (9,4) (17,7) (17,3) (3,13) (14,16) (16,27) (4,12) (21,26) (4,7) (25,1) (24,19) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph835", "image": "data/cycle/graph_visual/hard/graph835.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,18) (15,28) (25,14) (4,29) (24,12) (14,23) (22,23) (6,14) (5,32) (8,29) (7,16) (4,20) (3,18) (28,33) (18,27) (2,16) (25,28) (8,22) (7,30) (9,28) (12,30) (11,29) (17,21) (33,10) (32,14) (14,19) (33,13) (26,0) (2,26) (16,21) (23,31) (10,27) (8,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph258", "image": "data/cycle/graph_visual/hard/graph258.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (18,19) (26,4) (18,21) (14,27) (17,26) (8,6) (17,12) (1,22) (24,10) (3,10) (17,7) (6,7) (22,12) (24,21) (20,21) (13,24) (11,18) (11,15) (19,2) (7,16) (24,7) (9,14) (5,3) (27,25) (6,0) (27,23) (27,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1248", "image": "data/cycle/graph_visual/hard/graph1248.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (3,10) (25,1) (22,14) (7,5) (16,9) (7,23) (14,10) (12,26) (2,0) (18,21) (0,17) (3,24) (5,16) (8,25) (20,22) (11,22) (23,13) (7,11) (27,7) (0,6) (4,19) (11,8) (15,1) (6,2) (0,1) (11,21) (8,12) (4,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph204", "image": "data/cycle/graph_visual/hard/graph204.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (3,17) (11,12) (0,27) (19,1) (13,2) (3,16) (14,4) (22,25) (12,3) (23,8) (11,2) (11,9) (4,5) (23,5) (19,21) (10,3) (3,20) (15,6) (26,11) (27,20) (5,18) (21,25) (26,19) (18,1) (12,15) (7,18) (17,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1222", "image": "data/cycle/graph_visual/hard/graph1222.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,11) (11,19) (26,18) (6,19) (27,23) (9,15) (24,23) (5,16) (4,18) (1,11) (13,9) (5,25) (7,14) (12,21) (2,1) (15,10) (8,0) (1,0) (27,0) (3,20) (22,0) (17,10) (12,3) (23,20) (12,26) (16,7) (13,20) (19,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1291", "image": "data/cycle/graph_visual/hard/graph1291.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (4,5) (3,15) (12,26) (8,20) (23,13) (1,26) (22,13) (27,18) (1,0) (1,19) (7,25) (18,26) (11,18) (20,16) (17,14) (16,6) (6,1) (24,2) (2,21) (10,2) (1,9) (17,2) (2,7) (10,0) (11,3) (1,13) (4,12) (13,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph794", "image": "data/cycle/graph_visual/hard/graph794.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (27,1) (19,25) (17,14) (3,7) (22,11) (11,8) (4,1) (9,31) (7,30) (6,28) (21,20) (13,22) (20,18) (23,27) (19,28) (0,8) (11,25) (11,12) (17,3) (7,10) (16,1) (16,11) (5,14) (12,26) (5,15) (19,32) (9,32) (3,24) (16,21) (3,20) (29,26) (15,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1694", "image": "data/cycle/graph_visual/hard/graph1694.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,24) (21,11) (25,3) (12,23) (11,1) (9,16) (15,10) (5,20) (27,11) (28,22) (2,10) (29,27) (13,16) (12,14) (23,24) (21,30) (24,18) (24,22) (25,5) (2,0) (19,24) (15,31) (26,19) (28,6) (23,13) (29,7) (0,1) (8,29) (13,17) (31,13) (28,5) (29,4) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1481", "image": "data/cycle/graph_visual/hard/graph1481.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (11,24) (2,0) (25,11) (25,28) (10,1) (29,13) (4,7) (13,28) (22,16) (7,2) (28,20) (14,5) (0,12) (0,19) (1,8) (29,23) (21,17) (20,22) (5,19) (26,2) (15,14) (1,0) (8,7) (23,21) (23,3) (5,29) (17,27) (4,9) (10,19) (3,18) (6,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph340", "image": "data/cycle/graph_visual/hard/graph340.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,26) (11,25) (0,2) (16,25) (27,13) (23,17) (14,20) (25,27) (12,28) (4,21) (18,1) (12,6) (7,6) (14,10) (25,6) (15,6) (7,8) (12,5) (8,22) (19,23) (9,5) (3,21) (2,5) (26,15) (21,14) (24,11) (18,14) (26,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1982", "image": "data/cycle/graph_visual/hard/graph1982.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (15,18) (20,6) (1,16) (17,20) (4,32) (33,5) (2,18) (25,24) (4,6) (32,27) (34,2) (7,10) (14,13) (23,0) (3,26) (28,19) (4,22) (1,0) (9,7) (18,6) (11,24) (10,31) (7,14) (1,14) (22,29) (7,32) (10,26) (25,20) (18,21) (24,19) (30,21) (34,8) (11,12) (0,6) (17,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph664", "image": "data/cycle/graph_visual/hard/graph664.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,1) (3,5) (13,20) (24,18) (23,28) (12,23) (6,27) (10,29) (30,13) (24,3) (22,17) (31,13) (18,19) (14,4) (24,20) (27,4) (9,0) (9,5) (9,26) (3,16) (1,7) (14,8) (25,21) (6,21) (10,19) (24,1) (0,22) (19,15) (16,23) (6,17) (2,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1253", "image": "data/cycle/graph_visual/hard/graph1253.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,3) (8,14) (1,0) (5,0) (25,5) (14,4) (15,9) (16,21) (18,15) (12,7) (3,1) (26,27) (19,5) (15,13) (17,20) (7,6) (10,16) (3,22) (8,6) (27,5) (21,2) (22,8) (24,21) (23,6) (9,14) (15,20) (11,10) (25,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph117", "image": "data/cycle/graph_visual/hard/graph117.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,18) (3,19) (13,23) (22,5) (25,6) (9,25) (7,21) (14,13) (8,21) (10,20) (11,24) (4,3) (0,13) (5,0) (23,1) (17,20) (13,6) (4,10) (14,18) (2,24) (26,6) (21,18) (2,3) (16,8) (4,12) (10,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph289", "image": "data/cycle/graph_visual/hard/graph289.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (14,7) (0,19) (4,15) (21,23) (7,8) (9,3) (13,1) (20,3) (6,17) (0,1) (22,17) (18,24) (6,27) (8,12) (5,20) (0,10) (2,23) (4,23) (6,2) (19,16) (16,7) (13,18) (25,2) (26,7) (17,0) (23,11) (3,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1302", "image": "data/cycle/graph_visual/hard/graph1302.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (6,25) (18,1) (14,10) (23,19) (15,6) (21,3) (20,14) (27,13) (16,25) (5,2) (12,28) (27,25) (6,7) (26,19) (12,5) (8,22) (24,11) (26,15) (7,8) (5,9) (14,21) (11,25) (2,0) (1,0) (21,4) (26,14) (12,6) (18,14) (23,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph856", "image": "data/cycle/graph_visual/hard/graph856.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,21) (14,30) (4,9) (28,26) (26,27) (18,11) (10,3) (20,15) (17,32) (4,25) (26,8) (13,16) (30,12) (31,7) (28,2) (31,21) (19,33) (30,13) (27,24) (9,5) (0,23) (1,23) (1,9) (7,23) (14,2) (0,15) (26,6) (5,33) (10,18) (32,11) (27,32) (14,29) (0,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph244", "image": "data/cycle/graph_visual/hard/graph244.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,25) (19,21) (22,13) (1,15) (13,9) (18,15) (1,23) (23,7) (23,0) (14,4) (26,6) (22,27) (13,23) (20,5) (1,12) (19,10) (21,24) (4,24) (5,16) (11,17) (6,2) (3,21) (6,8) (17,24) (27,6) (13,20) (16,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph546", "image": "data/cycle/graph_visual/hard/graph546.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,28) (0,8) (13,17) (26,15) (25,10) (20,17) (29,3) (28,10) (4,1) (20,23) (28,6) (9,26) (15,16) (30,16) (2,26) (8,12) (12,24) (3,14) (24,2) (4,23) (22,27) (8,18) (5,6) (22,17) (28,11) (19,24) (7,26) (21,10) (11,0) (22,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1345", "image": "data/cycle/graph_visual/hard/graph1345.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (21,15) (26,16) (7,23) (5,25) (2,7) (1,0) (6,0) (11,23) (20,8) (6,14) (2,10) (27,13) (20,25) (2,0) (5,1) (4,28) (14,26) (10,15) (18,19) (26,22) (11,1) (0,18) (3,0) (8,24) (17,15) (3,18) (16,15) (1,9) (13,12) (27,4) (1,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1083", "image": "data/cycle/graph_visual/hard/graph1083.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (23,12) (0,6) (5,12) (19,9) (8,17) (6,24) (7,15) (16,20) (3,1) (4,19) (5,4) (19,6) (4,0) (3,4) (17,14) (10,22) (18,13) (6,21) (6,20) (4,7) (2,0) (1,0) (13,0) (14,24) (25,13) (22,4) (2,23) (0,3) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph512", "image": "data/cycle/graph_visual/hard/graph512.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,2) (16,13) (28,1) (21,11) (24,22) (29,21) (24,4) (3,19) (15,0) (4,7) (1,12) (15,4) (22,25) (23,27) (12,9) (6,13) (5,3) (10,4) (16,14) (20,7) (4,26) (6,30) (1,4) (17,3) (18,30) (23,17) (1,21) (8,24) (7,17) (14,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph267", "image": "data/cycle/graph_visual/hard/graph267.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,16) (25,6) (12,15) (18,2) (21,5) (10,25) (19,0) (15,26) (23,20) (26,13) (9,14) (13,20) (23,22) (9,2) (11,24) (20,16) (25,8) (8,17) (1,0) (10,3) (8,7) (7,5) (1,4) (27,12) (2,17) (18,13) (17,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1670", "image": "data/cycle/graph_visual/hard/graph1670.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (27,24) (4,23) (10,0) (20,3) (10,28) (20,26) (9,30) (21,19) (4,13) (17,15) (20,7) (8,20) (5,30) (11,18) (29,3) (12,4) (2,17) (30,18) (14,19) (23,7) (25,17) (1,14) (31,19) (16,26) (0,1) (13,18) (27,15) (22,3) (17,31) (7,28) (20,15) (11,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph966", "image": "data/cycle/graph_visual/hard/graph966.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (20,7) (23,33) (13,24) (8,25) (16,22) (13,18) (31,14) (9,12) (22,34) (17,9) (28,27) (18,3) (15,14) (14,10) (14,32) (16,2) (22,7) (5,9) (23,27) (8,11) (8,16) (29,28) (5,16) (27,1) (17,0) (20,27) (8,30) (4,21) (0,26) (19,11) (11,6) (1,18) (4,34) (31,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1041", "image": "data/cycle/graph_visual/hard/graph1041.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,2) (0,2) (25,10) (4,20) (5,19) (2,4) (4,0) (0,13) (1,8) (1,0) (7,0) (16,23) (22,14) (9,19) (12,1) (21,12) (16,25) (7,24) (15,19) (3,17) (6,8) (11,9) (16,19) (18,6) (14,0) (20,12) (0,3) (17,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph736", "image": "data/cycle/graph_visual/hard/graph736.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (25,9) (23,5) (9,22) (29,22) (13,12) (29,1) (0,31) (17,13) (18,11) (30,32) (27,14) (10,28) (3,16) (21,19) (5,3) (24,11) (20,30) (26,19) (20,11) (10,2) (2,1) (19,12) (15,2) (24,22) (5,6) (26,3) (24,8) (4,29) (28,14) (12,30) (8,7) (31,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph877", "image": "data/cycle/graph_visual/hard/graph877.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (15,4) (33,31) (8,28) (20,8) (12,24) (17,32) (13,9) (20,26) (26,6) (14,28) (21,13) (8,12) (32,11) (13,22) (14,7) (9,25) (27,1) (19,26) (30,11) (5,11) (29,15) (23,10) (8,3) (12,0) (29,18) (14,17) (2,7) (8,10) (0,33) (16,8) (26,1) (12,25) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1066", "image": "data/cycle/graph_visual/hard/graph1066.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (19,20) (0,3) (2,0) (5,3) (4,8) (22,7) (9,25) (16,0) (20,23) (8,11) (24,11) (0,1) (15,7) (1,20) (3,18) (7,12) (18,25) (17,12) (0,14) (17,3) (15,11) (16,21) (13,23) (14,24) (23,6) (5,1) (2,19) (10,22) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph532", "image": "data/cycle/graph_visual/hard/graph532.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,2) (0,2) (20,17) (16,7) (12,17) (25,21) (1,21) (6,29) (27,7) (23,14) (5,13) (24,10) (17,16) (14,4) (24,23) (10,3) (20,1) (26,24) (18,30) (11,3) (23,1) (4,8) (25,15) (1,22) (28,19) (9,19) (18,9) (16,13) (27,28) (29,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph357", "image": "data/cycle/graph_visual/hard/graph357.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (6,10) (8,17) (15,12) (26,24) (14,3) (12,16) (0,28) (25,19) (20,14) (11,23) (24,22) (17,13) (4,5) (9,7) (16,1) (26,10) (9,21) (21,14) (7,11) (21,4) (0,19) (18,5) (15,26) (26,2) (9,10) (27,23) (4,28) (17,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1469", "image": "data/cycle/graph_visual/hard/graph1469.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (21,24) (5,0) (21,2) (24,25) (15,13) (3,1) (8,6) (8,28) (6,26) (22,28) (10,3) (14,28) (23,8) (3,22) (4,14) (14,9) (12,7) (18,15) (15,9) (20,17) (6,7) (0,2) (15,20) (5,25) (16,10) (16,21) (0,1) (27,29) (5,19) (5,27) (11,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1639", "image": "data/cycle/graph_visual/hard/graph1639.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (27,28) (0,6) (13,2) (14,15) (1,0) (1,6) (16,9) (18,1) (22,21) (29,2) (4,5) (8,21) (25,14) (30,16) (0,3) (3,22) (20,27) (12,21) (22,26) (0,20) (0,24) (29,7) (25,11) (17,26) (19,16) (2,15) (4,27) (2,31) (23,30) (28,15) (15,12) (23,22) (2,0) (10,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph175", "image": "data/cycle/graph_visual/hard/graph175.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (23,15) (21,9) (7,12) (18,1) (0,21) (5,4) (11,14) (25,15) (2,6) (22,8) (16,0) (15,16) (5,11) (5,18) (26,2) (24,0) (3,5) (7,14) (13,9) (3,0) (10,24) (19,5) (20,8) (26,10) (5,20) (17,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph381", "image": "data/cycle/graph_visual/hard/graph381.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,26) (1,11) (4,12) (24,6) (14,16) (10,21) (23,25) (23,14) (24,20) (22,4) (17,7) (3,5) (7,4) (15,3) (27,21) (0,2) (15,0) (13,16) (19,22) (8,12) (3,17) (9,4) (28,13) (24,4) (1,21) (7,18) (1,4) (17,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1036", "image": "data/cycle/graph_visual/hard/graph1036.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (6,19) (5,4) (0,13) (14,16) (1,0) (14,3) (4,0) (5,22) (19,17) (0,2) (7,11) (22,19) (22,14) (3,0) (10,0) (25,23) (20,2) (8,4) (8,9) (21,1) (11,21) (10,2) (24,12) (17,10) (23,14) (12,5) (23,1) (18,19) (15,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1378", "image": "data/cycle/graph_visual/hard/graph1378.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (18,9) (12,9) (3,13) (16,15) (1,0) (6,0) (27,11) (21,23) (22,13) (26,7) (2,12) (23,26) (24,4) (5,26) (9,1) (6,26) (0,10) (1,8) (27,25) (28,6) (20,8) (15,1) (3,27) (18,24) (18,21) (18,3) (19,24) (20,14) (17,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1582", "image": "data/cycle/graph_visual/hard/graph1582.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (4,14) (25,10) (16,1) (0,2) (11,3) (12,8) (6,29) (14,26) (2,10) (2,28) (0,1) (18,13) (27,29) (1,17) (10,7) (23,24) (14,15) (9,12) (7,15) (30,21) (30,5) (9,22) (11,6) (21,0) (9,27) (17,25) (19,7) (20,9) (26,24) (13,26) (9,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1497", "image": "data/cycle/graph_visual/hard/graph1497.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,6) (4,9) (1,3) (23,8) (5,12) (26,4) (15,22) (0,13) (29,3) (17,7) (10,17) (2,7) (13,22) (19,4) (1,0) (21,20) (20,14) (26,5) (12,27) (5,16) (6,19) (2,3) (28,6) (24,6) (11,19) (24,14) (6,23) (4,25) (18,4) (13,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1826", "image": "data/cycle/graph_visual/hard/graph1826.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,18) (33,31) (0,12) (8,28) (8,20) (19,26) (8,3) (7,14) (2,0) (6,26) (7,2) (33,0) (21,13) (8,16) (0,3) (12,24) (12,8) (15,4) (13,22) (1,0) (10,23) (14,17) (1,27) (10,8) (28,14) (26,20) (30,11) (9,25) (9,13) (26,1) (4,6) (12,25) (11,32) (15,29) (32,17) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1550", "image": "data/cycle/graph_visual/hard/graph1550.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,28) (0,2) (17,14) (11,7) (18,14) (28,2) (14,12) (8,14) (26,10) (29,24) (13,28) (13,27) (8,6) (7,2) (20,6) (0,1) (5,16) (4,9) (13,0) (14,16) (25,10) (22,1) (16,21) (3,9) (20,15) (19,22) (17,23) (19,15) (9,27) (0,3) (26,20) (29,7) (30,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph517", "image": "data/cycle/graph_visual/hard/graph517.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (10,24) (12,6) (25,1) (18,4) (28,7) (3,26) (16,11) (16,9) (10,28) (0,30) (11,12) (6,20) (13,25) (3,24) (13,10) (21,18) (27,30) (15,3) (8,23) (9,0) (19,4) (16,14) (28,9) (1,5) (22,3) (26,8) (19,8) (8,29) (17,16) (2,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1901", "image": "data/cycle/graph_visual/hard/graph1901.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,34) (7,29) (17,6) (27,5) (4,15) (14,3) (0,3) (0,4) (8,18) (6,23) (1,0) (4,12) (30,14) (13,21) (9,34) (3,27) (0,2) (26,24) (9,26) (13,2) (14,2) (20,0) (16,34) (10,25) (33,7) (11,3) (31,3) (26,18) (9,1) (20,32) (3,19) (2,8) (32,25) (23,27) (25,3) (4,28) (22,5) (15,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1851", "image": "data/cycle/graph_visual/hard/graph1851.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (31,10) (3,18) (16,10) (21,18) (17,33) (22,31) (7,32) (27,29) (9,30) (31,30) (0,20) (1,4) (23,14) (32,21) (3,8) (32,24) (27,12) (2,0) (27,4) (32,25) (1,0) (9,19) (3,0) (11,12) (6,20) (2,8) (13,28) (8,4) (1,13) (8,10) (21,6) (13,14) (6,15) (15,17) (19,5) (9,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1097", "image": "data/cycle/graph_visual/hard/graph1097.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (7,24) (21,18) (6,8) (7,23) (1,15) (6,13) (14,24) (19,9) (22,25) (23,1) (19,21) (15,17) (13,23) (0,1) (3,0) (16,5) (4,12) (24,4) (19,16) (2,6) (23,0) (0,2) (10,17) (1,11) (3,21) (0,4) (5,20) (22,13) (13,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph599", "image": "data/cycle/graph_visual/hard/graph599.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (26,21) (12,18) (4,13) (5,18) (11,10) (22,17) (12,30) (9,15) (2,3) (20,14) (24,7) (11,2) (19,1) (23,9) (19,23) (8,22) (5,21) (25,1) (0,20) (13,6) (18,24) (10,19) (11,27) (16,3) (8,28) (24,29) (22,10) (30,15) (13,23) (14,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1855", "image": "data/cycle/graph_visual/hard/graph1855.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (29,13) (11,15) (2,9) (12,7) (12,1) (2,11) (2,0) (31,0) (6,8) (16,28) (17,22) (25,18) (12,28) (25,14) (15,33) (19,18) (26,22) (2,31) (6,3) (21,16) (6,26) (12,10) (5,13) (28,4) (11,19) (0,27) (30,4) (32,18) (1,0) (3,23) (13,30) (8,19) (24,28) (23,24) (20,18) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1677", "image": "data/cycle/graph_visual/hard/graph1677.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,4) (12,10) (1,10) (19,30) (16,5) (3,24) (21,20) (13,2) (11,10) (27,19) (21,31) (0,18) (31,25) (24,7) (31,28) (12,14) (26,28) (23,2) (9,18) (2,0) (5,15) (9,17) (8,13) (1,7) (20,10) (20,13) (5,29) (1,0) (6,11) (29,22) (0,28) (10,16) (23,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph426", "image": "data/cycle/graph_visual/hard/graph426.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,8) (5,2) (0,13) (3,17) (26,18) (16,24) (22,12) (19,29) (25,10) (0,2) (1,12) (23,14) (29,16) (15,19) (19,26) (26,27) (14,0) (25,7) (20,4) (6,21) (5,29) (2,4) (0,7) (9,11) (17,20) (28,26) (9,19) (12,20) (8,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1054", "image": "data/cycle/graph_visual/hard/graph1054.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (15,16) (3,14) (7,24) (17,25) (14,8) (15,20) (0,14) (17,1) (10,14) (3,0) (17,2) (1,0) (18,25) (5,23) (6,5) (16,21) (25,22) (11,16) (20,19) (24,22) (4,9) (2,4) (5,3) (19,25) (6,13) (2,0) (9,14) (18,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph305", "image": "data/cycle/graph_visual/hard/graph305.