[ { "id": "cycle-easy-graph290", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (2,0) (6,1) (8,7) (8,9) (2,6) (1,0) (4,7) (7,3) (4,5) (6,3) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph236", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (4,2) (4,0) (1,3) (8,7) (0,2) (8,6) (6,5) (1,0) (6,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph49", "image": "data/cycle/graph_visual/easy/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 7, and the edges are: (1,5) (6,7) (3,5) (3,7) (2,1) (0,3) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph140", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (9,4) (1,3) (8,1) (4,0) (4,7) (2,7) (5,7) (2,8) (6,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph256", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (4,8) (3,8) (7,2) (9,7) (0,1) (3,0) (0,4) (5,9) (2,3) (2,6) (1,2) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph58", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (1,6) (0,8) (5,7) (4,2) (3,2) (8,3) (1,4) (5,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph178", "image": "data/cycle/graph_visual/easy/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 7, and the edges are: (6,2) (3,7) (5,6) (7,0) (5,7) (4,0) (1,7) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph93", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (3,4) (0,7) (2,0) (0,4) (1,6) (4,8) (6,7) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph250", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (0,7) (6,7) (7,2) (3,5) (5,8) (4,8) (8,6) (0,1) (1,8) (0,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph12", "image": "data/cycle/graph_visual/easy/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 6, and the edges are: (2,6) (2,5) (0,3) (0,4) (0,5) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph139", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (7,4) (7,5) (8,0) (7,8) (9,5) (2,9) (1,7) (6,3) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph154", "image": "data/cycle/graph_visual/easy/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 5, and the edges are: (1,5) (4,0) (0,3) (1,0) (2,0) (1,2) (3,5) (4,1) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph261", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (2,0) (8,9) (0,3) (4,6) (4,7) (2,6) (5,0) (4,0) (1,0) (4,1) (8,4) (7,3) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph136", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (2,3) (3,5) (1,9) (3,0) (3,7) (9,6) (6,7) (4,3) (0,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph237", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (3,1) (0,8) (2,6) (1,0) (5,1) (4,2) (3,7) (0,7) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph16", "image": "data/cycle/graph_visual/easy/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 6, and the edges are: (2,6) (2,4) (1,3) (4,0) (2,5) (6,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph198", "image": "data/cycle/graph_visual/easy/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 7, and the edges are: (2,6) (0,3) (1,0) (6,5) (7,1) (0,4) (0,5) (7,5) (0,7) (0,2) (3,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph56", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (3,0) (8,7) (2,4) (5,6) (8,5) (5,1) (1,0) (1,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph202", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (8,7) (1,7) (3,4) (7,5) (6,7) (1,0) (1,2) (2,0) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph217", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (7,4) (8,2) (0,1) (7,0) (5,8) (3,6) (5,3) (5,4) (2,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph51", "image": "data/cycle/graph_visual/easy/graph51.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (5,7) (0,2) (3,7) (2,4) (5,6) (2,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph291", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (0,3) (3,6) (8,2) (5,4) (0,4) (9,3) (7,4) (0,1) (7,1) (2,0) (8,7) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph248", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (1,0) (0,7) (5,2) (0,3) (5,9) (8,5) (4,9) (2,0) (3,8) (9,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph67", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (2,0) (4,8) (1,8) (7,4) (5,6) (0,1) (3,8) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph174", "image": "data/cycle/graph_visual/easy/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 6, and the edges are: (2,1) (3,5) (0,1) (5,6) (0,4) (1,6) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph150", "image": "data/cycle/graph_visual/easy/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 4, and the edges are: (0,3) (2,1) (1,3) (4,3) (4,1) (0,1) (4,0) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph36", "image": "data/cycle/graph_visual/easy/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 7, and the edges are: (2,1) (4,5) (7,5) (3,2) (3,5) (4,6) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph133", "image": "data/cycle/graph_visual/easy/graph133.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (8,6) (5,8) (1,4) (5,1) (9,0) (3,9) (3,2) (7,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph134", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (7,1) (0,8) (7,5) (2,1) (0,6) (7,4) (0,3) (9,3) (2,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph220", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (3,7) (5,6) (1,7) (2,8) (0,3) (4,8) (0,1) (8,7) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph299", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (1,2) (4,7) (1,0) (0,3) (0,8) (5,7) (6,0) (9,3) (1,7) (6,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph260", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (5,1) (9,0) (0,7) (7,2) (8,4) (7,3) (0,1) (6,4) (7,5) (3,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph175", "image": "data/cycle/graph_visual/easy/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 6, and the edges are: (3,6) (0,2) (0,5) (0,1) (2,4) (5,1) (6,2) (0,4) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph145", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (7,9) (5,0) (6,1) (9,4) (6,7) (5,4) (5,8) (3,8) (2,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph207", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (1,8) (8,4) (6,5) (7,4) (4,0) (0,5) (0,2) (3,8) (3,0) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph91", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (2,4) (6,8) (7,1) (1,0) (0,5) (3,5) (2,6) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph123", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (6,8) (9,8) (2,0) (2,6) (4,2) (5,7) (7,1) (6,5) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph181", "image": "data/cycle/graph_visual/easy/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 7, and the edges are: (7,4) (0,1) (7,0) (1,5) (2,6) (0,6) (1,2) (3,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph135", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (1,0) (7,2) (7,6) (2,1) (7,4) (2,9) (4,3) (1,5) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph77", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (2,8) (5,3) (6,4) (4,3) (8,1) (7,4) (1,4) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph60", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (3,0) (5,7) (6,5) (2,8) (7,3) (7,1) (8,4) (8,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph30", "image": "data/cycle/graph_visual/easy/graph30.