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (17,21) (11,8) (26,15) (9,6) (22,26) (8,4) (16,8) (10,8) (11,26) (10,17) (14,2) (2,26) (20,0) (20,18) (13,9) (5,12) (23,20) (7,15) (7,5) (2,23) (1,15) (27,18) (6,2) (28,20) (7,25) (26,19) (22,3) (12,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph299", "image": "data/cycle/graph_visual/hard/graph299.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,17) (24,0) (16,0) (7,14) (25,15) (2,26) (1,18) (12,9) (5,18) (20,8) (0,3) (21,8) (11,5) (11,13) (14,16) (6,2) (24,27) (5,4) (21,9) (27,26) (15,23) (5,20) (3,22) (19,0) (10,7) (16,15) (5,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1162", "image": "data/cycle/graph_visual/hard/graph1162.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (21,9) (19,11) (15,19) (22,10) (14,3) (4,7) (19,14) (21,3) (13,24) (22,15) (0,16) (20,25) (9,1) (11,8) (16,13) (18,11) (17,24) (2,0) (26,12) (22,5) (19,17) (18,25) (1,2) (4,14) (1,0) (12,13) (6,24) (0,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1817", "image": "data/cycle/graph_visual/hard/graph1817.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (31,33) (9,13) (12,26) (16,15) (32,5) (13,26) (33,0) (10,15) (20,25) (1,25) (22,31) (8,14) (33,18) (19,5) (30,20) (27,12) (12,4) (17,0) (13,24) (16,24) (2,25) (21,11) (1,0) (6,11) (29,9) (2,0) (17,2) (30,5) (29,11) (28,23) (14,7) (24,23) (5,21) (8,5) (24,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph815", "image": "data/cycle/graph_visual/hard/graph815.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (16,19) (29,18) (19,13) (12,32) (23,30) (21,33) (1,11) (11,28) (30,17) (10,15) (7,27) (4,21) (15,12) (13,31) (21,0) (7,20) (8,31) (25,12) (15,5) (31,9) (23,32) (16,24) (12,6) (7,2) (18,22) (28,3) (14,11) (15,11) (20,33) (31,12) (16,26) (0,16) (10,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1309", "image": "data/cycle/graph_visual/hard/graph1309.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (15,22) (17,16) (3,27) (16,10) (8,28) (5,22) (13,15) (1,28) (23,18) (11,16) (5,27) (4,8) (6,14) (5,1) (19,14) (22,12) (0,3) (11,24) (0,27) (9,6) (0,4) (0,1) (23,1) (2,19) (1,21) (20,0) (25,4) (23,14) (23,11) (26,23) (2,0) (7,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph141", "image": "data/cycle/graph_visual/hard/graph141.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (23,26) (17,12) (24,20) (4,20) (23,8) (12,19) (7,25) (3,10) (8,14) (23,11) (26,2) (20,1) (5,6) (16,13) (12,15) (1,13) (15,22) (18,4) (0,17) (6,22) (26,0) (6,21) (9,21) (24,21) (9,3) (7,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1816", "image": "data/cycle/graph_visual/hard/graph1816.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (18,29) (10,31) (13,22) (32,23) (19,7) (28,25) (1,8) (18,26) (19,21) (3,0) (17,0) (21,33) (30,9) (14,28) (24,0) (24,2) (6,16) (6,9) (3,12) (0,33) (27,5) (11,24) (17,16) (28,4) (14,15) (23,17) (1,0) (13,12) (31,28) (21,5) (20,24) (17,26) (8,30) (0,2) (31,3) (2,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1429", "image": "data/cycle/graph_visual/hard/graph1429.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (28,17) (20,6) (4,27) (18,23) (4,11) (12,15) (28,25) (8,0) (24,5) (14,22) (17,9) (19,0) (0,1) (9,24) (15,25) (29,0) (2,3) (10,29) (13,9) (7,14) (21,20) (19,21) (18,10) (2,29) (5,23) (12,27) (0,16) (22,26) (1,7) (26,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph375", "image": "data/cycle/graph_visual/hard/graph375.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (26,0) (15,25) (16,5) (9,15) (25,4) (17,26) (7,25) (27,0) (28,24) (21,16) (25,24) (22,5) (23,16) (13,18) (20,12) (19,6) (8,22) (9,14) (16,7) (18,11) (25,6) (13,2) (0,11) (10,13) (4,2) (13,3) (5,1) (15,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph759", "image": "data/cycle/graph_visual/hard/graph759.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,8) (1,28) (14,19) (16,12) (22,21) (18,0) (15,13) (24,19) (4,30) (26,6) (31,29) (18,5) (1,9) (7,14) (1,25) (17,0) (32,16) (19,20) (0,10) (29,18) (19,23) (2,23) (16,23) (14,15) (11,26) (30,3) (9,21) (27,16) (1,29) (26,14) (30,9) (14,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1653", "image": "data/cycle/graph_visual/hard/graph1653.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (9,21) (19,20) (7,14) (12,16) (19,23) (2,23) (30,29) (18,14) (0,1) (1,9) (31,23) (18,0) (26,11) (14,26) (25,1) (21,22) (30,4) (15,13) (1,16) (30,3) (28,9) (19,24) (28,8) (14,15) (18,29) (10,0) (6,26) (19,14) (1,29) (17,0) (18,5) (27,16) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph210", "image": "data/cycle/graph_visual/hard/graph210.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (14,7) (18,21) (1,13) (22,6) (0,17) (22,20) (27,12) (3,0) (23,0) (12,18) (24,16) (3,10) (16,2) (9,15) (26,18) (17,4) (9,25) (12,20) (22,16) (9,22) (13,12) (5,24) (27,8) (3,7) (19,7) (11,5) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1160", "image": "data/cycle/graph_visual/hard/graph1160.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (16,12) (1,24) (9,18) (15,22) (0,24) (20,0) (23,6) (25,7) (14,8) (18,21) (10,26) (19,14) (5,9) (11,16) (2,22) (3,2) (13,9) (6,8) (3,0) (26,15) (14,0) (4,11) (13,12) (4,23) (2,17) (19,7) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph23", "image": "data/cycle/graph_visual/hard/graph23.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (0,10) (2,17) (2,7) (13,22) (16,19) (11,3) (16,6) (18,25) (5,4) (21,13) (6,1) (18,11) (17,13) (12,17) (23,2) (12,4) (18,1) (8,20) (1,9) (14,3) (24,7) (13,1) (15,1) (20,2) (2,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1033", "image": "data/cycle/graph_visual/hard/graph1033.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (22,25) (1,0) (14,3) (17,2) (24,22) (18,12) (16,15) (17,1) (25,18) (11,16) (21,16) (4,2) (24,7) (6,5) (0,14) (14,9) (10,14) (5,23) (20,19) (19,25) (3,5) (20,15) (6,13) (14,8) (9,4) (17,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1043", "image": "data/cycle/graph_visual/hard/graph1043.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (3,24) (8,21) (0,1) (2,10) (24,16) (13,8) (9,13) (17,16) (0,17) (18,14) (25,3) (0,3) (9,4) (10,4) (23,1) (25,19) (25,11) (6,4) (24,5) (20,11) (24,18) (22,23) (15,1) (20,8) (22,18) (0,2) (23,7) (10,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph730", "image": "data/cycle/graph_visual/hard/graph730.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (10,29) (29,9) (8,0) (9,14) (4,12) (27,0) (0,1) (10,24) (18,21) (20,3) (13,22) (5,25) (28,14) (5,30) (1,32) (20,5) (16,6) (3,29) (22,11) (17,25) (26,16) (17,21) (31,4) (9,15) (7,8) (21,19) (4,23) (4,26) (2,5) (8,21) (30,26) (13,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1039", "image": "data/cycle/graph_visual/hard/graph1039.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,0) (14,15) (2,7) (0,4) (0,3) (23,11) (19,18) (21,8) (6,14) (3,18) (0,6) (2,10) (4,13) (13,1) (11,1) (1,0) (17,15) (25,20) (12,13) (4,25) (1,5) (7,23) (10,15) (22,5) (8,20) (1,9) (15,16) (0,2) (24,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1737", "image": "data/cycle/graph_visual/hard/graph1737.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (13,21) (31,4) (17,7) (5,32) (9,16) (10,3) (21,18) (31,0) (22,23) (4,3) (8,7) (9,11) (0,1) (15,22) (2,7) (10,6) (13,30) (18,28) (7,4) (10,27) (4,30) (5,12) (0,2) (13,25) (19,10) (18,29) (26,14) (14,30) (11,25) (22,1) (6,5) (25,23) (24,7) (20,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1023", "image": "data/cycle/graph_visual/hard/graph1023.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,10) (10,24) (4,0) (13,16) (25,2) (16,9) (6,1) (11,18) (2,23) (7,12) (14,4) (2,3) (17,4) (3,0) (5,12) (17,9) (1,0) (2,0) (21,1) (20,7) (25,19) (18,17) (8,18) (1,20) (0,22) (25,16) (18,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph791", "image": "data/cycle/graph_visual/hard/graph791.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (6,26) (17,22) (3,8) (31,6) (17,28) (32,30) (20,3) (10,32) (23,1) (21,14) (14,9) (13,8) (16,20) (1,8) (4,2) (20,21) (28,7) (0,29) (26,3) (24,12) (29,9) (15,2) (20,11) (18,5) (3,25) (22,18) (7,16) (9,19) (10,19) (15,13) (29,12) (27,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph489", "image": "data/cycle/graph_visual/hard/graph489.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,12) (20,2) (25,8) (20,6) (4,25) (1,27) (0,22) (6,25) (0,15) (24,2) (5,17) (27,13) (17,10) (11,25) (23,16) (6,19) (16,7) (3,24) (1,18) (9,23) (19,0) (4,21) (26,8) (29,20) (18,23) (14,4) (17,15) (20,28) (19,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1611", "image": "data/cycle/graph_visual/hard/graph1611.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,5) (1,4) (15,14) (27,19) (25,1) (7,17) (3,7) (10,27) (21,27) (0,3) (13,9) (2,20) (6,8) (30,17) (14,26) (5,18) (24,14) (0,29) (10,0) (22,5) (13,21) (26,12) (0,1) (23,13) (2,1) (16,8) (6,21) (9,17) (2,0) (15,11) (5,31) (28,17) (14,28) (1,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph522", "image": "data/cycle/graph_visual/hard/graph522.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,8) (6,16) (25,30) (17,15) (4,9) (21,25) (3,24) (28,18) (15,26) (30,8) (28,6) (30,19) (11,15) (20,12) (12,29) (5,24) (18,11) (16,4) (16,14) (24,4) (12,2) (0,27) (19,3) (1,13) (26,22) (13,10) (23,9) (7,28) (29,27) (9,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph85", "image": "data/cycle/graph_visual/hard/graph85.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (21,3) (20,6) (15,19) (8,12) (9,23) (5,22) (19,1) (2,0) (13,7) (5,14) (9,1) (19,16) (24,4) (14,24) (5,3) (1,5) (10,14) (13,15) (13,11) (21,20) (8,18) (25,21) (17,13) (6,8) (2,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph733", "image": "data/cycle/graph_visual/hard/graph733.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (24,18) (10,2) (0,28) (11,27) (7,3) (31,20) (6,31) (0,23) (15,25) (13,17) (0,30) (29,19) (32,14) (25,31) (2,18) (23,9) (1,4) (26,8) (10,25) (6,7) (9,10) (11,22) (26,4) (15,19) (2,13) (28,14) (28,26) (27,16) (7,11) (17,12) (17,21) (29,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1367", "image": "data/cycle/graph_visual/hard/graph1367.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (0,22) (2,26) (8,20) (16,18) (23,8) (28,9) (1,0) (19,5) (18,1) (7,28) (20,5) (27,5) (24,0) (0,2) (5,21) (25,3) (6,2) (16,15) (13,9) (11,5) (27,15) (10,7) (0,16) (0,3) (15,26) (24,28) (4,5) (21,14) (14,12) (0,4) (11,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph187", "image": "data/cycle/graph_visual/hard/graph187.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (26,17) (9,21) (12,15) (0,3) (13,8) (18,9) (8,23) (19,18) (15,2) (22,16) (12,16) (24,0) (1,8) (16,7) (14,5) (14,3) (15,10) (24,25) (20,5) (14,6) (11,17) (6,16) (3,4) (2,18) (0,13) (13,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1147", "image": "data/cycle/graph_visual/hard/graph1147.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (18,4) (3,0) (16,12) (2,24) (21,13) (21,11) (2,0) (10,22) (0,1) (17,21) (20,26) (8,25) (0,4) (23,1) (16,15) (15,8) (2,10) (8,24) (19,22) (13,5) (0,14) (15,23) (1,7) (22,3) (18,21) (3,11) (6,14) (14,21) (24,9) (23,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph661", "image": "data/cycle/graph_visual/hard/graph661.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (27,17) (13,2) (23,27) (18,23) (5,3) (29,0) (0,23) (5,26) (30,0) (28,2) (7,5) (2,8) (14,1) (24,16) (18,24) (26,13) (12,6) (29,6) (27,25) (1,20) (22,4) (9,21) (11,28) (3,9) (18,15) (28,19) (14,4) (10,23) (26,4) (31,20) (23,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1999", "image": "data/cycle/graph_visual/hard/graph1999.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (7,2) (10,6) (27,10) (22,1) (10,19) (13,25) (4,30) (18,34) (5,6) (0,31) (17,7) (3,4) (0,1) (3,0) (29,18) (11,25) (9,16) (2,0) (4,32) (5,18) (15,22) (21,13) (24,7) (9,11) (2,20) (5,33) (18,28) (10,3) (13,30) (14,30) (14,26) (8,7) (12,5) (25,23) (21,31) (23,22) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1921", "image": "data/cycle/graph_visual/hard/graph1921.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (2,8) (32,11) (33,21) (10,31) (3,18) (5,34) (27,12) (23,31) (14,24) (6,21) (20,9) (9,30) (3,8) (6,15) (32,26) (17,34) (19,10) (1,0) (4,1) (30,27) (4,27) (18,21) (28,9) (12,16) (32,25) (8,4) (13,14) (13,1) (29,13) (10,8) (17,15) (6,22) (0,20) (32,31) (7,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph687", "image": "data/cycle/graph_visual/hard/graph687.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (8,21) (25,0) (24,29) (23,28) (14,21) (31,23) (19,9) (9,1) (12,14) (23,14) (18,5) (20,1) (4,2) (3,11) (19,10) (11,8) (24,13) (20,5) (22,15) (6,22) (17,16) (1,26) (15,30) (29,14) (28,0) (27,4) (7,23) (4,18) (17,22) (22,31) (16,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph974", "image": "data/cycle/graph_visual/hard/graph974.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (23,31) (11,14) (7,22) (1,24) (28,9) (10,32) (3,5) (21,6) (22,17) (13,34) (17,6) (27,32) (24,3) (33,9) (20,24) (21,26) (33,13) (22,0) (23,14) (19,25) (16,23) (1,8) (15,4) (33,2) (12,1) (18,19) (6,29) (9,0) (18,24) (10,19) (20,13) (5,30) (27,4) (16,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph583", "image": "data/cycle/graph_visual/hard/graph583.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (15,14) (9,16) (2,25) (24,22) (21,17) (0,24) (7,1) (22,27) (6,12) (8,11) (3,11) (0,11) (13,1) (1,12) (30,25) (25,20) (11,28) (23,9) (23,15) (10,13) (2,17) (24,29) (29,15) (18,4) (24,25) (18,26) (20,1) (6,26) (19,21) (5,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph26", "image": "data/cycle/graph_visual/hard/graph26.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,9) (16,25) (15,11) (12,2) (12,1) (16,6) (3,18) (19,25) (8,15) (23,6) (10,20) (14,24) (7,9) (8,1) (23,21) (24,19) (5,0) (22,3) (20,18) (6,0) (4,24) (13,17) (1,9) (13,3) (18,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph367", "image": "data/cycle/graph_visual/hard/graph367.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (24,18) (1,24) (16,11) (23,4) (9,5) (7,26) (17,26) (11,4) (22,15) (12,13) (6,8) (9,13) (27,0) (14,19) (3,0) (16,12) (9,18) (10,28) (15,28) (7,19) (0,25) (14,28) (3,2) (23,6) (8,14) (2,20) (2,22) (21,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph953", "image": "data/cycle/graph_visual/hard/graph953.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,21) (5,17) (7,3) (23,9) (5,26) (4,32) (10,27) (29,1) (29,22) (6,24) (10,29) (16,8) (27,28) (26,14) (13,34) (18,13) (7,8) (30,28) (18,6) (11,19) (10,31) (0,11) (14,33) (13,17) (2,24) (25,21) (17,12) (32,8) (10,15) (5,23) (32,20) (21,2) (24,4) (3,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1863", "image": "data/cycle/graph_visual/hard/graph1863.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (13,18) (12,14) (1,14) (8,7) (6,0) (18,2) (7,14) (16,0) (19,27) (20,17) (0,2) (21,18) (7,32) (24,11) (20,25) (9,11) (28,22) (3,26) (21,29) (25,24) (10,30) (33,2) (26,32) (1,0) (19,24) (4,6) (5,33) (0,3) (18,6) (31,4) (15,1) (4,22) (10,23) (10,7) (6,20) (17,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1487", "image": "data/cycle/graph_visual/hard/graph1487.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (9,1) (26,7) (4,24) (27,12) (13,3) (13,24) (6,0) (15,17) (27,28) (9,14) (1,15) (29,26) (3,18) (26,23) (20,24) (27,19) (0,1) (1,8) (0,2) (18,21) (11,0) (18,9) (23,21) (3,27) (10,26) (8,22) (29,5) (20,16) (25,18) (6,29) (2,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph998", "image": "data/cycle/graph_visual/hard/graph998.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (20,21) (13,2) (12,14) (11,10) (29,22) (10,25) (31,26) (4,19) (5,30) (1,7) (28,0) (11,6) (3,24) (5,15) (31,19) (18,9) (13,8) (9,17) (33,1) (23,2) (34,4) (27,28) (7,24) (10,16) (0,18) (23,33) (21,4) (10,12) (20,13) (34,32) (20,10) (28,19) (31,29) (5,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1527", "image": "data/cycle/graph_visual/hard/graph1527.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,4) (18,10) (15,28) (14,18) (26,9) (6,0) (12,18) (8,9) (18,28) (7,21) (9,13) (15,8) (28,19) (0,3) (2,0) (17,23) (5,2) (24,25) (26,27) (16,20) (2,17) (15,6) (22,3) (1,4) (25,14) (11,22) (21,20) (29,30) (30,20) (21,1) (11,2) (1,0) (8,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1035", "image": "data/cycle/graph_visual/hard/graph1035.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (6,12) (21,20) (22,11) (4,7) (24,15) (10,6) (4,9) (22,15) (13,1) (2,4) (12,8) (25,12) (1,2) (12,19) (5,11) (16,6) (15,18) (14,0) (17,16) (6,18) (0,1) (25,7) (14,23) (12,14) (2,0) (0,3) (0,20) (3,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph513", "image": "data/cycle/graph_visual/hard/graph513.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (16,30) (15,10) (20,0) (14,0) (6,28) (4,23) (1,17) (30,7) (13,26) (13,19) (1,3) (5,26) (17,12) (21,1) (25,13) (1,29) (0,7) (2,8) (23,8) (16,9) (5,4) (27,15) (30,5) (11,18) (11,27) (14,12) (25,24) (11,14) (20,28) (22,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1269", "image": "data/cycle/graph_visual/hard/graph1269.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (15,19) (4,20) (22,24) (14,8) (7,23) (7,17) (27,11) (11,10) (2,11) (2,4) (6,0) (23,15) (15,13) (5,9) (6,3) (16,7) (13,5) (22,18) (12,19) (1,4) (1,0) (9,25) (26,15) (22,26) (0,2) (3,23) (0,21) (11,22) (14,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph803", "image": "data/cycle/graph_visual/hard/graph803.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (27,32) (4,9) (31,21) (26,6) (15,0) (23,1) (32,17) (0,22) (16,13) (10,18) (14,30) (7,31) (30,12) (5,33) (7,23) (4,25) (2,28) (26,27) (3,10) (33,19) (29,14) (13,30) (20,15) (24,27) (28,26) (14,2) (18,11) (8,26) (1,9) (21,2) (5,9) (0,23) (32,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph573", "image": "data/cycle/graph_visual/hard/graph573.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (5,11) (3,7) (20,23) (2,1) (8,30) (0,14) (4,10) (26,12) (14,25) (12,2) (28,26) (17,1) (16,6) (15,30) (9,12) (2,15) (14,12) (15,24) (19,4) (22,13) (18,29) (6,11) (4,7) (28,6) (6,18) (7,25) (20,0) (21,16) (15,27) (22,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph335", "image": "data/cycle/graph_visual/hard/graph335.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (3,21) (27,19) (22,5) (18,11) (19,15) (17,28) (24,13) (17,26) (4,14) (3,14) (1,2) (12,28) (15,22) (25,20) (4,7) (25,18) (12,13) (14,19) (0,23) (16,13) (1,9) (9,21) (22,10) (11,19) (24,6) (0,16) (24,27) (8,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1389", "image": "data/cycle/graph_visual/hard/graph1389.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (23,4) (16,0) (19,4) (22,11) (24,21) (21,9) (25,14) (7,9) (4,1) (20,6) (0,1) (23,24) (3,18) (15,20) (1,20) (26,14) (6,18) (2,0) (28,5) (16,10) (12,1) (2,14) (26,0) (6,28) (28,8) (8,11) (17,21) (16,28) (27,23) (7,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph378", "image": "data/cycle/graph_visual/hard/graph378.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,14) (7,16) (23,26) (10,20) (10,18) (17,28) (22,28) (23,6) (13,12) (14,3) (25,17) (24,6) (4,0) (17,2) (12,21) (18,23) (5,9) (15,11) (25,15) (15,8) (1,15) (14,19) (7,14) (28,9) (12,28) (1,6) (17,4) (19,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph281", "image": "data/cycle/graph_visual/hard/graph281.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,19) (10,26) (2,25) (2,7) (11,25) (5,17) (20,11) (18,1) (5,14) (13,23) (22,13) (7,8) (21,17) (22,1) (0,9) (5,19) (4,7) (6,4) (22,15) (8,1) (12,14) (16,3) (0,19) (18,27) (23,3) (20,24) (21,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1028", "image": "data/cycle/graph_visual/hard/graph1028.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (2,0) (0,13) (25,13) (1,12) (4,5) (20,25) (4,11) (23,0) (17,25) (18,9) (21,2) (15,18) (10,1) (21,5) (8,7) (1,7) (25,24) (4,12) (14,15) (9,6) (3,0) (16,8) (22,2) (10,14) (19,25) (3,9) (20,7) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph490", "image": "data/cycle/graph_visual/hard/graph490.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (22,29) (20,17) (28,3) (24,12) (11,28) (24,2) (6,28) (8,12) (25,22) (29,15) (17,22) (10,23) (9,26) (8,16) (3,27) (10,28) (14,3) (19,10) (26,7) (13,17) (4,23) (26,15) (6,5) (20,21) (0,11) (24,18) (8,0) (2,26) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1793", "image": "data/cycle/graph_visual/hard/graph1793.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,1) (14,32) (31,20) (26,8) (19,29) (25,10) (0,4) (17,13) (30,0) (15,25) (12,17) (22,11) (23,9) (16,27) (31,25) (0,28) (28,26) (21,17) (0,23) (28,14) (29,5) (9,10) (2,18) (6,31) (10,2) (13,2) (3,7) (24,18) (0,3) (26,4) (11,7) (15,19) (2,0) (4,1) (6,7) (27,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph3", "image": "data/cycle/graph_visual/hard/graph3.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (23,7) (1,13) (25,20) (2,7) (19,18) (11,1) (21,8) (3,18) (6,14) (18,0) (22,5) (4,25) (10,2) (6,0) (8,20) (15,10) (9,1) (1,5) (13,4) (13,12) (15,16) (24,16) (14,15) (11,23) (15,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph485", "image": "data/cycle/graph_visual/hard/graph485.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (4,3) (19,27) (24,10) (21,13) (1,3) (20,2) (22,9) (6,19) (18,3) (24,8) (10,16) (16,2) (20,12) (14,11) (7,28) (13,25) (4,14) (17,10) (21,26) (22,21) (9,5) (21,23) (12,7) (12,25) (4,26) (6,22) (15,14) (29,0) (8,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph184", "image": "data/cycle/graph_visual/hard/graph184.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (25,1) (16,13) (6,1) (10,15) (26,13) (11,14) (1,18) (19,4) (11,5) (12,14) (20,0) (1,17) (8,3) (5,23) (25,21) (24,20) (9,16) (4,5) (11,15) (17,12) (23,8) (22,13) (14,0) (26,2) (7,2) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph924", "image": "data/cycle/graph_visual/hard/graph924.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (0,13) (5,27) (30,20) (19,30) (10,25) (1,23) (23,8) (19,34) (32,7) (3,19) (0,1) (33,29) (27,32) (9,15) (29,11) (13,20) (22,4) (29,26) (7,24) (10,26) (4,23) (6,16) (8,21) (28,1) (18,33) (31,6) (18,14) (28,12) (33,31) (24,8) (11,17) (4,2) (29,13) (16,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1859", "image": "data/cycle/graph_visual/hard/graph1859.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (26,8) (33,3) (4,13) (21,5) (10,7) (0,31) (7,32) (2,31) (15,31) (32,19) (30,18) (1,2) (33,8) (33,10) (20,6) (4,11) (12,29) (1,0) (3,22) (17,6) (12,18) (25,23) (23,0) (24,30) (9,19) (16,1) (21,20) (5,28) (28,12) (9,13) (27,0) (14,15) (33,2) (21,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph421", "image": "data/cycle/graph_visual/hard/graph421.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (25,17) (9,27) (21,0) (27,28) (1,17) (6,8) (7,10) (29,21) (14,4) (2,10) (13,16) (15,14) (24,14) (26,13) (3,11) (7,18) (6,29) (0,1) (7,15) (25,10) (20,9) (9,7) (1,12) (23,26) (19,9) (26,2) (12,5) (22,24) (9,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph982", "image": "data/cycle/graph_visual/hard/graph982.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (23,15) (9,18) (17,6) (8,18) (30,22) (8,34) (1,25) (2,34) (27,33) (8,19) (5,29) (31,7) (25,4) (12,13) (24,1) (19,31) (24,16) (1,15) (29,25) (28,10) (34,22) (16,13) (33,10) (0,21) (15,17) (4,32) (1,11) (3,14) (17,7) (3,25) (0,33) (5,20) (26,4) (27,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph407", "image": "data/cycle/graph_visual/hard/graph407.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (21,24) (0,15) (15,16) (7,23) (24,15) (20,9) (10,7) (11,3) (13,7) (2,19) (4,11) (8,11) (14,22) (2,17) (4,27) (20,17) (28,26) (25,29) (28,12) (22,10) (18,10) (8,5) (6,2) (21,17) (26,3) (11,10) (7,6) (2,29) (1,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1163", "image": "data/cycle/graph_visual/hard/graph1163.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (10,11) (2,11) (9,5) (7,23) (4,1) (19,12) (15,13) (9,24) (26,15) (5,13) (0,3) (15,19) (0,6) (22,26) (2,0) (4,2) (0,1) (20,4) (18,22) (25,22) (7,17) (16,7) (0,4) (6,3) (8,14) (0,11) (14,5) (23,22) (3,23) (15,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph787", "image": "data/cycle/graph_visual/hard/graph787.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,7) (1,13) (13,14) (30,9) (0,20) (32,24) (6,19) (5,19) (28,27) (15,6) (32,23) (1,4) (8,3) (27,4) (8,2) (31,29) (14,22) (30,10) (15,32) (10,8) (18,3) (21,31) (12,27) (18,21) (8,4) (11,12) (31,20) (9,25) (6,21) (17,9) (13,26) (10,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph768", "image": "data/cycle/graph_visual/hard/graph768.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (19,10) (27,3) (3,14) (18,23) (16,1) (15,0) (18,25) (26,25) (18,19) (24,32) (12,17) (6,16) (5,23) (6,11) (15,30) (29,11) (17,28) (21,5) (21,24) (9,20) (7,6) (1,13) (9,5) (10,12) (30,13) (8,25) (23,14) (4,22) (2,19) (4,1) (31,32) (17,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph575", "image": "data/cycle/graph_visual/hard/graph575.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,12) (9,21) (27,10) (6,9) (19,26) (15,18) (0,27) (23,0) (17,1) (7,13) (23,13) (26,3) (29,28) (13,9) (30,14) (22,19) (14,29) (8,5) (30,20) (17,25) (15,11) (5,2) (16,21) (11,30) (30,8) (24,8) (3,4) (26,13) (0,17) (11,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph667", "image": "data/cycle/graph_visual/hard/graph667.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (24,17) (15,12) (0,8) (6,12) (23,6) (9,11) (7,10) (2,12) (30,19) (14,5) (13,1) (27,11) (4,31) (17,22) (16,25) (3,8) (0,19) (31,0) (21,11) (2,18) (26,9) (25,11) (29,21) (28,25) (16,10) (23,30) (20,23) (5,17) (7,6) (8,1) (24,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph670", "image": "data/cycle/graph_visual/hard/graph670.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (7,22) (8,6) (29,9) (18,13) (4,29) (30,26) (3,28) (0,24) (14,27) (19,21) (19,13) (0,31) (11,4) (5,20) (4,26) (4,22) (10,29) (21,16) (25,17) (30,5) (0,8) (17,21) (21,8) (2,16) (14,9) (20,3) (5,25) (1,5) (10,23) (26,15) (9,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1820", "image": "data/cycle/graph_visual/hard/graph1820.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (32,21) (28,21) (23,17) (4,10) (24,0) (27,23) (25,32) (1,23) (12,27) (0,4) (21,8) (8,7) (16,33) (29,31) (20,5) (30,33) (23,22) (19,6) (30,4) (1,15) (6,31) (5,10) (9,11) (31,3) (3,14) (0,6) (0,2) (13,16) (21,2) (20,15) (1,0) (26,0) (18,9) (3,1) (21,10) (3,0) (17,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph677", "image": "data/cycle/graph_visual/hard/graph677.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (16,15) (21,15) (14,19) (25,4) (28,19) (14,23) (19,18) (19,11) (3,12) (26,0) (15,24) (20,28) (26,24) (14,21) (7,29) (4,1) (18,17) (23,2) (31,22) (9,25) (27,5) (29,21) (8,24) (12,10) (3,30) (9,6) (5,21) (6,31) (29,1) (13,26) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph696", "image": "data/cycle/graph_visual/hard/graph696.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,9) (3,21) (30,15) (19,25) (9,28) (1,28) (18,22) (14,28) (14,24) (29,2) (13,4) (17,18) (21,29) (1,27) (24,5) (15,28) (31,18) (20,22) (22,27) (11,24) (8,26) (10,12) (0,20) (1,7) (19,13) (4,8) (11,19) (21,11) (30,6) (0,16) (23,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1501", "image": "data/cycle/graph_visual/hard/graph1501.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (13,18) (1,4) (23,20) (27,23) (0,5) (7,8) (28,11) (18,2) (0,16) (13,26) (2,0) (3,0) (16,20) (24,0) (3,10) (10,25) (12,29) (17,2) (15,26) (1,0) (15,30) (14,29) (9,21) (9,28) (13,20) (25,19) (30,6) (22,2) (8,29) (8,17) (25,5) (0,4) (17,11) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1502", "image": "data/cycle/graph_visual/hard/graph1502.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (5,17) (23,0) (8,23) (23,6) (21,10) (25,3) (27,23) (0,1) (24,29) (27,21) (16,22) (28,11) (13,7) (16,3) (14,10) (20,24) (26,9) (15,13) (22,4) (15,8) (29,12) (26,19) (14,1) (24,25) (2,30) (14,17) (7,18) (19,18) (5,11) (20,17) (30,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1447", "image": "data/cycle/graph_visual/hard/graph1447.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,4) (8,26) (29,3) (20,3) (6,15) (5,13) (27,23) (21,5) (12,6) (18,10) (14,0) (19,4) (20,23) (4,25) (23,9) (21,16) (11,5) (22,2) (2,17) (0,1) (5,6) (0,24) (3,0) (12,7) (0,2) (25,29) (14,28) (24,26) (24,18) (27,14) (1,22) (22,21) (9,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1032", "image": "data/cycle/graph_visual/hard/graph1032.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (11,25) (6,0) (0,1) (11,20) (9,16) (10,14) (0,5) (22,4) (15,1) (22,14) (3,10) (7,21) (3,7) (24,12) (0,4) (6,2) (19,4) (18,21) (12,8) (0,2) (3,0) (0,17) (5,16) (22,11) (23,13) (7,5) (8,23) (11,8) (25,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph176", "image": "data/cycle/graph_visual/hard/graph176.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (3,12) (20,3) (20,13) (5,24) (2,1) (12,11) (18,4) (6,19) (9,15) (11,1) (26,18) (25,12) (16,5) (13,9) (17,10) (10,15) (16,19) (21,12) (26,23) (23,0) (8,0) (22,0) (14,7) (11,19) (20,23) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph467", "image": "data/cycle/graph_visual/hard/graph467.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,19) (15,13) (22,12) (23,18) (9,15) (26,28) (15,25) (17,25) (29,0) (2,19) (15,1) (10,21) (1,6) (14,17) (4,14) (6,27) (9,8) (6,23) (3,4) (11,28) (17,5) (29,24) (14,7) (12,28) (18,10) (16,12) (23,28) (29,2) (7,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1167", "image": "data/cycle/graph_visual/hard/graph1167.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (6,2) (17,18) (20,7) (22,21) (0,2) (16,2) (24,26) (17,21) (10,11) (7,9) (24,14) (12,22) (4,11) (2,26) (10,15) (17,2) (15,0) (7,6) (3,0) (20,8) (8,1) (15,13) (19,10) (0,1) (5,11) (3,25) (11,3) (7,10) (4,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1416", "image": "data/cycle/graph_visual/hard/graph1416.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (10,0) (10,3) (22,27) (16,5) (6,19) (29,11) (14,26) (20,8) (2,0) (2,6) (14,24) (2,8) (16,22) (3,0) (26,15) (12,8) (7,19) (6,18) (29,4) (11,16) (26,28) (0,1) (0,26) (4,13) (25,0) (19,1) (24,4) (17,24) (23,1) (16,21) (9,25) (16,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1741", "image": "data/cycle/graph_visual/hard/graph1741.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (16,25) (13,31) (6,7) (15,12) (10,7) (17,24) (17,22) (11,21) (2,18) (20,23) (19,30) (8,1) (25,28) (25,11) (9,26) (17,5) (1,0) (32,16) (29,21) (12,6) (12,2) (32,19) (1,14) (10,31) (23,30) (23,24) (32,3) (6,23) (5,0) (0,8) (8,4) (11,27) (11,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1994", "image": "data/cycle/graph_visual/hard/graph1994.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (23,5) (17,12) (1,0) (2,6) (9,30) (33,18) (5,30) (2,8) (6,24) (7,16) (2,12) (27,21) (1,17) (6,18) (0,9) (27,31) (3,5) (10,0) (14,1) (0,2) (16,26) (3,0) (34,22) (15,31) (32,12) (25,12) (13,20) (31,4) (5,21) (16,29) (11,23) (26,23) (4,0) (19,26) (20,34) (34,12) (28,16) (6,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph409", "image": "data/cycle/graph_visual/hard/graph409.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,12) (17,21) (26,23) (13,23) (0,24) (6,9) (2,13) (3,29) (12,7) (24,5) (3,22) (8,27) (10,25) (20,27) (1,16) (19,17) (9,5) (16,25) (16,28) (8,21) (14,11) (10,20) (18,22) (7,0) (15,22) (9,11) (8,13) (4,25) (29,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph55", "image": "data/cycle/graph_visual/hard/graph55.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (10,14) (16,8) (0,23) (25,17) (22,2) (20,25) (13,25) (21,2) (3,9) (21,5) (8,7) (4,11) (15,14) (24,25) (5,4) (9,6) (4,12) (1,10) (0,13) (18,9) (1,12) (18,15) (20,7) (7,1) (19,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1075", "image": "data/cycle/graph_visual/hard/graph1075.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (24,8) (3,0) (0,1) (13,3) (12,23) (10,19) (13,4) (22,15) (10,11) (22,10) (17,1) (24,7) (19,1) (9,25) (21,20) (19,23) (2,0) (16,14) (14,11) (23,9) (13,6) (20,0) (22,8) (18,11) (11,2) (3,2) (5,18) (5,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph969", "image": "data/cycle/graph_visual/hard/graph969.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (8,18) (34,9) (25,3) (24,26) (4,28) (20,32) (10,25) (4,15) (3,11) (17,6) (5,22) (7,34) (27,3) (6,23) (1,9) (30,14) (0,20) (26,18) (8,2) (2,13) (19,3) (16,34) (5,27) (9,26) (14,2) (7,29) (4,12) (13,21) (32,25) (15,5) (7,33) (14,3) (27,23) (3,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph871", "image": "data/cycle/graph_visual/hard/graph871.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (31,10) (15,17) (28,13) (16,10) (14,23) (20,6) (6,15) (19,5) (30,31) (13,1) (27,12) (3,8) (30,9) (32,25) (4,8) (19,9) (10,8) (17,33) (24,32) (13,14) (4,1) (11,12) (31,22) (3,18) (32,7) (0,20) (6,21) (2,8) (27,29) (9,26) (21,18) (27,4) (32,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1695", "image": "data/cycle/graph_visual/hard/graph1695.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (13,0) (18,7) (25,4) (6,22) (27,16) (1,0) (8,4) (3,0) (10,29) (19,2) (12,7) (6,24) (11,22) (2,13) (19,20) (25,30) (26,27) (26,22) (28,4) (17,6) (11,20) (10,12) (19,5) (24,1) (15,2) (4,29) (22,12) (21,30) (9,30) (23,6) (8,31) (2,0) (14,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1796", "image": "data/cycle/graph_visual/hard/graph1796.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,24) (0,1) (19,30) (4,11) (31,5) (8,6) (9,30) (15,27) (26,3) (0,15) (16,32) (20,22) (14,25) (10,22) (24,0) (27,7) (13,23) (4,23) (6,30) (14,5) (28,9) (17,20) (21,19) (17,21) (9,1) (6,16) (32,23) (1,31) (10,2) (27,29) (18,2) (26,25) (12,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph899", "image": "data/cycle/graph_visual/hard/graph899.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (21,10) (2,17) (7,9) (20,1) (18,21) (17,10) (30,13) (29,9) (33,6) (10,22) (27,23) (11,32) (7,30) (16,4) (29,4) (26,2) (15,10) (14,11) (5,33) (12,6) (1,10) (3,2) (10,28) (27,4) (25,30) (26,0) (10,11) (3,19) (31,14) (33,14) (26,24) (23,26) (8,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph943", "image": "data/cycle/graph_visual/hard/graph943.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,9) (13,16) (30,12) (23,7) (21,2) (10,18) (4,25) (18,11) (5,9) (3,10) (14,2) (24,27) (23,0) (13,30) (27,26) (32,11) (34,5) (32,17) (14,30) (31,7) (15,20) (33,31) (8,26) (2,28) (1,23) (34,21) (26,28) (29,14) (22,0) (19,33) (1,9) (6,26) (32,27) (15,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph97", "image": "data/cycle/graph_visual/hard/graph97.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,16) (2,6) (6,13) (19,9) (22,13) (4,12) (20,13) (4,24) (17,10) (5,20) (6,8) (25,22) (21,19) (1,23) (17,15) (11,1) (7,24) (24,14) (18,21) (0,23) (15,1) (23,13) (3,21) (19,16) (7,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph438", "image": "data/cycle/graph_visual/hard/graph438.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (2,11) (27,26) (6,0) (11,8) (2,5) (22,11) (14,25) (21,20) (20,29) (8,9) (6,15) (23,17) (9,26) (8,15) (18,12) (14,18) (25,24) (28,19) (3,22) (7,21) (17,2) (28,15) (18,28) (4,23) (4,1) (20,16) (13,9) (18,10) (1,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph749", "image": "data/cycle/graph_visual/hard/graph749.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (18,5) (6,31) (20,11) (20,16) (0,29) (3,20) (12,24) (14,21) (29,12) (8,13) (1,23) (29,9) (10,19) (26,6) (25,3) (21,20) (32,10) (19,9) (18,22) (15,13) (2,15) (16,7) (26,3) (9,14) (28,7) (28,17) (17,22) (4,2) (3,8) (8,1) (11,27) (32,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1400", "image": "data/cycle/graph_visual/hard/graph1400.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (29,25) (16,21) (26,10) (1,11) (14,0) (6,13) (13,15) (28,26) (27,9) (2,15) (9,24) (20,7) (20,22) (9,0) (21,10) (23,19) (25,0) (5,9) (14,12) (19,9) (15,3) (0,7) (21,4) (7,11) (7,8) (22,17) (18,8) (23,4) (27,13) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1993", "image": "data/cycle/graph_visual/hard/graph1993.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (12,5) (10,31) (29,23) (16,0) (4,20) (10,2) (1,15) (24,32) (21,32) (14,12) (19,3) (9,12) (22,8) (28,6) (15,9) (12,3) (3,0) (20,27) (17,16) (1,25) (26,33) (5,16) (8,29) (1,6) (11,0) (24,12) (20,33) (1,0) (18,32) (1,22) (34,9) (7,32) (0,2) (2,22) (9,13) (4,0) (23,30) (28,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph547", "image": "data/cycle/graph_visual/hard/graph547.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (23,6) (25,6) (21,30) (5,18) (28,11) (29,13) (7,26) (19,4) (23,26) (14,8) (4,21) (17,30) (0,24) (8,0) (27,13) (20,18) (15,2) (1,0) (10,24) (15,18) (10,11) (15,8) (3,25) (9,2) (24,12) (17,29) (16,1) (27,23) (24,22) (25,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph553", "image": "data/cycle/graph_visual/hard/graph553.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,22) (24,8) (16,18) (1,7) (17,26) (2,18) (12,15) (4,9) (20,27) (13,15) (15,23) (17,5) (17,15) (29,10) (27,30) (15,22) (26,29) (26,21) (17,8) (18,3) (0,19) (0,29) (25,7) (28,17) (20,14) (2,19) (12,20) (7,6) (11,19) (11,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph711", "image": "data/cycle/graph_visual/hard/graph711.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (0,10) (19,7) (27,4) (5,12) (22,10) (24,0) (32,14) (12,22) (7,22) (26,8) (14,29) (25,28) (0,20) (14,6) (24,9) (6,2) (11,29) (29,17) (1,12) (8,30) (23,30) (7,26) (18,27) (28,14) (14,13) (24,15) (3,20) (31,14) (30,27) (32,9) (14,16) (21,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph33", "image": "data/cycle/graph_visual/hard/graph33.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,22) (13,25) (23,12) (4,19) (6,19) (5,4) (14,17) (16,20) (1,3) (5,11) (19,9) (10,22) (8,17) (24,14) (5,12) (24,6) (21,6) (20,6) (0,6) (15,7) (3,4) (13,18) (4,7) (13,0) (23,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph294", "image": "data/cycle/graph_visual/hard/graph294.