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (1,2) (7,5) (0,7) (4,7) (3,6) (3,1) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph282", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (3,5) (9,5) (2,0) (6,9) (7,4) (1,0) (9,8) (0,8) (1,4) (2,1) (1,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph108", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (0,1) (4,2) (2,3) (4,1) (8,2) (7,1) (9,1) (4,6) (3,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph112", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (0,7) (3,5) (8,4) (4,0) (7,6) (6,1) (9,0) (2,0) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph71", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (1,4) (2,3) (5,2) (2,0) (4,7) (0,6) (8,6) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph1", "image": "data/cycle/graph_visual/easy/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 4, and the edges are: (3,4) (0,2) (1,4) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph246", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (4,0) (9,1) (0,3) (7,9) (7,6) (5,9) (0,5) (0,2) (5,2) (1,0) (3,8) (4,2) (9,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph227", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (2,4) (1,0) (8,5) (3,0) (7,8) (6,5) (5,1) (1,2) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph188", "image": "data/cycle/graph_visual/easy/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 7, and the edges are: (7,1) (4,0) (6,0) (3,0) (2,0) (5,0) (0,7) (7,4) (2,6) (3,2) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph158", "image": "data/cycle/graph_visual/easy/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 5, and the edges are: (4,0) (1,4) (3,2) (3,0) (0,1) (2,0) (4,2) (5,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph5", "image": "data/cycle/graph_visual/easy/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 5, and the edges are: (3,4) (2,1) (0,5) (3,5) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph221", "image": "data/cycle/graph_visual/easy/graph221.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,2) (0,1) (0,4) (7,6) (0,3) (8,6) (8,4) (1,6) (6,2) (7,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph83", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (6,7) (5,0) (4,5) (5,7) (6,1) (2,1) (3,8) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph106", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (5,8) (7,2) (1,5) (7,6) (0,1) (4,7) (2,1) (3,4) (9,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph243", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (1,4) (4,0) (0,7) (4,6) (0,3) (8,7) (0,6) (5,2) (0,1) (0,2) (8,0) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph34", "image": "data/cycle/graph_visual/easy/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 7, and the edges are: (2,4) (6,7) (6,5) (7,3) (7,1) (0,2) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph147", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (5,9) (0,5) (1,7) (4,8) (4,3) (2,6) (5,7) (6,0) (2,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph44", "image": "data/cycle/graph_visual/easy/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 7, and the edges are: (6,2) (0,7) (4,0) (3,2) (0,3) (0,5) (1,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph98", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (3,1) (0,3) (0,5) (3,7) (3,6) (4,2) (9,6) (4,6) (9,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph63", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (8,3) (7,6) (6,5) (0,8) (7,8) (2,5) (1,7) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph113", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (9,0) (3,1) (8,0) (2,7) (0,6) (5,8) (0,4) (3,0) (2,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph128", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (1,5) (1,0) (9,6) (2,1) (4,7) (2,6) (2,4) (5,8) (9,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph204", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (4,2) (5,1) (4,6) (3,2) (0,1) (2,0) (6,8) (5,7) (0,8) (2,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph191", "image": "data/cycle/graph_visual/easy/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 7, and the edges are: (3,5) (0,1) (2,0) (0,3) (6,5) (4,2) (1,2) (7,2) (5,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph149", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (9,5) (0,5) (7,4) (4,2) (7,1) (8,2) (6,5) (0,2) (9,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph186", "image": "data/cycle/graph_visual/easy/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 7, and the edges are: (4,3) (5,2) (0,2) (0,1) (4,7) (2,4) (2,6) (7,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph43", "image": "data/cycle/graph_visual/easy/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 7, and the edges are: (4,5) (6,4) (5,3) (5,7) (2,3) (0,7) (1,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph76", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (1,0) (8,6) (3,7) (6,1) (1,2) (5,6) (7,4) (6,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph266", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (8,6) (7,0) (3,4) (7,1) (8,4) (2,3) (9,2) (1,0) (0,2) (5,9) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph118", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (1,0) (3,6) (9,2) (1,4) (5,8) (9,1) (4,7) (4,8) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph146", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (6,9) (2,6) (6,0) (3,2) (8,9) (1,5) (3,5) (7,4) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph65", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (1,0) (5,3) (7,5) (4,2) (6,8) (8,2) (2,1) (4,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph293", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (9,2) (3,4) (0,3) (1,5) (7,2) (2,1) (0,2) (5,8) (7,4) (7,6) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph196", "image": "data/cycle/graph_visual/easy/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 7, and the edges are: (1,0) (2,0) (2,4) (3,1) (4,5) (7,1) (7,0) (1,6) (4,3) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph0", "image": "data/cycle/graph_visual/easy/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 4, and the edges are: (0,4) (3,1) (0,1) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph212", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (5,6) (0,4) (0,3) (2,4) (1,7) (5,1) (2,7) (1,0) (8,7) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph103", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (8,3) (5,7) (9,7) (7,0) (7,4) (8,6) (1,8) (3,2) (9,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph292", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (9,6) (6,0) (4,8) (0,1) (0,2) (9,8) (5,1) (5,3) (7,4) (2,3) (6,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph259", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (2,1) (8,4) (0,6) (1,4) (2,5) (9,7) (0,7) (4,6) (3,8) (0,2) (3,0) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph252", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (6,2) (4,6) (0,8) (3,0) (3,1) (7,4) (1,4) (6,9) (2,0) (4,0) (3,5) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph132", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (2,5) (6,2) (9,2) (9,0) (7,3) (1,8) (4,5) (1,3) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph141", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (7,8) (7,5) (7,6) (7,9) (9,1) (6,2) (3,2) (2,4) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph4", "image": "data/cycle/graph_visual/easy/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 5, and the edges are: (0,4) (3,5) (5,1) (1,2) (1,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph297", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (3,0) (8,9) (6,4) (1,4) (4,7) (5,3) (1,0) (4,8) (2,0) (6,2) (3,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph170", "image": "data/cycle/graph_visual/easy/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 6, and the edges are: (1,5) (1,0) (0,4) (1,3) (4,6) (6,2) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph234", "image": "data/cycle/graph_visual/easy/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 8, and the edges are: (5,8) (2,0) (2,7) (4,3) (0,1) (3,0) (7,4) (1,3) (6,8) (8,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-easy-graph25", "image": "data/cycle/graph_visual/easy/graph25.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (6,1) (3,0) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph8", "image": "data/cycle/graph_visual/easy/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 5, and the edges are: (3,0) (5,3) (1,0) (2,3) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-easy-graph286", "image": "data/cycle/graph_visual/easy/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 9, and the edges are: (3,4) (1,0) (8,2) (7,0) (1,5) (4,0) (5,8) (6,9) (2,3) (9,4) (3,0) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph965", "image": "data/cycle/graph_visual/medium/graph965.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (1,0) (2,10) (6,5) (5,0) (9,4) (0,2) (4,1) (8,0) (3,2) (7,0) (11,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph288", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (12,5) (10,14) (3,1) (4,9) (11,2) (5,13) (10,6) (4,10) (7,14) (3,0) (12,7) (9,11) (8,9) (1,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1300", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (9,2) (15,8) (9,1) (9,6) (13,2) (5,8) (9,4) (3,14) (0,1) (14,6) (15,2) (14,0) (7,16) (1,7) (2,10) (12,2) (11,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1466", "image": "data/cycle/graph_visual/medium/graph1466.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,10) (0,1) (5,19) (3,14) (2,10) (8,4) (18,1) (8,9) (0,11) (3,0) (2,0) (2,16) (14,15) (19,6) (5,12) (11,7) (5,4) (1,12) (14,19) (16,13) (0,10) (19,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1149", "image": "data/cycle/graph_visual/medium/graph1149.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (12,8) (1,3) (4,13) (0,1) (11,12) (3,14) (2,10) (5,8) (3,0) (9,7) (0,9) (6,5) (0,5) (0,2) (0,4) (13,2) (4,1) (3,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph246", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (6,5) (0,2) (10,3) (11,7) (11,13) (5,1) (9,8) (12,3) (2,7) (9,2) (11,3) (1,2) (5,14) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1244", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (0,5) (2,3) (4,0) (0,10) (10,11) (0,1) (6,14) (13,15) (8,5) (8,15) (7,1) (0,3) (2,0) (4,9) (2,15) (11,12) (15,4) (8,0) (6,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph440", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (9,5) (2,11) (11,10) (0,6) (7,13) (3,6) (1,4) (17,5) (14,7) (8,14) (9,15) (11,0) (15,3) (4,16) (15,7) (12,5) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph286", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (8,0) (4,5) (0,11) (3,12) (3,1) (13,6) (5,14) (12,8) (9,0) (13,9) (6,2) (10,12) (13,7) (14,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph342", "image": "data/cycle/graph_visual/medium/graph342.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (15,11) (15,1) (4,9) (9,0) (15,7) (13,10) (2,6) (10,3) (4,6) (1,0) (11,14) (7,8) (5,2) (10,1) (3,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1226", "image": "data/cycle/graph_visual/medium/graph1226.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (13,5) (7,5) (0,1) (0,2) (1,6) (4,2) (1,5) (8,9) (12,11) (3,0) (13,12) (15,14) (3,2) (8,6) (10,9) (14,11) (2,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph315", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (13,15) (12,2) (1,12) (5,9) (3,6) (7,10) (0,12) (8,12) (4,7) (6,14) (11,8) (2,15) (5,7) (2,4) (6,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph152", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (0,5) (3,7) (6,3) (4,2) (9,0) (11,6) (12,10) (3,1) (11,9) (0,10) (3,8) (6,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph594", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (6,14) (4,6) (6,7) (3,18) (8,14) (9,13) (15,12) (6,1) (13,17) (3,0) (19,14) (8,16) (11,12) (2,18) (0,19) (9,11) (5,6) (10,1) (18,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1487", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (6,18) (13,15) (9,14) (16,19) (15,9) (1,3) (0,2) (14,2) (0,1) (8,3) (10,4) (10,3) (7,11) (10,16) (6,7) (8,14) (17,5) (6,8) (0,5) (15,12) (5,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1301", "image": "data/cycle/graph_visual/medium/graph1301.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,12) (2,13) (13,14) (3,10) (0,10) (8,2) (11,8) (2,9) (16,13) (1,4) (0,2) (7,8) (0,3) (6,9) (5,7) (1,0) (16,0) (11,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph476", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (16,17) (2,4) (11,9) (6,12) (0,17) (13,5) (15,7) (4,3) (7,6) (15,3) (17,8) (10,17) (5,4) (13,14) (9,16) (6,16) (1,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph133", "image": "data/cycle/graph_visual/medium/graph133.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (12,1) (8,11) (9,5) (12,4) (2,5) (8,9) (4,5) (11,6) (10,11) (0,1) (9,3) (2,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph828", "image": "data/cycle/graph_visual/medium/graph828.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,23) (18,6) (12,11) (12,14) (15,3) (23,7) (0,15) (12,3) (1,19) (3,9) (5,16) (3,17) (10,2) (4,5) (21,19) (11,19) (4,13) (5,18) (11,2) (18,1) (17,20) (21,22) (8,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph60", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (6,5) (7,9) (3,11) (8,0) (4,1) (1,3) (9,2) (4,0) (10,4) (2,3) (5,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph219", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (13,12) (0,10) (10,1) (7,9) (8,10) (12,11) (6,8) (3,0) (6,9) (4,3) (4,11) (7,2) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1069", "image": "data/cycle/graph_visual/medium/graph1069.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (7,3) (3,6) (4,3) (5,1) (1,0) (7,2) (6,0) (8,4) (10,4) (12,4) (12,11) (5,6) (9,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1614", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (17,20) (10,13) (1,0) (5,9) (15,12) (12,16) (6,1) (11,2) (3,4) (10,12) (17,13) (14,17) (16,19) (12,18) (4,9) (0,3) (15,11) (8,2) (7,5) (0,2) (21,20) (2,6) (21,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph106", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (1,3) (5,1) (0,7) (7,3) (11,9) (4,2) (2,6) (10,0) (0,11) (4,11) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph791", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (14,17) (6,12) (8,22) (0,8) (15,9) (20,21) (15,5) (19,7) (18,19) (0,16) (4,17) (5,6) (1,8) (16,21) (7,4) (3,9) (0,15) (2,10) (6,10) (3,13) (23,6) (11,7) (20,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph341", "image": "data/cycle/graph_visual/medium/graph341.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (9,12) (11,2) (4,0) (6,8) (1,15) (7,3) (15,5) (13,9) (7,13) (6,1) (10,2) (14,0) (8,10) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph600", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (0,3) (14,11) (7,9) (1,4) (6,19) (16,4) (6,13) (17,2) (12,17) (5,4) (12,5) (20,10) (4,7) (6,18) (19,4) (20,6) (8,5) (14,13) (3,19) (15,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1280", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (7,16) (7,11) (8,10) (3,2) (1,13) (2,0) (6,2) (7,8) (0,1) (15,16) (0,9) (13,14) (3,0) (7,6) (3,5) (4,12) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph273", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (3,1) (5,2) (0,14) (8,4) (6,9) (6,1) (13,6) (0,9) (10,8) (6,8) (11,7) (12,5) (5,4) (7,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph834", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (22,12) (7,0) (7,23) (11,2) (21,10) (17,4) (1,2) (4,8) (20,6) (5,18) (22,9) (3,19) (13,10) (21,22) (15,8) (0,19) (19,14) (6,9) (14,5) (2,18) (2,10) (11,16) (4,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph952", "image": "data/cycle/graph_visual/medium/graph952.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (6,10) (8,3) (0,2) (4,6) (0,5) (1,0) (10,8) (9,4) (1,8) (7,5) (0,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph994", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (6,5) (6,2) (2,1) (11,5) (9,3) (2,0) (0,3) (7,11) (0,1) (4,2) (5,9) (10,1) (8,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph913", "image": "data/cycle/graph_visual/medium/graph913.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (4,9) (0,1) (2,4) (4,8) (3,6) (10,1) (7,4) (0,2) (8,1) (5,6) (3,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph745", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (8,17) (13,22) (16,14) (9,8) (7,14) (21,22) (4,16) (22,4) (22,2) (9,12) (2,0) (18,14) (6,13) (19,2) (5,11) (11,20) (7,10) (15,5) (5,13) (9,1) (3,17) (15,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph841", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (21,3) (16,2) (14,10) (4,8) (22,20) (13,9) (18,9) (10,0) (5,8) (24,23) (7,15) (0,3) (12,2) (19,1) (8,11) (6,13) (17,15) (23,9) (1,20) (3,9) (2,19) (8,23) (4,2) (0,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1272", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (10,2) (6,3) (1,0) (8,1) (0,3) (0,13) (10,7) (11,6) (16,15) (9,15) (0,2) (0,8) (7,4) (16,4) (0,15) (3,9) (7,12) (6,5) (8,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1761", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (2,18) (11,12) (14,19) (12,21) (3,0) (1,17) (24,15) (6,1) (7,23) (14,8) (20,10) (18,3) (8,22) (6,15) (20,14) (13,19) (6,16) (11,9) (4,6) (0,1) (0,15) (5,6) (9,18) (13,9) (23,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1036", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (2,0) (1,0) (7,3) (8,0) (5,10) (4,0) (12,11) (3,6) (3,0) (9,8) (3,4) (10,12) (2,12) (1,11) (9,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph703", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (8,19) (7,5) (8,12) (1,21) (7,3) (11,21) (9,16) (20,12) (6,2) (4,17) (13,1) (6,0) (3,10) (14,10) (15,5) (1,0) (16,0) (4,11) (7,18) (11,8) (11,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph860", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (4,9) (17,12) (13,1) (7,3) (15,23) (16,6) (5,11) (1,2) (7,16) (21,15) (4,2) (19,20) (14,22) (0,14) (12,8) (6,18) (6,10) (4,7) (12,6) (15,18) (12,24) (12,14) (11,22) (20,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph798", "image": "data/cycle/graph_visual/medium/graph798.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (8,17) (19,7) (11,4) (20,12) (2,19) (23,15) (4,9) (18,3) (11,15) (7,1) (15,17) (19,10) (7,6) (0,15) (6,22) (18,13) (17,22) (15,20) (0,16) (17,21) (5,17) (8,18) (14,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1109", "image": "data/cycle/graph_visual/medium/graph1109.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,0) (12,9) (10,8) (13,3) (1,4) (2,10) (4,0) (6,5) (0,1) (0,7) (12,11) (3,2) (0,6) (12,4) (5,0) (0,8) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1402", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (5,9) (1,17) (3,4) (5,2) (13,18) (0,13) (17,0) (8,3) (12,11) (11,9) (13,9) (13,6) (14,8) (15,0) (13,16) (17,8) (15,10) (0,1) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph942", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (7,8) (0,3) (2,1) (8,0) (4,6) (0,10) (5,8) (10,9) (2,0) (3,5) (1,0) (5,1) (1,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph618", "image": "data/cycle/graph_visual/medium/graph618.