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,18) (24,7) (26,4) (20,18) (15,9) (21,26) (4,14) (27,10) (12,8) (10,2) (5,6) (23,4) (24,19) (12,27) (17,23) (12,5) (13,22) (10,23) (14,0) (1,12) (11,18) (21,7) (3,7) (24,22) (8,16) (0,25) (17,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1242", "image": "data/cycle/graph_visual/hard/graph1242.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,5) (17,22) (0,1) (7,11) (24,12) (23,8) (26,13) (18,19) (16,21) (0,3) (4,24) (13,23) (15,6) (18,6) (19,23) (4,0) (2,17) (6,3) (12,16) (9,19) (4,7) (6,27) (2,14) (1,12) (2,19) (0,2) (25,15) (5,10) (12,0) (21,22) (20,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph985", "image": "data/cycle/graph_visual/hard/graph985.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (30,32) (29,21) (2,32) (23,17) (22,33) (7,28) (10,12) (22,13) (10,25) (5,7) (7,3) (11,13) (20,4) (16,27) (19,7) (32,33) (6,19) (0,12) (16,17) (15,17) (28,9) (32,1) (28,24) (15,26) (20,29) (8,2) (9,26) (17,20) (31,0) (14,8) (10,34) (14,28) (0,27) (11,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1375", "image": "data/cycle/graph_visual/hard/graph1375.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (4,9) (12,8) (16,19) (1,0) (2,28) (18,6) (18,15) (26,12) (10,6) (4,7) (7,3) (6,16) (15,23) (6,28) (7,25) (12,21) (5,11) (25,15) (0,14) (14,24) (12,14) (1,2) (4,17) (2,12) (1,13) (20,22) (22,11) (27,26) (0,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1906", "image": "data/cycle/graph_visual/hard/graph1906.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (5,2) (8,24) (31,32) (22,18) (16,7) (33,32) (6,33) (2,15) (30,9) (1,33) (26,6) (1,0) (7,29) (4,33) (20,16) (3,27) (25,12) (17,28) (15,13) (20,3) (34,19) (20,21) (9,19) (8,13) (26,3) (14,9) (28,11) (23,1) (10,18) (29,12) (17,22) (14,21) (20,11) (0,29) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph224", "image": "data/cycle/graph_visual/hard/graph224.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (13,10) (5,26) (16,8) (0,7) (9,22) (4,23) (3,24) (25,6) (18,27) (2,20) (4,27) (19,14) (4,8) (2,10) (14,5) (22,21) (24,13) (1,2) (21,10) (18,2) (17,11) (9,6) (27,7) (22,15) (0,19) (12,19) (27,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1031", "image": "data/cycle/graph_visual/hard/graph1031.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,10) (6,25) (13,9) (10,20) (22,18) (1,0) (15,1) (2,11) (21,15) (16,22) (12,14) (23,11) (25,17) (20,0) (17,4) (6,7) (2,12) (5,24) (10,9) (10,14) (5,3) (0,16) (25,22) (0,19) (15,11) (10,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1292", "image": "data/cycle/graph_visual/hard/graph1292.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (24,22) (2,25) (5,8) (23,22) (27,25) (23,9) (19,3) (4,12) (19,15) (22,13) (18,21) (11,5) (0,3) (7,12) (1,0) (6,23) (0,22) (14,17) (0,4) (2,1) (20,0) (19,4) (2,0) (7,10) (4,20) (16,11) (17,22) (26,10) (11,9) (25,22) (19,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph640", "image": "data/cycle/graph_visual/hard/graph640.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (30,10) (20,29) (2,24) (14,26) (11,19) (29,28) (9,23) (7,8) (5,26) (13,18) (28,27) (27,10) (10,25) (24,6) (31,17) (21,2) (4,24) (18,6) (5,17) (3,7) (29,1) (0,21) (8,4) (12,17) (22,5) (10,15) (21,23) (0,11) (14,13) (3,15) (16,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1046", "image": "data/cycle/graph_visual/hard/graph1046.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (17,20) (3,0) (19,25) (0,5) (16,11) (3,10) (20,1) (8,4) (22,23) (1,13) (24,21) (13,5) (21,15) (0,4) (23,1) (4,14) (16,7) (23,14) (17,16) (11,2) (7,19) (6,3) (24,8) (2,0) (24,9) (0,1) (18,1) (10,17) (25,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph983", "image": "data/cycle/graph_visual/hard/graph983.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (13,1) (33,11) (5,4) (2,12) (23,2) (27,7) (34,21) (6,21) (10,21) (20,19) (0,1) (8,19) (29,9) (14,3) (28,23) (7,6) (25,10) (5,6) (31,0) (14,8) (1,15) (11,26) (30,5) (5,32) (31,2) (20,29) (22,34) (33,16) (19,24) (18,31) (17,24) (5,19) (19,16) (12,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1729", "image": "data/cycle/graph_visual/hard/graph1729.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (22,20) (12,32) (2,0) (9,18) (1,31) (27,28) (4,25) (3,0) (27,30) (15,14) (30,8) (21,10) (21,4) (27,17) (14,21) (20,13) (15,7) (5,11) (31,0) (19,6) (26,21) (22,9) (12,6) (14,0) (29,5) (17,21) (27,6) (23,3) (22,23) (5,4) (12,24) (14,20) (16,5) (2,17) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1178", "image": "data/cycle/graph_visual/hard/graph1178.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (20,26) (14,23) (5,10) (22,2) (19,22) (24,17) (14,25) (6,11) (23,20) (15,21) (14,0) (4,18) (13,6) (24,0) (16,2) (23,9) (8,18) (5,6) (9,21) (12,5) (25,4) (21,5) (1,22) (26,7) (3,12) (22,24) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1947", "image": "data/cycle/graph_visual/hard/graph1947.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (27,32) (9,11) (5,11) (1,0) (3,0) (24,3) (26,2) (9,6) (14,24) (2,0) (28,16) (34,17) (3,33) (14,5) (25,34) (13,22) (34,12) (1,5) (27,12) (15,30) (18,24) (5,32) (29,14) (20,23) (2,14) (2,16) (19,24) (0,29) (22,25) (27,20) (32,21) (10,19) (30,32) (0,31) (8,5) (4,12) (7,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1719", "image": "data/cycle/graph_visual/hard/graph1719.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (7,30) (1,4) (5,14) (15,2) (23,27) (22,11) (17,14) (26,29) (22,13) (26,12) (20,3) (9,31) (1,27) (21,20) (3,0) (8,0) (11,16) (3,7) (9,32) (25,19) (8,11) (17,3) (19,28) (25,11) (5,15) (10,7) (16,1) (0,2) (11,12) (0,1) (21,16) (18,20) (19,32) (24,3) (28,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph382", "image": "data/cycle/graph_visual/hard/graph382.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (12,14) (8,28) (0,20) (24,13) (11,18) (21,1) (16,10) (8,3) (4,22) (23,25) (1,27) (6,1) (14,11) (5,25) (15,16) (0,14) (26,13) (12,17) (0,7) (26,20) (17,1) (4,5) (28,2) (23,9) (19,13) (7,2) (11,5) (15,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1546", "image": "data/cycle/graph_visual/hard/graph1546.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (26,30) (21,20) (0,2) (6,0) (22,15) (9,4) (17,10) (2,3) (5,16) (3,30) (24,6) (23,6) (23,8) (0,13) (12,27) (14,24) (6,19) (4,28) (5,12) (1,3) (18,4) (6,29) (19,11) (5,26) (14,20) (1,0) (17,7) (3,0) (22,13) (4,19) (13,7) (25,4) (7,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1917", "image": "data/cycle/graph_visual/hard/graph1917.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (33,21) (6,21) (34,5) (8,4) (0,1) (9,20) (9,30) (2,0) (3,8) (11,32) (13,1) (32,25) (18,3) (4,27) (14,24) (27,12) (32,26) (13,14) (10,8) (0,4) (1,4) (18,21) (15,17) (31,32) (22,6) (0,3) (15,6) (28,9) (19,7) (34,17) (10,31) (29,13) (27,30) (10,19) (23,31) (20,0) (8,2) (12,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph891", "image": "data/cycle/graph_visual/hard/graph891.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (20,27) (7,32) (30,23) (33,15) (29,23) (22,8) (10,31) (3,12) (16,5) (12,9) (20,9) (1,15) (18,32) (29,8) (4,20) (27,28) (22,2) (1,6) (6,28) (10,2) (19,3) (16,17) (26,33) (11,0) (25,1) (32,21) (24,12) (32,24) (5,12) (1,22) (13,9) (12,14) (16,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph280", "image": "data/cycle/graph_visual/hard/graph280.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,20) (6,16) (22,25) (1,21) (19,1) (12,8) (19,7) (14,26) (14,24) (8,18) (0,23) (11,26) (4,26) (16,11) (6,17) (0,10) (2,8) (6,2) (19,6) (25,9) (5,16) (15,24) (16,22) (10,3) (0,26) (13,4) (24,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph638", "image": "data/cycle/graph_visual/hard/graph638.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,25) (8,5) (21,5) (17,0) (20,30) (26,12) (22,12) (11,21) (9,29) (6,11) (27,23) (2,17) (24,13) (24,23) (25,20) (30,5) (0,31) (15,16) (8,14) (5,29) (15,10) (18,5) (14,7) (1,25) (16,24) (13,9) (28,11) (13,26) (24,3) (31,19) (4,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1486", "image": "data/cycle/graph_visual/hard/graph1486.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,10) (2,0) (22,16) (19,11) (18,23) (0,4) (7,15) (23,16) (16,1) (9,4) (10,27) (10,26) (28,12) (8,6) (17,0) (28,15) (1,0) (28,22) (24,25) (2,5) (1,20) (26,1) (24,17) (29,25) (6,4) (0,19) (0,3) (29,2) (3,21) (22,9) (7,13) (11,15) (14,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph591", "image": "data/cycle/graph_visual/hard/graph591.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (25,13) (9,5) (7,28) (8,24) (10,17) (9,22) (15,14) (29,0) (3,4) (14,11) (21,22) (21,13) (27,19) (2,20) (2,16) (10,16) (21,26) (4,14) (12,8) (4,26) (12,25) (6,19) (23,21) (29,20) (24,10) (18,3) (3,1) (12,7) (12,30) (22,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1827", "image": "data/cycle/graph_visual/hard/graph1827.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,23) (0,26) (7,29) (24,8) (31,22) (15,5) (29,21) (14,23) (13,26) (31,3) (15,6) (28,20) (17,18) (9,6) (18,19) (4,0) (0,3) (3,12) (1,29) (5,33) (25,4) (19,14) (26,24) (21,32) (16,15) (12,10) (30,19) (19,11) (0,1) (25,9) (27,5) (4,1) (24,15) (21,14) (5,0) (28,21) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1792", "image": "data/cycle/graph_visual/hard/graph1792.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (16,2) (25,30) (7,25) (26,1) (29,25) (25,13) (5,12) (11,6) (2,0) (29,1) (2,6) (17,20) (3,0) (13,18) (12,17) (27,8) (0,1) (5,1) (12,14) (23,28) (9,21) (1,15) (22,26) (18,8) (4,11) (16,14) (0,4) (32,27) (9,5) (12,24) (3,30) (10,7) (28,5) (19,13) (0,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph588", "image": "data/cycle/graph_visual/hard/graph588.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,23) (10,0) (19,2) (18,9) (25,28) (21,25) (2,16) (0,3) (9,24) (27,9) (6,13) (3,22) (25,8) (30,3) (27,20) (19,29) (1,28) (11,8) (0,15) (8,5) (15,17) (9,13) (1,20) (23,30) (2,12) (2,4) (8,4) (15,7) (23,26) (10,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1347", "image": "data/cycle/graph_visual/hard/graph1347.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (4,27) (7,21) (9,5) (26,2) (1,0) (22,2) (21,27) (14,0) (21,11) (9,6) (9,20) (2,16) (4,28) (14,12) (19,1) (12,23) (21,17) (2,13) (7,1) (19,23) (6,18) (27,26) (3,0) (15,8) (3,14) (23,25) (2,0) (9,26) (15,2) (8,10) (24,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph158", "image": "data/cycle/graph_visual/hard/graph158.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,12) (4,5) (21,25) (4,19) (1,25) (26,2) (11,5) (22,13) (9,16) (18,1) (20,0) (5,23) (26,13) (1,6) (15,10) (1,17) (11,14) (12,17) (8,3) (20,24) (14,0) (15,11) (8,23) (13,16) (7,0) (7,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph126", "image": "data/cycle/graph_visual/hard/graph126.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,8) (2,23) (7,11) (24,10) (16,4) (25,16) (25,0) (2,8) (19,1) (5,13) (3,26) (21,0) (8,4) (18,24) (20,13) (10,11) (9,10) (26,0) (3,6) (1,22) (10,20) (17,10) (12,15) (14,21) (6,12) (22,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph901", "image": "data/cycle/graph_visual/hard/graph901.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (10,21) (20,13) (31,15) (18,33) (29,22) (1,27) (2,31) (26,10) (19,4) (11,23) (18,21) (28,20) (13,6) (3,11) (27,9) (25,8) (11,34) (0,32) (16,22) (12,18) (11,5) (22,17) (25,18) (8,9) (24,21) (31,21) (30,5) (7,20) (14,1) (23,20) (29,0) (28,21) (4,25) (1,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1328", "image": "data/cycle/graph_visual/hard/graph1328.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,7) (12,11) (9,13) (4,18) (8,0) (12,26) (25,23) (28,21) (16,7) (26,18) (24,0) (10,15) (5,23) (6,19) (1,2) (19,16) (28,27) (0,1) (22,12) (9,15) (12,3) (5,16) (20,13) (1,11) (27,0) (28,20) (19,11) (20,3) (2,0) (17,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1696", "image": "data/cycle/graph_visual/hard/graph1696.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,3) (4,24) (5,9) (31,16) (7,26) (9,6) (10,31) (17,11) (1,27) (3,4) (6,14) (12,29) (11,24) (3,31) (20,27) (22,11) (1,0) (6,25) (27,9) (0,2) (18,2) (7,24) (23,19) (28,8) (29,17) (1,18) (6,10) (24,8) (29,15) (25,21) (0,3) (3,30) (13,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1218", "image": "data/cycle/graph_visual/hard/graph1218.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (13,11) (24,25) (24,27) (3,14) (13,8) (16,7) (1,8) (9,18) (0,3) (20,5) (12,16) (22,16) (2,0) (3,4) (5,14) (15,12) (17,11) (13,0) (27,17) (1,0) (4,0) (26,0) (16,6) (21,9) (6,14) (8,23) (18,19) (15,2) (15,10) (2,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph365", "image": "data/cycle/graph_visual/hard/graph365.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (11,0) (13,11) (12,3) (10,27) (26,24) (23,17) (16,18) (22,9) (28,8) (25,12) (5,7) (15,11) (14,13) (27,19) (26,7) (1,19) (6,17) (8,2) (0,4) (12,21) (28,4) (16,5) (12,7) (0,18) (17,20) (24,17) (11,22) (12,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph372", "image": "data/cycle/graph_visual/hard/graph372.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (4,19) (10,26) (18,10) (21,15) (8,16) (17,4) (14,12) (14,6) (8,22) (11,19) (6,20) (23,27) (0,9) (14,16) (2,23) (17,25) (1,15) (12,28) (1,7) (23,11) (21,13) (27,15) (0,16) (17,24) (24,26) (5,24) (24,22) (3,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph351", "image": "data/cycle/graph_visual/hard/graph351.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,28) (10,28) (9,5) (22,15) (14,19) (12,13) (24,1) (0,3) (4,23) (19,7) (15,28) (18,24) (0,25) (8,6) (2,3) (22,2) (14,8) (26,17) (26,7) (21,0) (12,16) (16,11) (11,4) (23,6) (13,9) (20,2) (0,27) (18,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph905", "image": "data/cycle/graph_visual/hard/graph905.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (12,8) (10,23) (11,34) (34,30) (21,13) (7,33) (31,13) (12,9) (16,32) (26,2) (25,8) (0,33) (17,22) (32,30) (24,26) (34,9) (15,1) (4,7) (8,3) (6,19) (28,20) (29,3) (25,20) (7,17) (21,34) (16,27) (19,26) (18,14) (5,32) (1,23) (18,11) (24,15) (26,5) (4,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph257", "image": "data/cycle/graph_visual/hard/graph257.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (27,14) (24,0) (20,19) (8,10) (27,24) (0,11) (17,16) (26,22) (13,26) (3,16) (26,7) (23,10) (13,14) (26,9) (24,4) (2,15) (2,22) (23,21) (16,25) (5,0) (12,23) (6,17) (9,20) (12,3) (3,26) (18,23) (1,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph603", "image": "data/cycle/graph_visual/hard/graph603.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,13) (16,26) (31,12) (29,18) (7,27) (15,10) (11,14) (28,10) (15,12) (21,31) (19,16) (12,6) (12,23) (31,8) (4,21) (29,23) (13,30) (25,12) (16,24) (28,3) (22,18) (30,17) (11,15) (7,2) (9,31) (11,20) (1,11) (20,7) (0,16) (5,15) (21,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph505", "image": "data/cycle/graph_visual/hard/graph505.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,12) (16,15) (11,18) (0,26) (28,3) (25,2) (2,27) (12,27) (4,17) (17,18) (28,1) (19,18) (7,14) (7,20) (22,25) (16,4) (10,20) (29,30) (0,4) (2,5) (25,10) (1,26) (26,20) (24,0) (23,1) (29,17) (18,9) (21,30) (28,13) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph766", "image": "data/cycle/graph_visual/hard/graph766.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (11,30) (26,1) (21,13) (29,18) (11,32) (9,25) (12,25) (2,7) (6,26) (3,8) (0,12) (31,17) (10,8) (12,24) (0,32) (9,13) (6,4) (26,20) (15,29) (16,8) (12,8) (27,1) (28,14) (4,15) (5,11) (28,8) (26,19) (10,23) (8,20) (22,13) (14,17) (14,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1795", "image": "data/cycle/graph_visual/hard/graph1795.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (32,30) (0,1) (3,0) (25,3) (6,31) (14,9) (10,32) (15,2) (0,29) (1,8) (28,17) (18,5) (3,8) (13,15) (28,7) (19,10) (13,8) (26,6) (16,7) (20,16) (29,9) (11,27) (21,14) (1,23) (3,20) (0,2) (11,20) (12,24) (22,17) (26,3) (22,18) (29,12) (19,9) (4,2) (20,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1037", "image": "data/cycle/graph_visual/hard/graph1037.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (15,21) (13,15) (2,11) (10,11) (6,3) (1,4) (15,22) (20,4) (7,16) (1,0) (7,17) (23,7) (9,24) (5,14) (19,12) (14,8) (25,22) (23,3) (22,18) (2,4) (6,0) (13,5) (0,11) (5,9) (15,19) (23,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph172", "image": "data/cycle/graph_visual/hard/graph172.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (24,1) (12,5) (1,6) (0,25) (8,18) (22,2) (2,25) (4,0) (14,4) (1,26) (17,16) (23,10) (25,18) (10,20) (7,20) (1,19) (18,15) (0,21) (18,11) (7,12) (9,17) (17,4) (20,26) (13,16) (3,2) (26,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1397", "image": "data/cycle/graph_visual/hard/graph1397.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (13,2) (4,27) (2,0) (12,23) (21,7) (4,28) (8,10) (18,6) (21,27) (2,26) (3,0) (16,2) (14,0) (8,15) (0,1) (21,11) (22,2) (9,26) (14,3) (24,20) (23,25) (23,19) (1,7) (9,20) (15,2) (1,19) (26,27) (17,21) (12,14) (6,9) (5,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1976", "image": "data/cycle/graph_visual/hard/graph1976.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (13,26) (19,18) (27,5) (15,16) (9,6) (28,19) (19,14) (29,1) (0,26) (1,4) (19,11) (2,23) (22,31) (28,20) (21,5) (10,12) (3,31) (34,21) (30,34) (3,12) (15,34) (23,14) (3,0) (24,8) (32,21) (14,21) (0,1) (29,7) (4,25) (15,24) (0,2) (25,9) (18,17) (33,29) (6,15) (24,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1574", "image": "data/cycle/graph_visual/hard/graph1574.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,8) (18,7) (20,25) (6,0) (11,25) (15,23) (22,24) (4,21) (16,1) (0,19) (28,1) (0,1) (23,21) (14,10) (0,3) (4,27) (10,3) (5,17) (7,11) (11,22) (2,30) (12,29) (7,30) (9,6) (0,2) (0,4) (22,14) (11,8) (16,13) (3,27) (8,12) (29,5) (26,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph443", "image": "data/cycle/graph_visual/hard/graph443.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,24) (22,11) (17,23) (17,6) (12,7) (13,11) (5,7) (9,22) (27,7) (12,25) (2,8) (19,1) (24,17) (0,18) (14,13) (26,29) (15,11) (27,10) (8,28) (5,16) (18,16) (17,20) (11,0) (12,21) (4,0) (1,12) (12,3) (4,29) (19,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph493", "image": "data/cycle/graph_visual/hard/graph493.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,11) (24,5) (16,7) (29,6) (7,1) (0,12) (4,15) (25,9) (1,27) (23,9) (7,10) (13,9) (20,15) (24,25) (17,16) (19,12) (12,17) (14,3) (3,8) (24,28) (26,3) (11,17) (26,5) (23,18) (21,2) (29,22) (4,2) (6,8) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph330", "image": "data/cycle/graph_visual/hard/graph330.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (7,26) (16,27) (8,2) (5,9) (9,6) (22,21) (23,10) (4,3) (25,12) (23,13) (0,2) (24,20) (15,17) (12,26) (10,12) (16,12) (28,20) (17,13) (14,23) (5,18) (23,4) (9,2) (6,1) (11,2) (17,24) (21,15) (23,11) (19,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1632", "image": "data/cycle/graph_visual/hard/graph1632.