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (9,2) (17,4) (10,12) (15,1) (8,16) (16,0) (16,14) (11,18) (0,5) (14,6) (13,15) (3,1) (10,7) (6,9) (8,17) (17,15) (14,12) (19,4) (20,10) (11,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1451", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (3,14) (16,8) (16,1) (7,3) (5,14) (6,13) (5,10) (14,15) (17,16) (2,3) (10,8) (9,12) (9,5) (3,11) (19,0) (19,8) (18,14) (4,10) (6,11) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1561", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (17,14) (2,6) (13,10) (16,21) (4,3) (3,7) (0,2) (6,10) (4,18) (20,9) (12,1) (11,0) (0,1) (5,14) (0,10) (8,5) (0,3) (13,14) (19,4) (5,19) (0,15) (16,12) (21,10) (7,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph728", "image": "data/cycle/graph_visual/medium/graph728.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (10,11) (4,13) (21,10) (1,19) (8,20) (1,15) (3,2) (22,12) (11,18) (11,14) (19,9) (8,22) (9,22) (19,10) (16,21) (5,17) (5,18) (13,14) (0,20) (6,13) (3,7) (11,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1445", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (0,1) (13,9) (14,19) (8,2) (11,5) (0,18) (7,15) (16,13) (12,17) (8,11) (14,11) (1,10) (1,17) (3,1) (4,0) (6,16) (0,2) (5,4) (14,12) (13,5) (3,0) (4,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph75", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (10,11) (6,3) (5,2) (9,10) (7,2) (4,9) (11,0) (2,10) (1,6) (2,3) (8,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph930", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (10,3) (7,0) (0,1) (3,7) (8,0) (9,1) (0,2) (9,10) (8,6) (5,10) (5,4) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1307", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (2,0) (4,9) (3,7) (14,0) (16,15) (2,1) (15,14) (11,1) (1,0) (6,10) (8,12) (5,11) (4,7) (0,12) (2,4) (6,12) (13,6) (7,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1172", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (11,14) (13,8) (13,1) (9,11) (5,11) (9,0) (10,7) (14,7) (2,14) (3,4) (11,12) (5,8) (7,3) (6,8) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph195", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (2,1) (8,0) (6,5) (7,9) (10,13) (4,9) (9,11) (1,4) (12,6) (8,5) (6,13) (3,5) (1,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph423", "image": "data/cycle/graph_visual/medium/graph423.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,17) (8,1) (2,9) (14,5) (16,15) (15,2) (14,6) (5,10) (8,15) (9,11) (12,13) (16,7) (3,4) (3,0) (14,3) (16,12) (16,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph100", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (11,8) (5,6) (9,11) (2,0) (7,3) (10,5) (11,2) (7,6) (8,6) (4,2) (1,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph221", "image": "data/cycle/graph_visual/medium/graph221.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (7,8) (10,5) (12,2) (11,4) (12,13) (6,0) (4,1) (3,0) (0,2) (2,11) (5,6) (9,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1722", "image": "data/cycle/graph_visual/medium/graph1722.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (8,15) (8,4) (22,21) (18,2) (9,22) (4,13) (2,0) (23,7) (1,2) (18,5) (6,9) (20,6) (10,21) (11,16) (0,7) (19,0) (5,14) (13,10) (3,19) (17,4) (3,0) (14,19) (2,11) (10,2) (12,22) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1073", "image": "data/cycle/graph_visual/medium/graph1073.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (4,8) (7,1) (0,2) (7,12) (7,11) (1,4) (12,5) (1,6) (3,12) (0,1) (7,10) (9,12) (3,0) (2,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph515", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (9,5) (18,13) (8,3) (8,17) (5,2) (0,15) (16,13) (11,12) (13,6) (13,9) (17,0) (17,1) (0,13) (3,4) (9,11) (10,15) (8,14) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1748", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (23,19) (12,23) (16,2) (15,2) (8,10) (20,2) (3,0) (0,2) (2,22) (11,21) (14,12) (21,4) (21,17) (0,14) (18,6) (3,14) (7,1) (4,24) (9,6) (9,20) (21,7) (9,5) (15,8) (2,13) (9,23) (19,1) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1341", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (0,3) (8,7) (12,5) (0,2) (8,15) (0,10) (11,13) (9,2) (13,14) (0,16) (7,5) (10,3) (0,1) (17,2) (9,6) (17,11) (8,17) (2,16) (1,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1590", "image": "data/cycle/graph_visual/medium/graph1590.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (7,19) (2,4) (0,2) (8,16) (12,0) (6,17) (5,3) (12,9) (6,15) (21,2) (21,11) (14,13) (20,18) (1,15) (1,0) (20,8) (17,10) (20,13) (19,4) (6,14) (20,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph13", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (8,0) (9,1) (5,4) (7,0) (5,10) (3,7) (6,8) (4,2) (9,10) (3,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph179", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (5,10) (2,8) (0,9) (8,11) (2,5) (12,2) (2,6) (7,3) (3,1) (1,9) (10,4) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph202", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (3,4) (10,11) (2,6) (13,5) (3,5) (12,8) (0,13) (11,0) (9,8) (10,2) (12,5) (6,1) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1516", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (10,3) (5,4) (7,11) (5,16) (0,4) (2,0) (7,9) (20,4) (0,3) (1,16) (17,6) (0,15) (13,12) (11,19) (8,17) (4,9) (15,12) (9,10) (10,0) (18,0) (14,2) (1,0) (17,14) (14,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph275", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (3,6) (3,13) (7,0) (9,4) (8,4) (2,10) (6,5) (14,10) (0,12) (1,8) (11,8) (8,5) (14,9) (1,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph451", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (9,6) (5,15) (12,1) (8,11) (14,15) (2,17) (4,16) (0,6) (8,15) (7,11) (2,11) (10,14) (8,9) (1,4) (9,13) (2,3) (17,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph937", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (8,0) (4,0) (5,10) (3,0) (5,4) (4,2) (10,3) (10,9) (0,1) (3,7) (1,9) (0,7) (2,0) (6,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph356", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (4,11) (11,13) (3,1) (10,12) (8,4) (12,14) (15,9) (15,10) (7,6) (1,15) (14,8) (2,9) (6,14) (5,0) (0,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1013", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (4,3) (0,3) (0,1) (4,9) (3,5) (7,8) (0,7) (6,0) (0,5) (4,0) (1,6) (2,0) (0,10) (11,4) (6,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1610", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (7,21) (3,20) (7,16) (11,4) (7,8) (11,3) (12,10) (10,15) (21,18) (2,4) (2,13) (11,10) (7,10) (5,11) (2,17) (8,1) (20,6) (14,17) (0,15) (2,0) (0,1) (9,15) (19,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph68", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (10,8) (7,8) (3,4) (5,11) (2,6) (10,4) (1,7) (5,9) (0,5) (10,2) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1488", "image": "data/cycle/graph_visual/medium/graph1488.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (4,6) (6,8) (12,13) (11,4) (12,16) (0,3) (0,4) (2,0) (13,9) (17,7) (10,9) (19,7) (14,18) (19,0) (9,1) (0,16) (0,1) (11,15) (14,0) (3,2) (14,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph496", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (13,15) (6,13) (2,15) (4,18) (11,7) (14,0) (3,15) (9,10) (0,9) (7,0) (7,16) (17,9) (11,1) (8,7) (5,9) (12,14) (10,4) (8,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph148", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (9,3) (7,2) (10,4) (2,3) (6,12) (11,10) (1,4) (0,4) (8,10) (10,2) (10,5) (3,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph605", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (3,13) (16,3) (0,14) (15,9) (5,10) (10,20) (18,0) (6,18) (8,2) (16,2) (11,20) (12,9) (7,0) (13,14) (11,6) (1,0) (17,4) (19,6) (12,3) (17,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph378", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (3,8) (1,0) (7,6) (16,10) (16,1) (13,8) (5,16) (14,9) (4,9) (2,3) (11,12) (6,12) (4,8) (10,13) (3,15) (16,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph697", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (0,8) (6,17) (8,10) (11,10) (11,4) (20,3) (5,2) (12,16) (0,3) (14,7) (14,16) (19,12) (21,13) (18,9) (1,13) (18,1) (12,17) (13,2) (21,15) (0,19) (15,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1044", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (4,1) (11,4) (1,0) (5,10) (0,5) (8,11) (6,8) (2,6) (3,8) (0,12) (5,6) (9,5) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph141", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (8,12) (2,12) (7,0) (8,7) (10,9) (9,3) (11,8) (7,5) (8,1) (7,6) (3,2) (12,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1588", "image": "data/cycle/graph_visual/medium/graph1588.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (20,9) (13,10) (0,15) (0,10) (16,12) (4,18) (14,13) (4,3) (7,3) (16,21) (19,4) (8,5) (14,17) (6,10) (2,6) (5,14) (11,0) (5,19) (1,0) (1,12) (10,21) (20,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1072", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (4,10) (0,5) (0,4) (0,2) (12,3) (6,3) (8,1) (5,6) (4,7) (12,4) (7,9) (1,0) (12,1) (2,4) (11,8) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph388", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (4,10) (5,0) (12,9) (6,16) (16,2) (10,3) (12,3) (0,6) (14,13) (9,8) (6,15) (11,16) (0,14) (0,1) (3,13) (2,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph31", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (7,5) (10,9) (9,2) (6,3) (5,1) (7,3) (4,1) (3,8) (0,3) (9,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1642", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (0,3) (17,11) (5,19) (9,20) (6,1) (7,6) (2,0) (0,1) (0,10) (2,21) (9,21) (0,11) (4,12) (12,18) (3,8) (12,7) (0,5) (18,22) (11,2) (0,14) (8,16) (22,0) (6,13) (15,20) (21,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1701", "image": "data/cycle/graph_visual/medium/graph1701.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (2,3) (0,1) (18,11) (13,16) (4,14) (0,4) (23,16) (21,0) (7,12) (2,10) (2,22) (0,2) (18,8) (0,5) (20,10) (17,4) (5,12) (1,6) (1,20) (3,0) (19,1) (16,9) (18,17) (15,18) (20,7) (17,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1681", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (16,9) (21,10) (6,13) (18,19) (0,2) (17,0) (20,13) (14,23) (5,9) (3,4) (0,1) (15,11) (21,0) (0,7) (13,22) (3,8) (17,8) (1,17) (19,8) (9,13) (5,2) (12,15) (0,23) (11,13) (11,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1298", "image": "data/cycle/graph_visual/medium/graph1298.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (2,12) (0,9) (12,14) (10,14) (10,5) (0,3) (9,7) (13,11) (6,10) (2,11) (5,3) (4,0) (2,0) (5,16) (11,15) (1,0) (6,4) (0,15) (1,15) (8,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph459", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (2,12) (0,4) (14,8) (0,6) (15,3) (9,1) (15,11) (17,5) (9,7) (5,10) (6,16) (13,9) (12,1) (6,3) (13,3) (1,8) (10,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1624", "image": "data/cycle/graph_visual/medium/graph1624.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (12,0) (15,7) (19,0) (2,5) (21,15) (3,10) (17,0) (11,15) (9,4) (9,7) (16,22) (19,11) (2,6) (0,1) (1,13) (16,1) (4,6) (1,10) (20,10) (17,22) (22,8) (3,14) (18,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph140", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (11,7) (8,9) (0,5) (1,4) (4,2) (0,12) (10,7) (4,6) (4,3) (7,5) (9,2) (12,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1041", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (10,7) (8,4) (12,7) (3,12) (6,5) (2,0) (6,10) (11,12) (3,0) (4,0) (5,0) (6,1) (0,1) (11,2) (7,4) (3,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1290", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (3,7) (10,8) (3,2) (4,10) (13,11) (4,1) (14,13) (15,14) (9,5) (8,6) (5,0) (0,1) (2,12) (13,16) (0,13) (15,10) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph99", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (9,5) (4,0) (3,10) (11,6) (8,5) (10,5) (1,0) (9,1) (2,1) (7,2) (6,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1668", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (13,5) (3,6) (1,22) (10,9) (22,16) (1,17) (3,10) (12,15) (2,20) (0,1) (21,10) (0,18) (11,10) (10,19) (14,21) (4,16) (8,11) (8,4) (13,20) (12,6) (7,11) (8,2) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1326", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (3,0) (5,17) (15,11) (15,9) (17,11) (12,13) (9,1) (10,0) (13,14) (2,0) (13,16) (4,6) (8,3) (2,1) (4,0) (11,7) (3,14) (12,5) (4,14) (0,1) (0,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph525", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (1,0) (4,17) (9,12) (0,14) (16,2) (0,18) (3,13) (6,16) (2,8) (3,15) (14,13) (10,9) (6,17) (6,18) (3,11) (10,5) (12,16) (7,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph347", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (7,2) (0,13) (1,5) (0,3) (6,14) (0,15) (10,5) (9,11) (7,9) (3,5) (2,4) (5,12) (5,11) (8,5) (14,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph855", "image": "data/cycle/graph_visual/medium/graph855.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (15,2) (20,0) (2,23) (7,15) (6,2) (21,7) (23,18) (10,8) (3,22) (2,14) (7,5) (18,20) (8,16) (12,11) (17,19) (1,15) (5,12) (8,4) (17,10) (13,9) (20,22) (20,24) (8,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph436", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (7,16) (5,0) (16,10) (9,13) (4,15) (15,12) (3,8) (14,15) (11,10) (8,5) (9,14) (7,1) (16,5) (13,17) (17,6) (2,9) (2,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1379", "image": "data/cycle/graph_visual/medium/graph1379.