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (8,25) (0,1) (11,29) (20,9) (30,15) (13,1) (14,23) (31,24) (18,25) (5,21) (25,26) (15,0) (0,2) (18,23) (1,4) (6,11) (28,17) (2,19) (30,13) (3,27) (16,17) (17,12) (24,21) (5,9) (16,1) (10,12) (22,4) (3,14) (6,16) (7,6) (10,19) (5,23) (19,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph518", "image": "data/cycle/graph_visual/hard/graph518.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (12,8) (24,17) (7,19) (20,8) (6,16) (0,25) (16,22) (6,18) (19,6) (11,30) (24,4) (14,24) (29,28) (22,27) (10,0) (26,29) (16,21) (4,11) (25,9) (11,16) (26,14) (1,19) (2,8) (26,15) (0,26) (2,6) (10,3) (13,4) (16,5) (23,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph316", "image": "data/cycle/graph_visual/hard/graph316.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,14) (13,17) (5,18) (4,21) (13,27) (4,19) (10,24) (23,27) (12,24) (1,0) (15,25) (9,2) (10,11) (8,0) (3,25) (17,28) (25,6) (23,22) (26,11) (15,18) (21,24) (6,23) (15,8) (16,1) (7,26) (20,18) (24,0) (2,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph70", "image": "data/cycle/graph_visual/hard/graph70.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (11,23) (12,6) (7,11) (11,3) (2,25) (18,4) (22,21) (14,9) (20,1) (2,17) (8,13) (19,15) (22,24) (13,15) (0,24) (1,10) (12,1) (9,23) (25,24) (5,1) (6,15) (11,0) (18,17) (25,20) (16,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph614", "image": "data/cycle/graph_visual/hard/graph614.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (24,2) (12,17) (13,18) (18,6) (20,29) (21,2) (9,23) (3,15) (4,8) (26,14) (3,7) (5,22) (21,0) (24,4) (10,27) (30,10) (5,17) (28,27) (0,11) (8,7) (21,23) (13,14) (15,10) (26,5) (19,11) (24,6) (29,28) (25,10) (8,16) (1,29) (31,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph88", "image": "data/cycle/graph_visual/hard/graph88.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,5) (5,3) (2,7) (8,20) (8,21) (22,15) (23,15) (1,18) (13,11) (5,11) (0,24) (12,9) (17,5) (7,14) (24,10) (0,16) (5,20) (6,2) (9,21) (0,3) (5,18) (16,15) (19,0) (14,16) (25,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1641", "image": "data/cycle/graph_visual/hard/graph1641.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,2) (26,6) (1,23) (6,30) (13,8) (26,3) (17,28) (27,11) (10,31) (13,15) (4,0) (0,3) (21,20) (4,2) (14,21) (22,18) (10,19) (29,9) (16,7) (12,24) (29,12) (3,20) (0,29) (20,11) (19,9) (3,25) (16,20) (5,18) (7,28) (22,17) (9,14) (1,8) (3,8) (1,0) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph530", "image": "data/cycle/graph_visual/hard/graph530.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,28) (26,13) (17,8) (13,18) (2,18) (6,30) (29,14) (19,25) (17,2) (20,13) (20,23) (20,16) (0,24) (15,26) (15,30) (7,8) (1,4) (25,5) (16,0) (29,8) (7,5) (9,21) (2,22) (9,28) (25,10) (17,11) (10,3) (1,0) (12,29) (23,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1221", "image": "data/cycle/graph_visual/hard/graph1221.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (22,12) (17,7) (24,10) (22,1) (18,19) (13,24) (12,17) (26,4) (8,6) (3,5) (3,10) (19,2) (0,1) (9,14) (27,23) (21,18) (0,6) (7,24) (19,27) (27,14) (11,15) (20,21) (27,25) (17,26) (7,6) (11,18) (24,21) (7,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph809", "image": "data/cycle/graph_visual/hard/graph809.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (18,4) (26,33) (24,28) (12,31) (1,15) (0,4) (2,1) (5,7) (12,23) (26,29) (28,27) (14,16) (9,22) (2,6) (21,22) (13,26) (18,22) (31,5) (14,26) (19,27) (32,17) (25,11) (21,26) (28,6) (17,19) (33,30) (32,14) (10,14) (25,10) (5,20) (27,12) (8,32) (22,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1233", "image": "data/cycle/graph_visual/hard/graph1233.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (12,17) (21,9) (6,5) (8,23) (2,26) (0,3) (6,21) (4,20) (20,1) (13,18) (4,19) (22,6) (11,23) (0,17) (3,9) (24,21) (3,10) (15,12) (0,1) (14,27) (15,22) (16,8) (1,13) (23,7) (0,2) (7,26) (20,12) (23,27) (25,24) (0,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph425", "image": "data/cycle/graph_visual/hard/graph425.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (12,11) (9,27) (0,3) (18,27) (6,28) (1,6) (14,20) (21,12) (14,25) (24,15) (16,6) (19,13) (24,29) (13,9) (20,10) (23,28) (22,25) (23,7) (1,17) (8,14) (5,6) (0,15) (4,6) (2,18) (26,8) (9,11) (15,6) (3,18) (19,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1170", "image": "data/cycle/graph_visual/hard/graph1170.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,2) (6,14) (5,22) (23,12) (9,21) (11,0) (17,20) (16,0) (12,7) (8,4) (15,18) (1,6) (19,8) (5,26) (3,26) (0,1) (10,12) (11,20) (2,21) (9,25) (0,24) (7,6) (21,8) (23,22) (0,13) (18,25) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1625", "image": "data/cycle/graph_visual/hard/graph1625.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (14,24) (26,8) (1,28) (0,1) (28,15) (4,8) (22,27) (24,11) (21,3) (28,14) (17,18) (2,0) (29,2) (28,9) (13,19) (20,0) (5,24) (1,7) (4,13) (30,6) (21,11) (25,19) (16,0) (22,20) (30,15) (31,18) (23,14) (29,21) (9,10) (1,27) (12,10) (22,18) (19,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1775", "image": "data/cycle/graph_visual/hard/graph1775.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (15,17) (29,21) (1,32) (0,1) (13,22) (7,5) (6,19) (32,25) (10,20) (11,18) (14,28) (23,28) (4,20) (8,14) (7,28) (29,0) (13,11) (27,16) (20,17) (12,0) (16,17) (3,7) (3,0) (9,28) (4,0) (8,2) (27,0) (2,0) (19,7) (17,22) (10,24) (9,26) (32,30) (15,26) (12,32) (31,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph154", "image": "data/cycle/graph_visual/hard/graph154.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (1,19) (26,20) (17,9) (4,14) (25,2) (13,16) (0,25) (1,24) (9,26) (25,18) (1,6) (4,17) (16,17) (15,18) (20,10) (21,0) (4,0) (11,18) (2,3) (7,12) (7,20) (18,8) (10,23) (12,5) (1,26) (2,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph841", "image": "data/cycle/graph_visual/hard/graph841.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (2,17) (15,24) (6,1) (20,6) (7,26) (4,25) (23,22) (10,15) (0,33) (23,18) (3,29) (16,17) (9,28) (13,17) (27,14) (20,5) (31,0) (10,8) (26,24) (25,1) (5,16) (12,23) (10,14) (22,11) (24,3) (9,32) (23,14) (11,13) (23,21) (33,30) (19,25) (8,28) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1365", "image": "data/cycle/graph_visual/hard/graph1365.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (19,16) (17,11) (8,6) (5,20) (16,5) (20,13) (2,6) (19,10) (27,22) (7,26) (23,1) (15,18) (1,12) (0,1) (6,25) (0,23) (9,13) (15,1) (21,19) (7,23) (24,17) (4,24) (28,25) (13,23) (3,21) (27,6) (13,22) (4,14) (21,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph237", "image": "data/cycle/graph_visual/hard/graph237.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (20,22) (7,27) (8,25) (5,16) (17,0) (13,23) (0,1) (8,11) (15,1) (5,7) (7,11) (4,27) (3,10) (0,6) (10,14) (16,9) (12,26) (11,21) (12,8) (7,23) (14,22) (1,25) (22,11) (19,4) (3,24) (6,2) (18,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1060", "image": "data/cycle/graph_visual/hard/graph1060.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (24,20) (12,5) (25,10) (13,22) (17,24) (8,12) (2,0) (17,9) (23,10) (2,10) (12,23) (24,4) (0,1) (21,0) (0,18) (15,9) (7,22) (4,14) (3,7) (19,18) (3,0) (0,14) (12,1) (6,5) (21,7) (4,23) (8,16) (11,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph747", "image": "data/cycle/graph_visual/hard/graph747.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (11,2) (5,13) (2,9) (21,26) (13,27) (6,8) (30,2) (12,28) (4,29) (22,18) (18,17) (31,0) (3,23) (12,1) (20,16) (4,28) (25,14) (6,25) (3,6) (11,19) (23,24) (8,19) (22,15) (16,28) (12,10) (18,19) (7,12) (18,31) (11,32) (26,0) (30,13) (28,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph327", "image": "data/cycle/graph_visual/hard/graph327.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,5) (26,2) (23,6) (17,27) (1,8) (17,2) (7,24) (12,27) (4,28) (0,13) (8,21) (7,20) (9,3) (13,4) (15,5) (23,20) (9,23) (27,22) (25,11) (16,20) (19,21) (4,21) (27,6) (7,18) (21,10) (5,4) (0,9) (14,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1791", "image": "data/cycle/graph_visual/hard/graph1791.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (22,11) (11,27) (12,17) (3,0) (1,0) (3,7) (25,10) (29,19) (25,15) (10,2) (32,14) (27,16) (10,9) (0,28) (18,24) (5,29) (7,11) (28,26) (4,1) (25,31) (19,15) (0,30) (21,17) (4,26) (23,0) (17,13) (20,31) (2,0) (14,28) (9,23) (2,13) (18,2) (6,7) (8,26) (31,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1327", "image": "data/cycle/graph_visual/hard/graph1327.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (5,15) (26,4) (6,0) (3,1) (7,13) (5,12) (4,24) (5,26) (17,9) (13,21) (0,13) (22,11) (16,7) (0,3) (2,7) (6,27) (12,25) (23,3) (20,18) (19,10) (2,28) (4,8) (19,4) (23,6) (6,22) (24,14) (20,14) (0,1) (2,0) (17,4) (19,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph824", "image": "data/cycle/graph_visual/hard/graph824.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (21,2) (1,15) (29,2) (32,1) (17,25) (15,8) (17,22) (20,22) (13,26) (2,32) (7,20) (22,5) (4,0) (25,3) (14,31) (26,10) (12,32) (27,24) (8,6) (4,16) (18,14) (33,16) (26,3) (29,9) (19,3) (9,30) (7,11) (28,17) (20,24) (27,6) (4,13) (25,23) (18,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1927", "image": "data/cycle/graph_visual/hard/graph1927.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (14,1) (34,11) (16,22) (20,23) (18,21) (0,4) (1,32) (18,33) (25,18) (0,1) (6,13) (10,26) (28,20) (31,21) (8,9) (24,21) (11,23) (31,2) (7,20) (0,32) (11,3) (31,15) (11,5) (19,4) (0,3) (21,28) (21,10) (8,25) (25,4) (1,27) (12,18) (2,0) (5,30) (22,17) (13,20) (22,29) (0,29) (27,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1271", "image": "data/cycle/graph_visual/hard/graph1271.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (17,13) (2,10) (18,11) (0,10) (1,26) (13,23) (1,6) (27,18) (16,20) (7,25) (19,1) (22,13) (5,4) (2,24) (13,1) (12,26) (16,6) (17,2) (17,14) (1,0) (7,2) (18,26) (20,8) (4,12) (11,3) (2,21) (9,1) (15,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph304", "image": "data/cycle/graph_visual/hard/graph304.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (14,15) (25,16) (3,17) (13,16) (1,8) (6,20) (18,24) (8,14) (2,23) (22,5) (26,9) (10,7) (23,12) (4,14) (14,23) (17,27) (3,2) (21,1) (7,9) (19,5) (21,20) (13,11) (4,0) (28,26) (10,6) (22,12) (3,25) (11,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1385", "image": "data/cycle/graph_visual/hard/graph1385.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (10,26) (8,5) (22,17) (23,6) (22,25) (10,7) (25,2) (3,19) (22,24) (12,27) (11,16) (4,19) (11,5) (21,19) (23,22) (22,13) (0,2) (0,1) (25,7) (19,15) (4,12) (4,0) (2,1) (28,7) (14,17) (11,9) (21,18) (20,4) (0,20) (0,22) (9,23) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1965", "image": "data/cycle/graph_visual/hard/graph1965.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (4,25) (28,20) (2,0) (15,24) (27,5) (32,21) (13,26) (19,18) (0,3) (29,33) (15,16) (4,0) (34,21) (14,19) (21,14) (23,2) (23,14) (17,18) (30,34) (25,9) (24,8) (6,9) (0,26) (5,21) (34,15) (24,26) (3,12) (15,6) (19,11) (1,29) (1,4) (31,3) (28,19) (22,31) (10,12) (1,0) (7,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph783", "image": "data/cycle/graph_visual/hard/graph783.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (29,6) (17,0) (14,32) (10,13) (19,25) (4,15) (2,11) (3,4) (29,23) (13,5) (30,24) (29,0) (10,16) (28,20) (31,10) (21,19) (16,18) (10,11) (20,5) (0,32) (1,7) (1,25) (9,22) (30,21) (30,26) (1,27) (7,22) (8,19) (23,21) (11,15) (12,10) (28,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1299", "image": "data/cycle/graph_visual/hard/graph1299.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,13) (11,12) (15,8) (26,14) (1,0) (17,10) (12,6) (21,18) (17,4) (6,1) (9,15) (25,17) (3,0) (16,10) (22,12) (0,4) (14,3) (0,2) (20,10) (6,23) (23,18) (14,7) (19,2) (15,1) (17,2) (24,23) (5,9) (15,25) (0,5) (16,27) (19,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph717", "image": "data/cycle/graph_visual/hard/graph717.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (29,20) (12,14) (18,13) (7,6) (22,17) (15,1) (13,4) (31,2) (32,9) (23,30) (27,2) (9,26) (21,18) (10,16) (28,25) (23,4) (10,20) (8,1) (7,3) (11,21) (3,16) (14,10) (18,27) (24,0) (9,6) (24,19) (0,15) (17,24) (28,9) (5,24) (7,1) (8,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph925", "image": "data/cycle/graph_visual/hard/graph925.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (18,32) (13,18) (7,13) (6,7) (23,29) (13,0) (2,24) (3,11) (31,16) (27,6) (27,34) (28,15) (9,26) (23,24) (7,1) (8,29) (17,21) (19,20) (33,30) (9,2) (5,30) (19,12) (34,8) (14,22) (3,4) (28,6) (25,34) (4,22) (17,23) (19,16) (10,5) (4,1) (11,31) (32,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph681", "image": "data/cycle/graph_visual/hard/graph681.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (22,29) (24,11) (28,14) (4,29) (5,23) (1,29) (10,28) (22,9) (3,16) (3,26) (0,31) (15,2) (5,6) (11,20) (1,2) (13,17) (19,12) (27,14) (30,12) (5,3) (24,22) (25,9) (19,21) (30,1) (13,12) (26,19) (24,8) (11,18) (8,7) (10,2) (20,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph646", "image": "data/cycle/graph_visual/hard/graph646.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (14,1) (13,18) (15,27) (14,19) (10,0) (11,6) (20,7) (12,4) (18,11) (7,23) (31,19) (4,23) (22,3) (30,9) (20,8) (28,10) (30,5) (18,30) (13,4) (26,16) (17,2) (3,29) (15,17) (20,15) (25,17) (21,19) (27,24) (28,7) (17,31) (20,3) (20,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph639", "image": "data/cycle/graph_visual/hard/graph639.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,28) (17,14) (4,18) (29,9) (21,2) (3,18) (26,7) (18,1) (19,16) (13,21) (25,28) (23,27) (29,14) (6,28) (14,25) (8,10) (2,16) (8,7) (30,12) (28,30) (30,31) (23,14) (24,10) (12,20) (23,22) (27,15) (29,4) (5,14) (0,26) (16,7) (8,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1776", "image": "data/cycle/graph_visual/hard/graph1776.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (16,24) (17,28) (3,22) (0,2) (19,10) (5,7) (1,0) (11,30) (6,5) (28,27) (13,11) (23,31) (27,15) (13,3) (31,5) (0,14) (21,1) (27,22) (23,13) (8,12) (29,14) (4,18) (22,18) (20,0) (32,1) (2,23) (19,8) (25,26) (1,26) (24,6) (29,2) (32,23) (1,9) (12,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph203", "image": "data/cycle/graph_visual/hard/graph203.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (20,4) (22,17) (25,22) (12,7) (14,17) (12,4) (16,11) (21,18) (4,19) (15,19) (22,24) (6,23) (10,7) (22,23) (11,5) (9,11) (19,3) (13,22) (10,26) (23,9) (25,2) (0,20) (25,27) (8,5) (22,0) (1,2) (21,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph654", "image": "data/cycle/graph_visual/hard/graph654.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (18,11) (6,3) (2,11) (10,12) (12,7) (13,30) (15,22) (24,23) (3,23) (16,20) (0,31) (12,1) (21,26) (28,4) (6,8) (28,16) (13,27) (31,19) (17,18) (29,4) (28,24) (25,14) (13,5) (8,19) (22,18) (0,26) (2,30) (2,9) (19,18) (25,6) (12,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1773", "image": "data/cycle/graph_visual/hard/graph1773.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (10,12) (9,2) (28,26) (13,0) (4,25) (4,29) (4,0) (2,19) (21,32) (4,32) (32,18) (27,6) (4,30) (7,17) (10,29) (22,26) (2,0) (16,13) (31,25) (24,1) (30,8) (7,12) (6,24) (6,22) (3,0) (15,27) (0,5) (30,23) (16,6) (1,0) (14,2) (20,19) (12,22) (11,20) (11,22) (19,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1748", "image": "data/cycle/graph_visual/hard/graph1748.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (12,7) (0,26) (5,13) (19,8) (28,4) (32,11) (2,30) (0,31) (13,30) (12,1) (18,17) (29,4) (25,14) (12,28) (15,22) (2,11) (27,13) (18,19) (31,18) (24,23) (16,28) (25,6) (8,6) (21,26) (28,24) (3,23) (10,12) (1,0) (11,19) (9,2) (0,2) (20,16) (3,6) (18,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph755", "image": "data/cycle/graph_visual/hard/graph755.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (11,8) (14,31) (5,9) (16,22) (18,3) (11,19) (18,13) (8,29) (25,0) (9,17) (28,27) (16,2) (17,0) (1,27) (7,32) (27,30) (4,21) (7,20) (23,27) (14,22) (16,5) (27,20) (26,28) (14,10) (23,31) (1,18) (4,13) (12,9) (14,15) (8,16) (11,6) (8,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph260", "image": "data/cycle/graph_visual/hard/graph260.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (16,21) (15,18) (9,15) (5,25) (24,21) (25,24) (19,5) (3,1) (14,8) (8,22) (6,8) (9,14) (3,10) (27,26) (0,5) (22,3) (15,20) (7,12) (10,11) (5,27) (23,6) (20,17) (16,10) (6,7) (13,15) (21,2) (14,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1026", "image": "data/cycle/graph_visual/hard/graph1026.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (5,6) (23,8) (7,23) (1,6) (25,14) (21,12) (19,24) (1,0) (18,2) (4,6) (5,0) (16,6) (22,25) (14,20) (6,25) (13,9) (10,20) (15,6) (8,14) (11,12) (0,3) (13,19) (18,9) (0,2) (3,18) (0,15) (1,17) (11,9) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph404", "image": "data/cycle/graph_visual/hard/graph404.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,20) (2,29) (11,19) (24,4) (0,23) (1,15) (6,3) (17,12) (14,1) (10,13) (22,13) (23,7) (18,24) (21,26) (13,23) (19,16) (5,16) (6,27) (28,7) (19,21) (4,17) (6,25) (23,1) (9,6) (24,15) (25,29) (8,21) (20,5) (27,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1349", "image": "data/cycle/graph_visual/hard/graph1349.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (25,17) (27,7) (10,2) (9,11) (22,6) (13,4) (12,1) (20,28) (17,9) (20,25) (0,2) (13,1) (20,19) (27,3) (14,8) (25,15) (9,5) (11,4) (23,5) (0,1) (15,0) (14,4) (24,2) (15,6) (18,1) (27,6) (21,6) (26,2) (1,26) (12,16) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1712", "image": "data/cycle/graph_visual/hard/graph1712.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (4,0) (7,11) (0,3) (2,23) (19,22) (14,8) (15,1) (5,30) (19,5) (4,5) (0,31) (0,1) (16,31) (21,6) (0,5) (7,6) (27,20) (19,8) (2,12) (12,5) (11,25) (17,24) (13,1) (32,21) (6,5) (16,19) (10,24) (5,28) (18,31) (26,23) (19,20) (14,3) (29,2) (2,0) (29,9) (10,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1652", "image": "data/cycle/graph_visual/hard/graph1652.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (8,18) (23,24) (27,14) (4,29) (1,3) (2,10) (5,20) (4,15) (4,30) (16,20) (9,31) (27,7) (21,18) (0,2) (0,1) (1,2) (1,8) (23,9) (2,13) (28,21) (14,21) (30,22) (3,19) (25,30) (17,9) (25,6) (29,26) (29,7) (4,0) (25,5) (28,17) (14,11) (12,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1721", "image": "data/cycle/graph_visual/hard/graph1721.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (25,5) (23,29) (0,14) (29,21) (7,16) (5,31) (1,0) (1,17) (29,12) (30,24) (27,24) (13,25) (14,1) (2,0) (32,15) (32,6) (8,15) (12,25) (10,12) (31,14) (24,4) (26,17) (13,19) (28,31) (8,9) (20,1) (23,3) (26,30) (6,16) (2,5) (2,11) (18,8) (7,24) (22,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1703", "image": "data/cycle/graph_visual/hard/graph1703.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (29,19) (12,1) (1,28) (14,24) (10,16) (28,14) (26,8) (0,20) (27,1) (11,19) (2,32) (22,18) (14,23) (29,3) (19,25) (32,13) (1,0) (30,21) (24,6) (7,30) (11,21) (18,20) (32,22) (28,15) (9,28) (11,24) (17,0) (5,21) (15,31) (9,10) (4,13) (4,8) (22,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph650", "image": "data/cycle/graph_visual/hard/graph650.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (27,24) (27,6) (3,26) (16,31) (20,24) (15,1) (20,7) (16,4) (2,14) (6,8) (13,26) (28,9) (8,15) (29,2) (26,10) (9,29) (22,17) (0,4) (18,14) (17,21) (7,11) (22,5) (23,18) (13,4) (20,22) (25,3) (3,12) (2,19) (17,25) (25,23) (1,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph663", "image": "data/cycle/graph_visual/hard/graph663.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (17,1) (12,25) (9,18) (30,13) (18,4) (0,28) (17,15) (23,31) (14,27) (5,20) (3,19) (8,21) (27,23) (27,29) (2,31) (2,1) (21,15) (30,16) (4,5) (8,26) (6,2) (28,10) (3,14) (13,6) (11,16) (28,7) (22,24) (5,24) (18,12) (4,19) (14,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1490", "image": "data/cycle/graph_visual/hard/graph1490.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,4) (0,6) (11,29) (19,7) (3,0) (3,5) (15,1) (20,4) (20,3) (21,25) (29,6) (18,25) (6,14) (20,24) (22,26) (0,1) (2,0) (24,26) (29,17) (28,22) (10,17) (2,4) (6,25) (8,16) (23,24) (14,13) (2,27) (20,19) (21,12) (22,8) (0,15) (9,12) (27,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph432", "image": "data/cycle/graph_visual/hard/graph432.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,16) (24,6) (28,17) (10,22) (15,3) (16,27) (11,17) (5,13) (0,17) (3,21) (4,25) (27,17) (16,24) (13,23) (20,7) (9,12) (6,7) (29,16) (1,10) (6,18) (22,24) (27,25) (19,22) (9,25) (8,17) (26,21) (15,20) (5,4) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1376", "image": "data/cycle/graph_visual/hard/graph1376.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (22,19) (25,5) (26,25) (8,24) (10,11) (15,27) (13,6) (25,1) (26,6) (7,12) (9,15) (8,2) (7,4) (9,3) (0,1) (21,20) (3,14) (18,17) (0,16) (5,15) (17,4) (10,6) (26,0) (17,20) (28,26) (0,2) (21,16) (8,0) (27,23) (19,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1530", "image": "data/cycle/graph_visual/hard/graph1530.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (24,26) (2,0) (19,2) (7,9) (25,24) (7,11) (11,23) (19,4) (0,18) (21,9) (28,10) (1,0) (28,0) (10,8) (20,5) (1,16) (12,17) (26,19) (22,14) (29,23) (4,5) (30,2) (21,4) (27,0) (14,21) (14,6) (16,17) (26,3) (15,26) (12,15) (10,9) (13,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1807", "image": "data/cycle/graph_visual/hard/graph1807.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,0) (9,1) (0,22) (32,17) (8,26) (9,5) (12,30) (26,28) (24,27) (14,29) (13,16) (4,9) (0,23) (10,18) (4,25) (33,19) (20,15) (14,2) (3,10) (7,31) (11,18) (26,27) (31,21) (26,6) (15,0) (32,27) (14,30) (23,1) (2,21) (11,32) (0,2) (2,28) (23,7) (5,33) (13,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph641", "image": "data/cycle/graph_visual/hard/graph641.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (27,22) (10,25) (1,11) (30,6) (27,26) (0,23) (19,25) (18,4) (12,8) (22,14) (29,27) (16,20) (29,4) (17,19) (31,0) (24,6) (4,17) (6,25) (3,16) (20,0) (2,13) (14,9) (16,13) (18,1) (11,15) (0,12) (24,5) (27,16) (28,22) (21,23) (1,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph946", "image": "data/cycle/graph_visual/hard/graph946.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (20,11) (15,27) (10,12) (4,29) (16,13) (13,0) (20,19) (6,16) (4,25) (19,2) (7,17) (2,9) (0,3) (32,34) (22,26) (22,12) (11,22) (24,1) (30,26) (21,32) (31,4) (24,33) (14,2) (29,10) (6,27) (22,6) (23,30) (19,5) (18,32) (28,6) (8,30) (32,4) (25,33) (12,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1616", "image": "data/cycle/graph_visual/hard/graph1616.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (23,14) (9,27) (27,11) (5,20) (30,11) (24,9) (10,23) (27,13) (15,17) (14,15) (0,3) (19,1) (6,22) (24,8) (20,24) (25,21) (1,3) (18,24) (26,16) (18,12) (0,2) (25,17) (6,31) (16,8) (23,2) (30,7) (14,4) (8,29) (9,28) (10,1) (31,25) (0,1) (23,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph540", "image": "data/cycle/graph_visual/hard/graph540.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,22) (0,19) (8,12) (22,24) (28,8) (8,11) (0,6) (25,11) (12,29) (27,4) (5,17) (22,14) (25,20) (3,10) (6,9) (7,11) (23,15) (29,5) (3,27) (0,1) (1,28) (23,21) (10,14) (4,21) (30,7) (30,2) (16,13) (7,18) (1,16) (26,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph714", "image": "data/cycle/graph_visual/hard/graph714.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (22,11) (18,32) (16,6) (4,25) (14,2) (7,17) (25,31) (29,4) (32,21) (24,6) (11,20) (26,22) (2,9) (22,12) (22,6) (27,6) (12,10) (19,2) (12,7) (20,19) (30,23) (0,3) (29,10) (1,24) (8,30) (16,13) (0,13) (19,5) (32,4) (4,30) (26,28) (15,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1257", "image": "data/cycle/graph_visual/hard/graph1257.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (23,2) (0,2) (5,24) (1,0) (0,3) (13,10) (7,1) (9,0) (4,19) (11,19) (21,17) (18,6) (8,22) (24,22) (0,16) (17,4) (17,24) (12,21) (11,23) (4,0) (6,14) (27,15) (3,9) (26,23) (14,16) (27,14) (15,1) (16,8) (25,24) (10,26) (15,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1051", "image": "data/cycle/graph_visual/hard/graph1051.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (16,2) (14,18) (4,11) (17,5) (22,6) (0,15) (20,12) (7,6) (20,13) (0,2) (7,21) (19,2) (15,22) (3,0) (12,15) (25,20) (17,23) (19,8) (7,1) (4,9) (18,0) (15,11) (8,17) (4,0) (19,10) (17,24) (0,1) (18,3) (17,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph879", "image": "data/cycle/graph_visual/hard/graph879.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (11,21) (20,12) (6,7) (14,1) (13,31) (23,24) (32,10) (11,9) (5,17) (29,25) (33,2) (8,1) (24,17) (23,6) (6,12) (31,21) (0,5) (12,15) (16,32) (19,30) (27,9) (11,28) (8,0) (17,26) (32,3) (23,22) (11,25) (4,8) (30,23) (19,33) (2,18) (10,7) (25,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1157", "image": "data/cycle/graph_visual/hard/graph1157.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (5,11) (11,15) (6,1) (18,1) (23,5) (8,3) (12,14) (13,26) (22,13) (14,11) (1,25) (23,8) (0,3) (9,16) (24,20) (2,7) (16,13) (20,0) (17,1) (19,4) (0,14) (2,0) (7,0) (10,15) (4,5) (25,21) (26,2) (12,17) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph451", "image": "data/cycle/graph_visual/hard/graph451.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,24) (5,4) (16,1) (15,26) (17,8) (7,9) (14,21) (23,11) (18,5) (11,7) (17,0) (16,12) (10,6) (9,10) (0,28) (3,14) (20,14) (28,23) (24,22) (13,17) (26,2) (15,12) (4,21) (21,9) (10,27) (19,25) (19,4) (0,26) (19,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1845", "image": "data/cycle/graph_visual/hard/graph1845.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,32) (27,7) (23,20) (9,6) (11,24) (17,32) (9,5) (29,31) (7,24) (8,24) (32,31) (3,33) (32,10) (0,1) (8,30) (4,24) (9,28) (18,2) (0,3) (23,13) (21,27) (17,11) (29,15) (6,14) (3,4) (6,26) (0,2) (12,29) (6,10) (22,25) (16,31) (19,27) (4,0) (23,11) (1,18) (3,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1402", "image": "data/cycle/graph_visual/hard/graph1402.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,15) (7,1) (25,2) (26,18) (22,24) (26,6) (3,11) (26,5) (9,23) (1,20) (8,11) (17,2) (20,25) (11,27) (0,11) (21,17) (21,19) (29,24) (0,1) (13,1) (10,13) (15,29) (28,24) (9,16) (1,12) (6,12) (22,25) (18,4) (24,0) (23,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1935", "image": "data/cycle/graph_visual/hard/graph1935.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (34,17) (0,2) (13,33) (0,5) (31,20) (27,16) (32,7) (25,15) (17,21) (3,6) (32,0) (33,18) (11,31) (25,22) (0,3) (20,10) (5,8) (34,10) (32,13) (24,27) (19,23) (3,1) (24,22) (2,21) (15,28) (11,18) (4,23) (9,11) (18,1) (4,26) (30,31) (31,26) (29,7) (15,12) (17,14) (1,0) (25,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1435", "image": "data/cycle/graph_visual/hard/graph1435.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (14,23) (13,17) (8,15) (27,24) (20,10) (4,5) (7,26) (7,5) (12,8) (7,0) (26,17) (14,27) (26,1) (29,12) (21,18) (17,3) (1,0) (3,0) (29,19) (22,17) (0,2) (25,12) (7,9) (16,2) (16,20) (6,26) (10,18) (11,21) (23,22) (16,17) (28,8) (11,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1833", "image": "data/cycle/graph_visual/hard/graph1833.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (27,23) (27,0) (7,17) (1,12) (18,19) (24,1) (0,1) (25,0) (26,2) (5,19) (31,29) (7,6) (13,2) (33,27) (16,10) (17,30) (23,4) (8,16) (27,1) (13,22) (19,30) (31,14) (19,9) (15,23) (21,17) (11,3) (4,17) (11,27) (28,22) (32,22) (5,8) (26,29) (20,27) (29,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1772", "image": "data/cycle/graph_visual/hard/graph1772.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (2,6) (23,11) (6,28) (30,9) (3,5) (0,1) (12,30) (26,23) (6,20) (1,17) (26,19) (9,0) (13,20) (16,26) (12,32) (12,2) (8,2) (12,22) (6,18) (31,4) (21,5) (5,25) (2,0) (31,18) (27,29) (31,15) (14,1) (16,7) (0,10) (21,27) (12,17) (16,28) (5,23) (24,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1684", "image": "data/cycle/graph_visual/hard/graph1684.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (15,0) (19,17) (21,10) (31,28) (0,2) (5,14) (9,0) (1,0) (8,9) (29,17) (28,27) (30,2) (26,13) (14,3) (11,24) (25,5) (12,4) (30,18) (0,3) (3,13) (0,4) (14,20) (4,21) (25,21) (24,23) (1,3) (10,23) (30,1) (23,16) (0,22) (28,9) (12,29) (27,5) (17,6) (22,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1403", "image": "data/cycle/graph_visual/hard/graph1403.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (8,4) (3,17) (20,1) (11,15) (10,22) (13,26) (0,16) (27,7) (0,3) (28,1) (14,23) (23,18) (15,27) (7,24) (5,3) (7,12) (19,2) (20,25) (0,1) (24,14) (25,9) (29,3) (0,26) (0,2) (6,23) (16,22) (29,21) (0,4) (17,12) (28,11) (5,26) (11,8) (20,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph277", "image": "data/cycle/graph_visual/hard/graph277.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (26,3) (7,16) (9,16) (27,0) (8,25) (18,4) (9,0) (11,16) (4,19) (26,8) (13,23) (9,10) (10,13) (12,11) (8,22) (3,24) (2,21) (3,21) (5,1) (24,10) (8,19) (20,18) (12,6) (15,16) (25,1) (14,3) (17,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1064", "image": "data/cycle/graph_visual/hard/graph1064.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,0) (11,2) (0,3) (2,12) (1,0) (2,0) (0,19) (21,15) (5,24) (9,13) (10,14) (23,11) (16,0) (22,18) (12,14) (4,0) (20,10) (9,10) (25,17) (7,6) (22,25) (15,11) (4,17) (5,3) (22,16) (15,1) (10,5) (10,8) (6,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1236", "image": "data/cycle/graph_visual/hard/graph1236.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (19,16) (3,24) (27,21) (0,1) (6,4) (24,16) (8,26) (3,0) (8,13) (17,1) (2,10) (18,24) (23,1) (11,20) (25,11) (27,10) (24,5) (4,9) (7,23) (13,9) (23,25) (10,12) (15,18) (17,0) (3,27) (22,18) (14,4) (25,22) (2,0) (20,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph436", "image": "data/cycle/graph_visual/hard/graph436.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,24) (13,11) (24,11) (26,29) (3,2) (22,5) (27,17) (4,0) (14,23) (8,1) (9,26) (13,16) (3,25) (8,14) (21,1) (12,22) (17,3) (16,25) (9,7) (23,2) (20,6) (10,6) (7,10) (14,15) (23,12) (5,19) (21,29) (4,14) (28,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1209", "image": "data/cycle/graph_visual/hard/graph1209.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (23,13) (24,17) (1,23) (24,21) (24,4) (0,1) (21,3) (15,18) (14,4) (11,17) (13,22) (21,19) (6,26) (20,13) (7,23) (6,8) (2,6) (23,0) (15,1) (25,7) (1,12) (6,27) (27,22) (19,10) (13,9) (16,19) (20,5) (5,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph745", "image": "data/cycle/graph_visual/hard/graph745.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (13,9) (2,1) (11,10) (0,3) (13,10) (5,3) (23,5) (17,26) (27,10) (2,17) (20,29) (21,23) (32,20) (27,24) (22,28) (15,14) (16,8) (20,11) (30,24) (6,10) (7,19) (16,27) (14,1) (28,23) (1,11) (32,25) (19,32) (25,18) (15,31) (2,12) (29,23) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1654", "image": "data/cycle/graph_visual/hard/graph1654.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,9) (4,8) (28,14) (24,5) (6,30) (24,11) (2,29) (0,16) (18,17) (15,30) (20,22) (1,27) (0,1) (18,22) (23,14) (7,1) (12,10) (21,3) (20,0) (26,8) (22,27) (11,21) (28,1) (15,28) (13,19) (4,13) (29,21) (31,18) (25,19) (28,9) (11,19) (24,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph396", "image": "data/cycle/graph_visual/hard/graph396.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (8,21) (17,20) (9,21) (23,12) (8,19) (26,27) (11,2) (7,12) (28,3) (1,6) (0,16) (0,24) (0,3) (13,0) (27,2) (4,8) (15,18) (25,18) (9,25) (10,12) (11,20) (6,14) (21,28) (7,6) (26,5) (0,11) (22,5) (22,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1188", "image": "data/cycle/graph_visual/hard/graph1188.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (9,20) (22,26) (23,18) (1,0) (16,24) (3,26) (10,23) (26,14) (4,24) (17,16) (10,8) (3,16) (2,22) (0,11) (20,19) (12,3) (23,12) (2,15) (14,13) (1,25) (26,7) (17,6) (0,5) (25,13) (26,9) (24,0) (21,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1311", "image": "data/cycle/graph_visual/hard/graph1311.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (15,19) (8,1) (0,7) (19,9) (26,19) (24,16) (5,2) (26,5) (20,12) (0,1) (0,3) (23,14) (17,20) (16,28) (18,26) (2,4) (1,12) (13,0) (2,0) (22,12) (6,21) (14,0) (25,7) (9,11) (8,6) (27,26) (3,17) (20,4) (19,16) (25,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph723", "image": "data/cycle/graph_visual/hard/graph723.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (30,31) (16,12) (4,14) (17,32) (27,11) (29,10) (22,29) (32,6) (19,13) (27,31) (1,26) (28,27) (15,25) (5,29) (1,25) (5,12) (18,22) (21,7) (8,30) (1,7) (17,0) (19,12) (9,11) (2,7) (20,28) (4,31) (32,18) (22,26) (23,16) (11,3) (16,3) (26,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1424", "image": "data/cycle/graph_visual/hard/graph1424.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (25,29) (14,12) (16,21) (0,2) (13,27) (15,3) (13,6) (0,14) (7,8) (3,0) (4,23) (25,0) (8,18) (0,1) (9,5) (10,21) (21,4) (19,23) (9,19) (9,27) (28,26) (22,20) (7,0) (13,15) (24,9) (17,22) (20,7) (11,1) (0,9) (10,26) (7,11) (2,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1557", "image": "data/cycle/graph_visual/hard/graph1557.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (6,18) (29,5) (0,4) (24,18) (16,15) (27,16) (26,25) (0,1) (3,0) (2,17) (17,7) (5,6) (28,22) (14,3) (25,19) (8,27) (16,21) (23,27) (27,1) (9,14) (13,14) (28,25) (29,10) (20,19) (24,11) (3,5) (14,0) (17,25) (9,4) (22,30) (15,20) (2,4) (12,14) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph355", "image": "data/cycle/graph_visual/hard/graph355.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,15) (16,0) (15,5) (12,7) (19,7) (0,8) (26,25) (26,0) (6,26) (8,24) (20,17) (22,19) (23,27) (17,4) (1,25) (18,17) (9,3) (16,21) (21,20) (26,28) (9,15) (11,10) (7,4) (8,2) (10,6) (6,13) (3,14) (5,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph6", "image": "data/cycle/graph_visual/hard/graph6.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (6,0) (12,9) (14,6) (20,3) (21,6) (4,2) (17,10) (12,0) (25,6) (13,14) (24,20) (7,19) (24,19) (22,23) (25,16) (21,11) (8,22) (15,1) (18,25) (5,3) (17,20) (24,22) (8,15) (20,4) (2,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph524", "image": "data/cycle/graph_visual/hard/graph524.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (30,4) (27,26) (2,15) (12,20) (26,11) (25,23) (0,30) (1,18) (9,28) (5,21) (25,22) (17,23) (27,23) (19,8) (29,6) (20,13) (14,2) (13,5) (30,27) (27,7) (27,3) (1,10) (5,16) (19,6) (21,24) (11,2) (21,18) (1,19) (8,9) (25,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1862", "image": "data/cycle/graph_visual/hard/graph1862.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (0,5) (25,4) (29,8) (22,30) (31,17) (27,31) (7,28) (21,32) (24,19) (29,9) (0,3) (1,11) (28,5) (18,13) (0,1) (5,26) (12,23) (21,11) (23,13) (29,5) (10,16) (20,13) (23,24) (11,27) (12,15) (10,3) (16,2) (24,25) (29,6) (24,22) (2,0) (19,28) (24,11) (14,15) (16,13) (33,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1635", "image": "data/cycle/graph_visual/hard/graph1635.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (31,30) (12,22) (19,27) (22,16) (2,6) (14,10) (27,25) (1,2) (0,3) (23,28) (0,1) (5,18) (19,17) (3,22) (6,28) (17,14) (7,5) (4,0) (26,30) (20,21) (26,28) (1,13) (5,31) (26,21) (18,4) (26,11) (14,26) (12,27) (0,5) (22,8) (2,0) (9,25) (12,29) (10,24) (14,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph360", "image": "data/cycle/graph_visual/hard/graph360.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (2,1) (3,21) (16,7) (5,28) (12,6) (24,10) (4,19) (3,24) (4,18) (9,16) (23,13) (12,11) (25,1) (27,9) (25,8) (8,26) (0,21) (11,16) (8,22) (10,28) (19,8) (3,14) (26,3) (17,6) (16,15) (20,18) (28,9) (10,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph608", "image": "data/cycle/graph_visual/hard/graph608.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (8,2) (21,0) (12,6) (16,4) (1,14) (13,27) (0,30) (17,23) (17,14) (1,20) (24,18) (24,10) (27,19) (28,14) (6,25) (3,4) (6,20) (31,15) (7,31) (24,13) (29,1) (9,30) (7,5) (16,1) (28,22) (28,31) (1,26) (11,13) (24,0) (1,27) (8,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph825", "image": "data/cycle/graph_visual/hard/graph825.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (33,12) (24,19) (32,16) (33,0) (5,9) (25,26) (6,28) (30,22) (28,20) (2,3) (32,21) (2,5) (23,11) (7,28) (18,11) (1,15) (20,29) (12,17) (3,4) (29,8) (11,6) (2,12) (1,29) (14,33) (14,32) (28,25) (12,28) (4,30) (31,15) (19,9) (27,10) (0,10) (13,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1335", "image": "data/cycle/graph_visual/hard/graph1335.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (2,22) (14,12) (5,25) (3,5) (2,11) (9,10) (1,0) (24,12) (0,19) (14,10) (20,28) (28,0) (15,1) (8,10) (6,7) (22,16) (9,13) (10,20) (22,18) (11,23) (17,25) (0,26) (6,25) (10,5) (2,20) (17,4) (15,21) (27,16) (15,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1150", "image": "data/cycle/graph_visual/hard/graph1150.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (5,11) (4,0) (25,15) (9,13) (2,26) (3,0) (10,24) (18,1) (22,8) (18,5) (6,2) (15,23) (21,9) (4,5) (1,0) (7,12) (0,24) (14,11) (16,15) (20,5) (26,10) (0,21) (7,14) (0,2) (5,19) (16,0) (8,20) (17,16) (3,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1428", "image": "data/cycle/graph_visual/hard/graph1428.