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,14) (11,6) (8,2) (6,3) (12,16) (12,13) (9,15) (8,14) (2,0) (0,15) (3,5) (4,1) (15,7) (12,10) (15,3) (0,1) (0,13) (4,2) (14,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph36", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (3,8) (9,3) (6,2) (7,1) (5,9) (5,4) (10,2) (7,2) (7,3) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph160", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (1,4) (3,9) (11,10) (4,0) (7,2) (10,5) (3,2) (2,10) (12,3) (10,4) (10,8) (12,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph636", "image": "data/cycle/graph_visual/medium/graph636.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (19,12) (13,1) (1,0) (10,14) (10,3) (5,7) (11,14) (8,11) (16,0) (12,8) (9,16) (7,17) (2,6) (6,0) (20,11) (7,3) (8,18) (1,4) (4,11) (15,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1786", "image": "data/cycle/graph_visual/medium/graph1786.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (8,11) (22,17) (11,12) (18,5) (18,1) (0,2) (12,14) (2,10) (12,3) (0,15) (3,15) (13,4) (2,11) (24,20) (3,17) (0,3) (9,3) (16,5) (7,23) (18,6) (1,0) (19,1) (20,3) (23,21) (19,11) (5,4) (21,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph661", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (4,6) (8,0) (3,10) (17,14) (11,0) (4,1) (2,21) (15,16) (12,8) (19,16) (19,2) (17,10) (5,17) (8,7) (2,12) (15,18) (20,13) (3,11) (10,9) (20,21) (6,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1261", "image": "data/cycle/graph_visual/medium/graph1261.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (14,4) (13,5) (2,11) (15,7) (0,1) (14,1) (10,3) (1,11) (12,1) (6,3) (8,13) (16,1) (7,9) (9,16) (0,2) (10,16) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph689", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (18,16) (0,5) (18,14) (14,13) (0,13) (9,20) (21,8) (10,15) (1,21) (3,2) (4,10) (13,19) (4,6) (20,2) (3,4) (7,8) (18,15) (17,5) (12,10) (11,3) (21,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph906", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (10,5) (2,0) (7,9) (0,3) (4,1) (9,6) (2,8) (7,5) (0,1) (4,0) (3,4) (4,2) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph705", "image": "data/cycle/graph_visual/medium/graph705.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (2,6) (1,15) (5,16) (6,13) (6,0) (18,16) (3,21) (1,12) (21,0) (20,7) (9,13) (19,10) (11,17) (17,19) (13,19) (6,8) (5,20) (1,21) (13,7) (15,4) (4,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph664", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (10,7) (1,17) (13,11) (14,18) (14,15) (6,5) (9,13) (9,16) (14,3) (19,2) (15,7) (21,1) (12,4) (9,6) (9,20) (0,11) (12,7) (9,7) (10,17) (1,8) (2,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1509", "image": "data/cycle/graph_visual/medium/graph1509.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (18,11) (3,5) (1,18) (14,9) (14,8) (1,0) (5,4) (10,14) (6,15) (2,12) (5,12) (11,15) (19,17) (6,12) (14,13) (7,8) (20,2) (2,0) (14,16) (6,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1439", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (4,10) (9,10) (1,11) (11,7) (13,6) (0,9) (7,0) (9,5) (17,9) (18,4) (8,7) (12,14) (1,0) (13,15) (13,8) (14,0) (2,15) (7,16) (15,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph266", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (7,12) (4,3) (9,3) (0,9) (2,8) (0,14) (10,9) (9,1) (6,8) (7,10) (11,9) (5,14) (2,5) (13,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph659", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (17,2) (15,14) (17,16) (6,17) (20,16) (8,12) (16,1) (7,4) (18,11) (7,5) (10,18) (7,8) (11,12) (17,14) (3,5) (19,10) (20,8) (17,13) (9,12) (7,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1129", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (12,8) (7,0) (0,9) (6,2) (1,0) (1,8) (5,9) (1,10) (0,13) (11,13) (2,4) (2,0) (1,5) (0,3) (6,10) (3,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph264", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (3,8) (7,14) (8,2) (4,5) (14,9) (2,6) (13,4) (12,3) (5,12) (11,0) (10,5) (1,7) (0,7) (12,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph670", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (13,14) (6,13) (12,18) (21,0) (3,17) (7,4) (6,19) (7,10) (14,15) (6,0) (5,12) (1,3) (4,5) (19,4) (20,11) (4,17) (19,8) (6,20) (9,5) (16,6) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph231", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (11,9) (4,6) (11,8) (4,5) (4,2) (5,7) (12,2) (8,10) (11,12) (8,0) (13,10) (1,6) (12,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph262", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (1,7) (3,0) (2,3) (10,13) (4,10) (10,3) (12,2) (5,9) (14,6) (0,8) (11,10) (8,7) (14,12) (9,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1348", "image": "data/cycle/graph_visual/medium/graph1348.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (14,8) (4,0) (8,2) (14,4) (16,3) (16,0) (5,11) (8,13) (0,2) (15,1) (14,17) (12,9) (10,0) (17,7) (11,15) (0,1) (6,4) (12,11) (15,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1673", "image": "data/cycle/graph_visual/medium/graph1673.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (21,0) (8,3) (14,6) (3,18) (16,11) (4,19) (3,0) (1,16) (8,19) (8,21) (11,12) (7,16) (5,3) (22,10) (2,1) (17,8) (15,9) (13,10) (18,9) (4,16) (10,3) (6,12) (20,13) (0,2) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1250", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (0,13) (13,1) (3,0) (1,0) (11,10) (14,7) (14,8) (2,3) (10,9) (4,13) (8,10) (12,11) (11,2) (15,9) (0,2) (5,11) (1,5) (6,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1678", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (16,7) (2,11) (15,1) (20,1) (18,9) (4,14) (9,19) (16,17) (13,5) (1,12) (3,0) (0,1) (22,18) (11,16) (17,10) (21,8) (0,2) (6,3) (8,4) (1,14) (21,13) (10,3) (20,17) (19,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1731", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (13,14) (1,0) (0,18) (22,2) (11,16) (12,20) (22,6) (2,10) (17,4) (23,7) (3,16) (3,13) (23,9) (12,3) (18,6) (8,0) (20,17) (23,6) (2,0) (14,0) (16,21) (19,9) (5,10) (15,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph23", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (3,5) (9,8) (2,3) (4,10) (4,8) (0,6) (9,6) (1,5) (6,2) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1520", "image": "data/cycle/graph_visual/medium/graph1520.