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (7,1) (14,3) (14,0) (29,5) (27,29) (2,0) (28,27) (2,16) (8,15) (21,18) (26,2) (4,9) (22,6) (21,7) (27,21) (13,21) (9,6) (1,0) (29,10) (26,9) (15,12) (20,9) (26,23) (19,1) (11,8) (20,25) (0,3) (23,19) (14,2) (17,2) (2,24) (12,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1740", "image": "data/cycle/graph_visual/hard/graph1740.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (27,3) (22,24) (14,31) (0,3) (23,8) (2,1) (11,31) (22,30) (9,31) (2,25) (1,0) (16,29) (2,0) (10,2) (13,10) (15,28) (20,17) (0,6) (26,24) (4,15) (18,16) (7,29) (0,13) (30,5) (11,19) (26,18) (29,15) (29,8) (21,23) (27,8) (17,12) (28,32) (23,19) (2,26) (4,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph40", "image": "data/cycle/graph_visual/hard/graph40.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (24,25) (15,11) (6,4) (10,1) (18,3) (2,6) (19,0) (5,2) (16,22) (7,9) (24,17) (7,15) (4,9) (17,0) (11,19) (13,23) (0,12) (22,15) (25,23) (20,16) (14,1) (16,1) (10,21) (3,10) (8,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1422", "image": "data/cycle/graph_visual/hard/graph1422.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (26,29) (28,8) (24,17) (6,4) (0,4) (5,13) (7,11) (0,5) (18,19) (29,9) (15,14) (15,21) (3,21) (3,0) (10,26) (26,23) (23,27) (8,11) (25,28) (3,26) (26,12) (0,18) (1,24) (0,2) (6,25) (1,0) (20,14) (13,25) (2,20) (17,22) (1,16) (11,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1176", "image": "data/cycle/graph_visual/hard/graph1176.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (7,12) (20,10) (9,6) (5,9) (3,0) (16,25) (0,7) (20,26) (3,22) (2,0) (10,25) (16,8) (17,21) (13,2) (5,24) (13,8) (22,18) (13,23) (11,14) (25,4) (17,19) (15,22) (11,9) (24,23) (4,0) (0,1) (12,26) (16,1) (8,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph410", "image": "data/cycle/graph_visual/hard/graph410.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (1,10) (25,11) (19,10) (13,29) (29,6) (2,7) (9,4) (5,29) (4,7) (5,14) (28,20) (22,16) (8,1) (17,27) (28,25) (12,0) (17,21) (3,23) (13,28) (23,29) (19,0) (3,18) (2,26) (23,21) (8,7) (24,11) (14,15) (22,20) (19,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1239", "image": "data/cycle/graph_visual/hard/graph1239.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (1,10) (8,25) (0,4) (25,19) (4,9) (24,3) (16,4) (6,18) (20,12) (21,26) (13,16) (17,8) (27,17) (8,1) (0,3) (24,5) (0,27) (1,0) (6,16) (13,7) (11,18) (12,25) (0,2) (22,9) (3,19) (15,23) (4,24) (26,9) (14,15) (12,2) (15,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph695", "image": "data/cycle/graph_visual/hard/graph695.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (11,29) (19,3) (29,25) (24,8) (17,11) (30,19) (23,4) (21,4) (20,13) (18,14) (31,19) (22,10) (31,6) (18,8) (24,7) (20,30) (10,26) (15,16) (8,23) (9,15) (7,27) (27,5) (1,0) (6,16) (13,29) (28,29) (12,28) (1,26) (2,4) (13,0) (23,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1201", "image": "data/cycle/graph_visual/hard/graph1201.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (15,20) (18,24) (0,1) (2,19) (1,27) (20,10) (12,0) (4,0) (14,15) (18,6) (3,7) (0,26) (5,17) (17,23) (9,16) (11,19) (25,6) (8,20) (0,3) (0,24) (2,0) (6,1) (8,18) (24,9) (2,10) (13,17) (27,4) (7,22) (22,13) (11,3) (21,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1932", "image": "data/cycle/graph_visual/hard/graph1932.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (26,19) (25,7) (14,20) (20,22) (15,6) (33,23) (0,2) (17,5) (17,32) (16,29) (27,25) (0,4) (7,4) (33,10) (21,7) (21,1) (5,1) (4,15) (16,11) (31,9) (29,19) (10,0) (28,25) (8,17) (24,34) (2,6) (10,9) (16,23) (18,28) (3,33) (13,17) (1,0) (22,16) (14,30) (12,18) (24,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph823", "image": "data/cycle/graph_visual/hard/graph823.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (25,12) (30,11) (29,18) (9,25) (29,15) (5,11) (8,20) (6,4) (27,1) (17,32) (31,33) (0,12) (24,12) (22,13) (11,32) (26,20) (13,9) (33,0) (4,15) (28,8) (8,10) (8,16) (12,8) (28,14) (26,19) (3,8) (7,14) (2,7) (1,26) (6,26) (14,17) (10,23) (21,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph885", "image": "data/cycle/graph_visual/hard/graph885.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (1,16) (13,11) (22,28) (12,6) (5,7) (24,18) (6,25) (1,29) (33,1) (28,8) (23,17) (13,24) (6,20) (27,13) (3,4) (1,26) (24,10) (28,31) (20,1) (32,14) (30,9) (14,28) (30,0) (21,0) (7,31) (0,24) (27,19) (31,33) (17,14) (8,2) (27,1) (16,4) (31,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph620", "image": "data/cycle/graph_visual/hard/graph620.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,17) (1,11) (6,27) (17,22) (20,13) (29,10) (12,23) (10,19) (21,6) (1,24) (9,5) (27,4) (22,0) (21,25) (24,18) (30,13) (15,19) (3,24) (28,23) (9,0) (31,13) (8,14) (3,5) (2,22) (23,16) (3,16) (14,4) (19,18) (26,9) (7,1) (24,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph218", "image": "data/cycle/graph_visual/hard/graph218.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (6,0) (11,7) (4,19) (22,11) (6,2) (10,3) (13,23) (8,12) (25,8) (7,23) (15,1) (11,8) (0,17) (24,3) (7,5) (21,11) (27,4) (1,25) (21,18) (14,22) (5,16) (16,9) (10,14) (26,12) (22,20) (0,1) (7,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1953", "image": "data/cycle/graph_visual/hard/graph1953.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (9,27) (5,11) (20,7) (8,25) (15,31) (10,26) (23,11) (25,4) (5,30) (8,9) (21,28) (0,1) (34,11) (29,22) (31,2) (20,28) (14,1) (13,6) (20,23) (4,19) (11,3) (32,1) (32,0) (27,1) (2,0) (21,18) (22,16) (33,18) (21,10) (0,29) (12,18) (22,17) (24,21) (21,31) (18,25) (20,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph17", "image": "data/cycle/graph_visual/hard/graph17.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (18,15) (7,6) (5,15) (23,25) (7,12) (10,16) (22,8) (11,10) (20,17) (22,3) (20,6) (9,15) (21,2) (16,21) (8,14) (24,25) (4,14) (1,3) (5,0) (8,6) (14,9) (21,24) (15,13) (5,19) (3,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1194", "image": "data/cycle/graph_visual/hard/graph1194.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (3,0) (24,26) (1,0) (0,2) (2,17) (7,6) (5,11) (2,6) (10,7) (11,3) (19,10) (10,11) (8,20) (22,21) (15,0) (9,7) (17,21) (12,22) (20,7) (10,15) (11,4) (2,26) (8,1) (17,18) (24,14) (16,2) (15,13) (3,25) (4,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1553", "image": "data/cycle/graph_visual/hard/graph1553.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (12,0) (24,4) (14,2) (9,19) (19,23) (8,23) (18,6) (15,6) (13,23) (22,17) (21,16) (15,27) (12,16) (2,0) (24,12) (13,29) (5,10) (19,18) (1,12) (3,6) (17,2) (25,6) (2,30) (8,20) (28,25) (26,19) (3,0) (7,4) (0,1) (28,30) (7,5) (11,7) (4,0) (22,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph454", "image": "data/cycle/graph_visual/hard/graph454.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (21,6) (0,17) (27,24) (15,22) (20,12) (10,21) (21,24) (5,6) (23,4) (12,15) (1,19) (27,14) (6,29) (28,22) (12,17) (28,4) (11,23) (25,20) (26,0) (9,29) (7,3) (3,9) (1,20) (13,18) (2,26) (16,8) (8,23) (29,26) (28,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1439", "image": "data/cycle/graph_visual/hard/graph1439.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,27) (11,24) (16,23) (10,29) (21,19) (11,6) (19,17) (20,14) (5,2) (17,4) (26,12) (20,7) (17,29) (16,29) (14,27) (1,0) (8,19) (0,4) (27,3) (11,2) (9,22) (9,2) (12,13) (7,25) (19,28) (3,0) (10,15) (0,2) (2,15) (11,25) (0,13) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1782", "image": "data/cycle/graph_visual/hard/graph1782.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (28,15) (0,2) (25,27) (19,29) (9,23) (13,17) (9,10) (25,26) (4,0) (5,1) (10,31) (24,13) (0,1) (11,18) (17,30) (4,12) (16,23) (16,8) (7,21) (20,14) (16,22) (17,5) (15,3) (22,20) (10,0) (19,18) (28,16) (14,29) (7,4) (6,17) (2,6) (32,24) (25,7) (21,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph242", "image": "data/cycle/graph_visual/hard/graph242.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (8,19) (26,2) (27,21) (25,18) (22,23) (5,22) (7,6) (15,18) (12,23) (9,21) (12,10) (3,27) (17,20) (13,0) (25,9) (4,8) (11,0) (21,8) (5,26) (6,14) (11,20) (1,6) (11,2) (7,12) (3,0) (0,16) (0,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph164", "image": "data/cycle/graph_visual/hard/graph164.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (13,9) (25,15) (26,18) (15,8) (6,15) (17,2) (3,22) (26,21) (19,11) (20,25) (23,17) (21,7) (18,12) (0,6) (8,11) (5,2) (16,20) (11,2) (9,24) (14,22) (18,14) (4,1) (9,8) (21,1) (23,4) (10,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1524", "image": "data/cycle/graph_visual/hard/graph1524.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (20,11) (0,12) (0,27) (24,14) (1,12) (6,2) (19,5) (9,5) (25,4) (3,27) (23,21) (16,24) (4,22) (6,10) (28,19) (4,13) (10,20) (21,13) (15,16) (18,0) (14,13) (17,22) (30,4) (21,10) (5,14) (0,1) (26,7) (30,7) (28,8) (3,22) (29,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1137", "image": "data/cycle/graph_visual/hard/graph1137.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (11,18) (16,4) (3,0) (5,13) (19,3) (15,11) (18,6) (0,12) (2,0) (2,24) (20,26) (24,3) (15,13) (19,25) (7,1) (16,6) (17,26) (1,8) (12,14) (8,25) (25,12) (9,21) (0,1) (17,8) (22,15) (10,16) (4,9) (23,9) (4,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1432", "image": "data/cycle/graph_visual/hard/graph1432.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,29) (14,3) (11,28) (0,13) (5,20) (17,13) (17,11) (9,18) (13,15) (2,18) (8,25) (8,1) (0,1) (3,0) (4,3) (10,15) (16,7) (26,24) (12,16) (27,0) (6,16) (13,8) (6,14) (21,9) (19,18) (12,22) (23,16) (27,24) (5,14) (2,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph65", "image": "data/cycle/graph_visual/hard/graph65.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (22,9) (0,19) (2,10) (8,4) (9,6) (10,13) (7,0) (17,11) (25,4) (3,24) (24,6) (2,1) (7,4) (15,22) (14,19) (11,2) (16,8) (13,23) (5,18) (10,21) (18,2) (4,20) (22,21) (12,19) (14,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1191", "image": "data/cycle/graph_visual/hard/graph1191.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (15,1) (0,1) (21,3) (19,22) (10,4) (16,5) (19,4) (2,8) (25,20) (4,14) (14,11) (21,19) (0,21) (16,11) (12,13) (12,0) (11,26) (8,15) (7,25) (15,18) (20,8) (11,9) (24,22) (23,14) (6,21) (0,17) (7,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1567", "image": "data/cycle/graph_visual/hard/graph1567.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,13) (29,21) (18,0) (17,29) (16,28) (24,19) (10,26) (16,22) (21,30) (30,19) (21,27) (0,1) (26,6) (14,15) (2,20) (15,16) (7,8) (30,10) (12,28) (4,26) (3,7) (20,11) (1,5) (25,16) (30,9) (18,17) (5,23) (8,15) (5,20) (9,14) (20,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph754", "image": "data/cycle/graph_visual/hard/graph754.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,25) (8,14) (14,28) (0,30) (17,8) (18,7) (10,25) (15,23) (26,24) (13,31) (5,27) (13,32) (22,9) (5,7) (15,13) (16,2) (9,2) (28,21) (7,6) (26,13) (13,12) (7,1) (21,30) (19,14) (11,9) (0,4) (3,8) (3,2) (20,8) (29,12) (25,21) (1,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph812", "image": "data/cycle/graph_visual/hard/graph812.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (24,20) (33,13) (11,14) (22,17) (32,10) (28,9) (3,5) (15,4) (16,23) (30,5) (23,14) (12,1) (8,1) (21,6) (2,33) (4,27) (24,3) (32,27) (22,7) (0,22) (24,1) (33,9) (23,31) (26,21) (0,9) (6,29) (6,17) (16,3) (18,24) (20,13) (25,19) (19,10) (18,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1464", "image": "data/cycle/graph_visual/hard/graph1464.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (13,17) (8,25) (16,7) (3,14) (15,13) (0,13) (28,11) (6,14) (20,5) (2,18) (18,9) (16,12) (1,8) (11,17) (3,4) (26,24) (15,10) (1,0) (9,21) (8,13) (19,18) (5,14) (0,3) (29,15) (27,24) (6,16) (27,0) (16,23) (22,12) (2,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1552", "image": "data/cycle/graph_visual/hard/graph1552.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (17,8) (4,10) (18,25) (0,2) (19,20) (29,18) (28,1) (4,16) (28,26) (1,0) (10,24) (27,20) (3,4) (21,8) (6,23) (10,15) (0,13) (11,24) (2,3) (30,15) (7,21) (28,12) (21,28) (22,3) (5,0) (28,14) (28,13) (27,23) (5,27) (9,25) (30,18) (2,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1214", "image": "data/cycle/graph_visual/hard/graph1214.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (14,19) (24,13) (17,11) (8,4) (7,27) (0,1) (22,15) (9,22) (12,19) (4,27) (0,7) (21,10) (6,25) (2,18) (0,2) (21,22) (18,27) (16,8) (1,2) (5,14) (0,19) (2,20) (10,2) (23,4) (10,13) (5,26) (27,11) (3,24) (6,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1425", "image": "data/cycle/graph_visual/hard/graph1425.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (3,0) (18,23) (14,0) (3,10) (13,7) (17,24) (22,16) (5,2) (26,1) (11,15) (29,25) (16,23) (24,25) (16,1) (28,12) (29,2) (2,0) (6,4) (0,17) (1,20) (3,21) (15,28) (15,7) (10,26) (4,9) (0,1) (27,10) (8,6) (22,9) (0,19) (11,19) (28,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph297", "image": "data/cycle/graph_visual/hard/graph297.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (6,9) (23,11) (9,2) (16,12) (26,7) (21,15) (14,23) (23,4) (27,19) (27,24) (23,13) (15,17) (10,12) (9,5) (6,1) (23,10) (8,2) (4,3) (18,5) (25,12) (26,16) (24,17) (0,2) (13,17) (12,22) (20,21) (11,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph353", "image": "data/cycle/graph_visual/hard/graph353.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (18,16) (9,13) (21,14) (22,0) (5,20) (27,5) (5,19) (26,2) (23,8) (28,24) (6,2) (15,26) (10,7) (28,7) (11,17) (25,3) (12,14) (1,18) (21,5) (28,9) (27,15) (3,0) (4,5) (16,15) (0,16) (8,20) (5,11) (24,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1759", "image": "data/cycle/graph_visual/hard/graph1759.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (7,2) (19,11) (25,28) (15,4) (15,0) (29,14) (10,30) (26,7) (1,0) (31,26) (22,11) (14,17) (3,32) (27,0) (24,2) (17,1) (26,18) (20,28) (2,0) (24,23) (8,10) (17,31) (12,26) (5,3) (10,28) (23,9) (21,0) (6,30) (13,2) (2,22) (4,10) (32,24) (16,8) (30,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1753", "image": "data/cycle/graph_visual/hard/graph1753.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (7,12) (0,31) (24,23) (4,29) (3,6) (12,10) (1,0) (19,11) (9,2) (18,17) (25,14) (12,28) (21,26) (30,2) (18,31) (19,18) (26,0) (28,24) (2,0) (1,12) (15,22) (5,13) (3,23) (4,28) (11,2) (27,13) (8,19) (16,28) (6,25) (6,8) (22,18) (30,13) (11,32) (16,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph11", "image": "data/cycle/graph_visual/hard/graph11.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (20,25) (12,18) (13,19) (24,23) (12,13) (24,11) (20,17) (15,0) (19,24) (15,10) (22,12) (2,8) (15,3) (7,24) (9,2) (4,18) (21,6) (0,24) (5,25) (8,3) (4,1) (14,15) (0,25) (14,16) (6,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1206", "image": "data/cycle/graph_visual/hard/graph1206.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (11,10) (11,4) (19,12) (16,12) (17,23) (8,10) (2,13) (26,27) (24,8) (14,16) (13,20) (5,2) (19,1) (14,7) (17,6) (15,25) (0,3) (26,0) (1,0) (15,23) (12,18) (21,0) (25,8) (17,0) (18,9) (1,25) (22,3) (13,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph52", "image": "data/cycle/graph_visual/hard/graph52.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,21) (13,21) (15,2) (19,9) (15,3) (13,15) (20,7) (7,8) (10,21) (0,9) (17,8) (0,7) (14,0) (23,4) (25,9) (19,23) (11,1) (10,24) (20,18) (16,22) (7,11) (6,13) (12,14) (9,5) (22,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1717", "image": "data/cycle/graph_visual/hard/graph1717.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (3,0) (16,0) (23,32) (28,3) (16,19) (12,30) (2,7) (29,23) (32,21) (21,4) (15,5) (20,7) (25,12) (15,11) (0,2) (13,19) (17,30) (16,24) (12,15) (27,7) (29,18) (15,10) (9,31) (31,8) (6,12) (0,1) (31,12) (1,11) (28,10) (22,18) (11,14) (0,21) (16,26) (11,20) (13,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph561", "image": "data/cycle/graph_visual/hard/graph561.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (1,17) (26,24) (11,3) (7,19) (8,12) (7,9) (10,2) (9,22) (30,21) (13,26) (25,17) (9,20) (23,24) (9,12) (7,15) (14,4) (11,6) (29,6) (13,18) (27,9) (21,0) (29,27) (16,1) (14,15) (28,2) (25,10) (30,5) (7,10) (1,0) (26,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1519", "image": "data/cycle/graph_visual/hard/graph1519.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (0,2) (5,16) (9,13) (29,12) (23,25) (11,1) (0,4) (1,2) (11,19) (22,12) (19,27) (10,15) (1,0) (12,11) (16,7) (0,27) (0,24) (3,12) (6,19) (14,7) (0,8) (26,18) (9,15) (13,20) (26,5) (0,3) (21,28) (20,28) (20,3) (30,23) (23,28) (18,4) (10,17) (16,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph616", "image": "data/cycle/graph_visual/hard/graph616.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (8,4) (15,6) (24,11) (18,30) (14,3) (1,29) (13,30) (26,28) (10,3) (25,17) (8,28) (17,11) (22,5) (2,16) (10,24) (0,15) (0,29) (10,4) (8,0) (23,26) (13,22) (24,20) (7,23) (13,31) (15,12) (15,19) (7,16) (27,8) (9,1) (13,0) (6,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph248", "image": "data/cycle/graph_visual/hard/graph248.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,21) (17,23) (26,4) (17,9) (24,22) (24,7) (10,2) (15,9) (21,26) (5,12) (0,14) (12,1) (3,7) (10,27) (24,19) (20,18) (8,16) (22,13) (23,4) (23,10) (4,14) (27,12) (0,18) (11,18) (8,12) (25,0) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph320", "image": "data/cycle/graph_visual/hard/graph320.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (18,21) (4,20) (22,24) (26,10) (2,1) (16,11) (12,27) (20,0) (7,28) (23,9) (22,25) (0,22) (5,8) (5,11) (6,23) (2,25) (19,3) (23,22) (19,21) (13,22) (4,12) (15,19) (25,7) (4,19) (11,9) (17,22) (14,17) (7,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph777", "image": "data/cycle/graph_visual/hard/graph777.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,29) (28,23) (23,21) (27,16) (11,1) (32,25) (20,32) (10,6) (15,14) (27,24) (12,2) (16,8) (17,26) (10,27) (25,18) (15,31) (22,28) (3,0) (23,5) (5,4) (2,1) (5,3) (19,7) (17,2) (14,1) (24,30) (11,10) (20,29) (32,19) (11,20) (9,13) (13,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph921", "image": "data/cycle/graph_visual/hard/graph921.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (3,33) (22,25) (15,30) (0,29) (5,32) (30,32) (12,34) (5,14) (24,14) (20,27) (5,11) (12,4) (5,1) (14,29) (24,3) (0,31) (9,6) (13,22) (14,2) (2,26) (25,34) (19,24) (21,32) (23,20) (32,27) (16,28) (7,19) (8,5) (17,34) (18,24) (10,19) (2,16) (12,27) (9,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1354", "image": "data/cycle/graph_visual/hard/graph1354.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (17,21) (24,9) (10,2) (2,7) (25,16) (2,11) (13,5) (8,19) (27,22) (6,19) (5,14) (27,28) (1,4) (1,19) (5,21) (0,27) (11,26) (1,0) (23,25) (15,23) (13,20) (6,26) (9,8) (27,3) (12,20) (18,1) (23,27) (25,12) (18,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1276", "image": "data/cycle/graph_visual/hard/graph1276.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (0,4) (24,20) (17,5) (18,27) (2,7) (11,20) (12,14) (4,6) (4,7) (8,1) (0,19) (18,1) (23,3) (25,2) (15,22) (7,8) (21,17) (13,23) (21,23) (2,0) (0,3) (13,22) (0,1) (3,16) (14,5) (9,0) (1,22) (11,25) (26,10) (10,19) (5,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph212", "image": "data/cycle/graph_visual/hard/graph212.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (10,7) (0,27) (27,24) (22,14) (26,13) (19,9) (25,10) (11,3) (25,17) (23,2) (18,9) (6,9) (14,15) (14,4) (17,1) (9,7) (26,21) (7,15) (7,16) (5,12) (1,0) (8,6) (20,24) (9,26) (10,2) (11,1) (13,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph909", "image": "data/cycle/graph_visual/hard/graph909.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (25,11) (10,32) (5,17) (12,6) (11,21) (25,16) (22,12) (9,28) (32,16) (14,8) (10,7) (34,13) (1,8) (32,4) (9,11) (24,17) (25,31) (29,11) (34,30) (0,8) (23,24) (6,23) (2,33) (17,27) (30,23) (1,18) (31,15) (12,19) (2,20) (3,34) (7,6) (0,5) (23,26) (21,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph422", "image": "data/cycle/graph_visual/hard/graph422.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (19,6) (23,1) (10,3) (1,19) (16,6) (19,7) (8,20) (27,22) (4,13) (18,6) (0,26) (4,24) (2,8) (26,28) (17,24) (2,6) (14,26) (11,29) (29,4) (11,16) (0,10) (5,16) (22,16) (25,9) (21,16) (12,8) (25,0) (24,14) (15,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph38", "image": "data/cycle/graph_visual/hard/graph38.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (1,15) (2,6) (6,13) (16,5) (19,9) (8,6) (25,22) (3,21) (10,17) (15,17) (4,24) (1,11) (5,20) (19,21) (19,16) (4,12) (21,18) (23,0) (13,23) (22,13) (7,24) (23,1) (13,20) (23,7) (24,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1062", "image": "data/cycle/graph_visual/hard/graph1062.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (9,15) (14,7) (14,3) (17,25) (23,18) (11,12) (1,15) (0,4) (17,2) (15,25) (9,5) (24,14) (7,13) (18,10) (4,17) (22,6) (21,23) (16,10) (23,17) (1,6) (12,20) (12,6) (15,8) (14,19) (19,2) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph968", "image": "data/cycle/graph_visual/hard/graph968.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (12,30) (3,21) (31,27) (17,15) (2,7) (0,12) (30,26) (0,33) (11,12) (24,33) (5,11) (6,29) (34,28) (32,13) (25,23) (5,3) (29,4) (34,2) (27,28) (8,1) (9,22) (7,10) (20,28) (24,32) (14,7) (9,1) (21,16) (18,30) (19,16) (22,34) (6,21) (23,10) (15,27) (33,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph390", "image": "data/cycle/graph_visual/hard/graph390.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (6,0) (3,10) (7,24) (19,2) (28,19) (18,19) (18,21) (21,24) (8,28) (15,27) (17,12) (7,17) (6,9) (27,17) (12,23) (14,10) (14,24) (22,1) (18,11) (24,13) (3,5) (21,22) (16,11) (25,27) (6,7) (4,26) (27,26) (7,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1455", "image": "data/cycle/graph_visual/hard/graph1455.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (18,9) (12,2) (1,20) (15,17) (9,3) (19,27) (6,13) (27,9) (22,3) (14,10) (0,5) (3,0) (13,9) (10,0) (0,2) (20,26) (19,2) (28,23) (4,8) (21,25) (7,15) (8,5) (25,28) (2,16) (0,4) (25,8) (1,0) (4,2) (11,8) (29,23) (23,24) (28,1) (0,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1217", "image": "data/cycle/graph_visual/hard/graph1217.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,14) (25,22) (11,6) (26,14) (7,27) (16,8) (9,18) (10,5) (16,19) (0,27) (25,17) (16,24) (14,3) (8,25) (9,5) (20,27) (1,27) (10,13) (6,21) (3,12) (23,14) (11,3) (0,19) (8,10) (2,19) (0,1) (0,2) (15,3) (16,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph541", "image": "data/cycle/graph_visual/hard/graph541.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (14,11) (25,12) (8,12) (6,19) (14,4) (22,21) (21,26) (24,10) (21,13) (20,29) (2,20) (9,5) (3,1) (9,22) (30,12) (14,15) (12,7) (4,3) (22,6) (21,23) (25,13) (29,0) (2,16) (17,10) (16,10) (8,24) (26,4) (19,27) (7,28) (3,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1072", "image": "data/cycle/graph_visual/hard/graph1072.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (4,25) (13,21) (22,2) (6,5) (10,6) (9,19) (11,5) (5,21) (6,12) (21,24) (8,5) (0,22) (0,3) (22,18) (18,7) (4,17) (1,22) (24,16) (9,23) (1,0) (23,20) (0,14) (0,2) (14,23) (3,12) (25,20) (15,2) (4,0) (14,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph682", "image": "data/cycle/graph_visual/hard/graph682.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (2,17) (16,8) (10,6) (11,1) (21,28) (23,25) (1,14) (23,19) (10,11) (4,5) (10,27) (5,3) (15,29) (1,2) (31,11) (23,29) (15,14) (0,3) (28,24) (26,20) (10,13) (13,9) (17,22) (7,19) (5,23) (11,20) (30,20) (12,2) (18,25) (16,27) (27,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph504", "image": "data/cycle/graph_visual/hard/graph504.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (11,2) (27,17) (24,25) (18,9) (17,28) (29,0) (29,8) (3,28) (26,11) (28,14) (29,12) (15,7) (5,18) (20,4) (1,19) (19,21) (5,25) (21,3) (22,12) (23,3) (2,16) (5,4) (27,6) (23,10) (3,15) (11,12) (13,11) (19,26) (1,18) (29,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1697", "image": "data/cycle/graph_visual/hard/graph1697.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (22,3) (5,30) (27,24) (14,1) (12,4) (20,26) (17,31) (19,31) (20,8) (29,3) (6,11) (13,18) (26,16) (3,20) (0,2) (10,0) (21,19) (23,7) (15,27) (17,25) (23,4) (20,7) (2,17) (13,4) (1,0) (10,28) (17,15) (11,18) (28,7) (20,15) (18,30) (30,9) (14,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph590", "image": "data/cycle/graph_visual/hard/graph590.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (3,18) (21,18) (1,10) (29,1) (8,13) (13,0) (11,25) (24,25) (21,20) (25,14) (17,30) (5,15) (26,28) (3,25) (23,24) (21,22) (19,28) (2,26) (17,9) (20,10) (16,4) (2,18) (7,17) (26,5) (1,30) (25,8) (15,16) (16,27) (18,12) (6,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph458", "image": "data/cycle/graph_visual/hard/graph458.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (4,13) (3,27) (1,18) (15,0) (15,6) (29,22) (25,15) (14,8) (2,27) (2,26) (5,9) (9,17) (11,4) (16,12) (27,7) (20,22) (28,6) (21,6) (1,26) (2,10) (23,6) (20,25) (25,17) (1,12) (1,13) (5,24) (20,19) (4,14) (9,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph623", "image": "data/cycle/graph_visual/hard/graph623.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (10,2) (23,9) (31,5) (14,20) (15,29) (13,22) (19,26) (6,0) (18,22) (4,13) (0,2) (23,16) (11,15) (8,15) (20,22) (21,7) (29,26) (24,14) (3,1) (5,30) (25,13) (12,7) (16,22) (26,31) (9,3) (17,21) (25,17) (14,29) (28,14) (10,1) (19,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph143", "image": "data/cycle/graph_visual/hard/graph143.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (14,23) (24,23) (26,9) (8,4) (2,11) (2,0) (19,7) (16,7) (10,24) (5,13) (20,1) (15,1) (21,1) (17,20) (23,1) (25,8) (22,24) (3,6) (11,17) (17,16) (10,3) (9,19) (21,18) (12,16) (14,4) (13,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph689", "image": "data/cycle/graph_visual/hard/graph689.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (29,14) (16,2) (1,18) (2,21) (4,18) (6,28) (16,19) (30,12) (23,14) (30,28) (27,23) (31,30) (5,14) (10,8) (21,13) (29,9) (7,8) (14,17) (7,26) (3,18) (22,8) (25,28) (27,15) (0,26) (24,10) (20,12) (22,23) (14,25) (11,28) (16,7) (4,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph535", "image": "data/cycle/graph_visual/hard/graph535.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (26,2) (16,30) (15,26) (4,23) (29,3) (24,12) (28,10) (0,8) (24,19) (1,4) (3,28) (13,17) (20,23) (10,25) (28,11) (22,27) (26,9) (6,28) (17,20) (24,2) (14,3) (21,10) (8,12) (5,6) (18,8) (7,26) (29,22) (16,15) (17,22) (11,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph397", "image": "data/cycle/graph_visual/hard/graph397.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (27,26) (11,18) (3,5) (24,13) (18,21) (27,25) (17,12) (22,21) (14,24) (28,19) (10,3) (4,26) (7,20) (7,6) (7,17) (27,15) (21,24) (19,2) (6,9) (22,1) (18,19) (12,23) (27,17) (10,14) (7,24) (16,11) (0,6) (8,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1286", "image": "data/cycle/graph_visual/hard/graph1286.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (27,17) (14,5) (2,0) (15,2) (13,8) (3,14) (18,2) (6,16) (22,16) (19,18) (1,8) (12,16) (10,15) (27,24) (11,17) (0,13) (15,12) (16,7) (3,4) (9,21) (23,8) (5,20) (24,25) (11,13) (1,0) (0,3) (9,18) (26,0) (14,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1266", "image": "data/cycle/graph_visual/hard/graph1266.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (25,4) (5,11) (19,4) (0,13) (27,7) (6,21) (6,22) (5,26) (12,5) (0,1) (24,12) (7,15) (14,18) (26,6) (7,13) (20,13) (4,16) (4,23) (8,17) (6,0) (19,9) (22,10) (14,24) (19,6) (2,23) (17,20) (3,4) (1,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph111", "image": "data/cycle/graph_visual/hard/graph111.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 26, and the edges are: (7,11) (0,21) (26,20) (4,1) (14,25) (17,25) (25,3) (10,8) (6,5) (13,21) (16,23) (13,18) (18,14) (10,16) (17,24) (17,12) (15,13) (2,5) (1,3) (17,10) (14,19) (9,25) (11,25) (14,26) (19,2) (22,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph511", "image": "data/cycle/graph_visual/hard/graph511.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (24,12) (29,0) (25,17) (16,15) (2,30) (21,7) (28,6) (13,30) (15,25) (17,5) (10,18) (28,11) (7,14) (28,12) (28,27) (2,19) (9,8) (23,29) (12,20) (17,14) (23,18) (14,4) (4,3) (22,10) (23,6) (9,15) (26,29) (15,1) (14,19) (1,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph782", "image": "data/cycle/graph_visual/hard/graph782.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (27,14) (27,7) (16,20) (4,15) (21,32) (23,24) (30,25) (14,21) (2,13) (4,30) (28,17) (5,20) (9,32) (8,18) (28,31) (25,6) (3,19) (11,14) (22,30) (7,29) (8,1) (18,21) (5,25) (12,9) (29,4) (17,9) (3,1) (9,23) (4,0) (2,10) (1,2) (29,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1436", "image": "data/cycle/graph_visual/hard/graph1436.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (15,1) (4,17) (0,1) (5,26) (10,14) (21,0) (11,2) (22,16) (12,25) (23,15) (0,28) (18,25) (20,2) (2,0) (29,20) (6,25) (8,29) (20,10) (10,5) (5,3) (27,0) (22,2) (10,13) (19,22) (28,16) (12,14) (11,15) (7,6) (10,9) (17,9) (24,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1693", "image": "data/cycle/graph_visual/hard/graph1693.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (5,7) (23,0) (31,20) (28,19) (17,27) (27,23) (3,9) (0,29) (14,4) (27,25) (0,3) (0,30) (13,2) (26,5) (29,6) (18,24) (23,10) (6,12) (23,18) (20,1) (26,13) (0,2) (22,4) (3,5) (8,2) (9,21) (11,28) (2,28) (16,24) (18,15) (0,1) (4,23) (4,0) (26,4) (1,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1957", "image": "data/cycle/graph_visual/hard/graph1957.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (6,22) (28,33) (2,3) (30,21) (2,0) (10,25) (19,11) (15,13) (5,32) (30,28) (16,25) (34,26) (8,6) (30,13) (29,9) (34,16) (4,21) (16,2) (27,20) (30,12) (1,0) (14,22) (24,18) (9,19) (19,6) (32,17) (4,31) (24,0) (20,13) (7,31) (27,22) (26,1) (6,32) (18,8) (23,8) (16,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1675", "image": "data/cycle/graph_visual/hard/graph1675.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (6,18) (0,3) (7,4) (24,9) (17,20) (22,31) (22,26) (2,22) (24,19) (26,3) (2,0) (5,7) (6,0) (25,24) (11,8) (1,14) (7,10) (21,18) (4,6) (18,12) (13,1) (27,4) (21,28) (29,10) (0,1) (16,10) (14,11) (30,17) (7,14) (18,2) (6,20) (23,19) (0,15) (20,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph886", "image": "data/cycle/graph_visual/hard/graph886.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 33, and the edges are: (19,6) (17,7) (25,8) (28,3) (17,11) (24,16) (5,31) (12,8) (32,16) (26,2) (7,21) (23,26) (33,26) (9,26) (24,15) (3,8) (33,0) (18,14) (21,13) (9,12) (27,20) (7,4) (22,1) (4,19) (10,23) (18,11) (25,20) (5,32) (9,30) (15,1) (32,30) (26,19) (13,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph477", "image": "data/cycle/graph_visual/hard/graph477.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (17,24) (10,20) (29,12) (29,5) (24,7) (27,24) (14,12) (8,22) (22,24) (4,17) (1,15) (19,4) (6,14) (0,13) (23,28) (3,9) (21,18) (26,10) (16,8) (14,16) (9,1) (23,2) (23,11) (17,26) (19,11) (15,27) (16,0) (15,25) (6,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1526", "image": "data/cycle/graph_visual/hard/graph1526.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,10) (19,16) (0,16) (0,3) (5,22) (30,24) (14,13) (14,9) (28,9) (27,5) (30,25) (1,0) (1,29) (18,11) (28,7) (21,5) (0,24) (26,2) (11,5) (26,8) (23,0) (17,21) (7,12) (5,6) (20,5) (4,0) (15,16) (28,15) (27,3) (20,8) (0,2) (29,15) (18,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1674", "image": "data/cycle/graph_visual/hard/graph1674.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 31, and the edges are: (19,21) (13,17) (2,10) (20,11) (22,9) (28,10) (8,7) (1,0) (20,31) (27,14) (12,13) (24,11) (25,9) (31,0) (12,19) (5,3) (5,6) (22,29) (16,3) (30,1) (28,14) (2,0) (1,29) (30,12) (15,2) (2,1) (22,24) (26,3) (18,11) (4,29) (23,5) (8,24) (19,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph514", "image": "data/cycle/graph_visual/hard/graph514.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (2,30) (9,6) (5,24) (7,24) (24,29) (18,27) (19,5) (18,26) (15,2) (14,26) (25,20) (28,3) (8,5) (16,25) (9,12) (8,21) (1,13) (15,10) (25,1) (26,4) (6,29) (3,15) (5,22) (21,23) (26,17) (9,17) (15,13) (3,4) (4,0) (11,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph271", "image": "data/cycle/graph_visual/hard/graph271.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (7,6) (7,1) (6,22) (4,11) (17,24) (20,13) (0,26) (21,8) (14,18) (12,20) (17,5) (8,17) (20,27) (15,11) (16,2) (15,12) (19,15) (22,15) (17,26) (17,15) (19,10) (2,19) (25,26) (18,0) (9,4) (7,23) (3,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph709", "image": "data/cycle/graph_visual/hard/graph709.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,21) (4,6) (8,15) (6,8) (28,23) (4,1) (27,19) (0,12) (12,26) (7,25) (9,27) (2,1) (1,22) (19,11) (30,4) (6,11) (31,8) (13,3) (14,2) (3,1) (5,17) (32,5) (17,4) (20,15) (17,18) (23,10) (15,29) (16,26) (12,11) (16,28) (20,7) (24,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph738", "image": "data/cycle/graph_visual/hard/graph738.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (15,0) (27,20) (13,18) (18,16) (11,14) (0,11) (30,21) (19,12) (25,8) (23,1) (7,30) (31,4) (17,10) (31,11) (32,9) (6,24) (23,28) (2,27) (22,15) (3,9) (10,16) (5,26) (29,31) (22,20) (10,2) (12,6) (7,8) (19,22) (31,5) (1,19) (32,28) (5,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1047", "image": "data/cycle/graph_visual/hard/graph1047.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 25, and the edges are: (3,19) (19,15) (9,23) (7,12) (2,1) (4,19) (11,5) (4,12) (17,14) (18,21) (22,23) (20,4) (23,6) (16,11) (5,8) (0,25) (20,0) (10,22) (21,19) (24,22) (7,10) (25,2) (9,11) (22,13) (1,0) (17,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph970", "image": "data/cycle/graph_visual/hard/graph970.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 34, and the edges are: (23,27) (6,23) (3,11) (19,3) (8,18) (25,10) (27,3) (7,33) (6,17) (13,21) (14,3) (15,4) (14,30) (5,27) (7,29) (16,34) (25,32) (13,2) (5,22) (20,32) (4,28) (14,2) (26,9) (7,34) (0,20) (5,15) (2,8) (3,25) (26,18) (31,3) (12,4) (26,24) (9,1) (9,34)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph715", "image": "data/cycle/graph_visual/hard/graph715.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (23,16) (13,30) (10,2) (6,13) (18,26) (28,17) (0,2) (9,12) (19,13) (22,25) (27,11) (20,9) (4,3) (4,25) (32,29) (7,20) (32,23) (19,9) (1,6) (15,20) (8,26) (18,9) (26,21) (24,4) (16,4) (24,6) (10,29) (28,12) (28,14) (22,5) (27,26) (6,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1592", "image": "data/cycle/graph_visual/hard/graph1592.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 30, and the edges are: (28,22) (25,19) (2,0) (16,21) (1,27) (0,4) (16,27) (13,14) (18,6) (19,20) (0,3) (16,15) (9,4) (0,14) (11,24) (29,5) (29,10) (2,4) (17,2) (17,25) (27,8) (27,23) (5,3) (14,3) (14,12) (28,25) (14,9) (17,7) (24,18) (22,30) (5,6) (0,1) (26,25) (15,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1351", "image": "data/cycle/graph_visual/hard/graph1351.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 28, and the edges are: (1,28) (21,8) (9,25) (23,27) (2,0) (2,3) (20,27) (13,27) (1,0) (21,28) (8,17) (2,13) (4,10) (12,28) (24,11) (0,5) (28,15) (20,19) (3,22) (14,28) (4,16) (10,15) (6,23) (18,25) (7,21) (5,26) (13,0) (3,4) (18,28) (10,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1733", "image": "data/cycle/graph_visual/hard/graph1733.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (10,5) (2,0) (1,7) (25,9) (31,16) (20,19) (23,24) (16,19) (0,13) (29,23) (3,11) (28,15) (6,27) (12,19) (29,1) (8,28) (24,2) (31,18) (2,9) (3,0) (4,22) (26,6) (13,7) (27,4) (17,23) (13,18) (8,11) (3,4) (6,7) (4,32) (32,30) (17,21) (22,14) (5,30) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph282", "image": "data/cycle/graph_visual/hard/graph282.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 27, and the edges are: (5,18) (5,11) (26,27) (0,3) (16,0) (10,7) (21,9) (22,3) (13,11) (5,27) (6,2) (5,17) (0,24) (19,0) (2,26) (7,14) (15,23) (16,15) (1,18) (20,8) (27,24) (14,16) (4,5) (21,8) (25,15) (5,20) (12,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1713", "image": "data/cycle/graph_visual/hard/graph1713.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 32, and the edges are: (8,10) (26,18) (16,8) (4,15) (17,1) (17,31) (25,28) (2,7) (0,15) (6,30) (9,23) (0,27) (1,0) (19,11) (7,26) (31,26) (28,10) (0,2) (2,22) (14,17) (21,0) (32,3) (5,3) (4,10) (24,23) (26,12) (13,2) (30,31) (24,2) (28,20) (11,22) (30,10) (24,32) (0,3) (29,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1460", "image": "data/cycle/graph_visual/hard/graph1460.png", "conversations": [ { "from": "human", "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 29, and the edges are: (0,1) (29,12) (19,3) (15,14) (4,16) (21,26) (16,6) (15,11) (29,25) (25,20) (4,24) (17,12) (7,28) (27,6) (8,1) (24,3) (0,27) (26,29) (28,18) (16,8) (15,23) (19,25) (5,24) (11,18) (9,22) (13,10) (9,4) (1,13) (2,12) (9,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] } ]