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (20,0) (16,14) (8,18) (18,6) (20,12) (9,17) (1,17) (16,13) (15,9) (0,4) (10,20) (0,5) (2,10) (11,19) (3,0) (5,15) (17,2) (19,8) (7,3) (3,11) (6,0) (1,0) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1328", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (6,10) (16,13) (8,11) (4,15) (6,14) (5,3) (9,0) (0,3) (1,0) (4,0) (17,12) (17,7) (3,12) (2,12) (15,1) (8,6) (4,2) (2,0) (13,14) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph138", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (2,11) (9,3) (7,12) (1,5) (3,7) (6,1) (3,8) (12,5) (12,10) (5,11) (0,3) (9,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1622", "image": "data/cycle/graph_visual/medium/graph1622.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (10,17) (21,0) (19,18) (4,0) (6,1) (21,17) (13,11) (2,19) (1,0) (22,13) (9,17) (16,20) (14,4) (17,14) (11,7) (14,12) (5,3) (16,10) (4,13) (0,3) (10,8) (15,13) (18,14) (5,2) (3,1) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1138", "image": "data/cycle/graph_visual/medium/graph1138.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (2,0) (3,0) (8,7) (5,10) (1,0) (6,5) (9,8) (11,2) (11,4) (0,6) (2,12) (4,1) (7,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph27", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (10,1) (4,3) (0,7) (5,4) (7,10) (6,9) (4,7) (1,6) (2,7) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph360", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (4,5) (1,2) (10,0) (11,16) (3,9) (3,11) (2,16) (4,12) (2,8) (12,6) (6,1) (13,14) (7,1) (1,10) (13,15) (2,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph161", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (1,8) (7,10) (4,7) (4,3) (11,1) (6,11) (6,9) (1,12) (5,4) (2,7) (1,10) (7,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1065", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (3,0) (0,10) (2,1) (0,1) (0,2) (1,6) (6,4) (8,12) (5,1) (12,5) (11,0) (4,0) (3,5) (8,9) (8,7) (12,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph313", "image": "data/cycle/graph_visual/medium/graph313.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,4) (2,8) (10,1) (3,11) (6,11) (9,3) (7,1) (15,2) (13,12) (2,13) (6,1) (0,10) (1,2) (14,13) (4,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph926", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (0,4) (2,0) (6,9) (2,3) (8,9) (4,7) (6,0) (5,3) (3,0) (10,4) (2,6) (4,8) (1,5) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1375", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (11,14) (0,14) (14,10) (17,13) (1,17) (6,7) (9,15) (4,3) (12,8) (17,5) (16,17) (13,7) (5,11) (2,16) (3,1) (8,10) (0,2) (1,0) (15,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph865", "image": "data/cycle/graph_visual/medium/graph865.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (14,15) (18,5) (23,19) (22,10) (17,21) (22,13) (24,7) (19,1) (2,3) (24,23) (1,16) (6,13) (11,14) (8,22) (13,4) (3,12) (8,21) (5,20) (23,9) (18,11) (19,10) (0,20) (11,2) (10,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1641", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (14,4) (17,16) (4,0) (21,8) (21,13) (16,7) (3,6) (15,1) (14,1) (1,0) (7,19) (11,16) (0,3) (18,9) (5,13) (17,20) (22,18) (10,17) (11,2) (12,1) (2,0) (3,10) (9,19) (0,5) (4,8) (20,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1345", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (0,3) (5,16) (8,9) (10,3) (6,1) (17,11) (13,16) (6,16) (0,7) (0,15) (1,0) (8,2) (2,6) (16,11) (4,6) (10,4) (0,16) (0,2) (0,4) (8,12) (14,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph225", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (13,12) (9,0) (4,2) (10,11) (2,7) (0,3) (2,11) (10,5) (12,5) (7,8) (1,11) (3,6) (1,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1525", "image": "data/cycle/graph_visual/medium/graph1525.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (18,11) (4,9) (12,13) (4,0) (3,4) (15,14) (7,16) (19,8) (3,0) (15,10) (1,5) (15,11) (12,9) (2,13) (12,0) (0,2) (1,0) (16,6) (17,6) (20,8) (19,3) (1,8) (9,18) (16,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph718", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (9,7) (15,12) (17,6) (14,21) (16,1) (8,17) (11,7) (19,17) (5,4) (12,13) (2,14) (10,0) (19,11) (0,15) (14,4) (18,0) (9,10) (21,9) (3,10) (20,21) (5,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph940", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (0,9) (9,10) (3,8) (4,0) (4,8) (2,0) (8,2) (5,2) (1,8) (7,6) (0,1) (0,7) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph643", "image": "data/cycle/graph_visual/medium/graph643.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (10,15) (13,17) (8,20) (5,0) (4,1) (2,3) (10,11) (4,3) (13,6) (13,0) (20,6) (10,4) (15,18) (14,13) (7,8) (18,12) (14,18) (16,5) (3,9) (2,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1732", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (22,16) (0,2) (0,1) (19,0) (6,4) (13,23) (11,19) (15,11) (1,14) (18,3) (10,1) (15,7) (3,0) (9,7) (8,22) (10,3) (2,5) (9,4) (0,4) (0,12) (20,16) (6,2) (15,22) (17,23) (10,21) (17,0) (16,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1100", "image": "data/cycle/graph_visual/medium/graph1100.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (2,8) (13,2) (12,6) (3,0) (13,7) (4,0) (10,2) (2,0) (3,11) (0,1) (4,1) (10,4) (9,10) (5,10) (12,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1703", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (16,2) (3,12) (3,11) (2,0) (7,10) (22,0) (18,16) (9,5) (15,6) (23,22) (9,13) (21,14) (19,0) (14,3) (14,17) (3,0) (1,19) (8,20) (16,19) (1,0) (5,14) (16,8) (10,5) (8,10) (11,6) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph25", "image": "data/cycle/graph_visual/medium/graph25.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (3,5) (1,6) (0,4) (8,7) (10,0) (3,4) (4,9) (10,6) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph445", "image": "data/cycle/graph_visual/medium/graph445.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (6,13) (5,7) (14,17) (4,7) (2,15) (16,2) (8,12) (6,3) (12,1) (8,11) (9,5) (6,15) (2,4) (13,17) (12,16) (0,12) (7,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1145", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (11,3) (1,0) (10,4) (0,2) (12,4) (0,7) (9,8) (12,8) (13,1) (0,5) (6,11) (7,10) (3,14) (2,8) (8,14) (6,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1447", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (0,2) (8,11) (19,16) (0,4) (12,11) (18,9) (0,1) (14,6) (3,0) (1,19) (0,6) (17,18) (3,2) (14,19) (4,6) (17,12) (13,17) (18,7) (7,10) (5,7) (18,14) (7,15) (3,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1529", "image": "data/cycle/graph_visual/medium/graph1529.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (9,10) (0,3) (3,11) (11,0) (2,19) (19,16) (4,6) (20,13) (20,2) (8,7) (3,6) (2,0) (8,12) (14,17) (2,12) (5,17) (4,0) (3,10) (1,0) (15,18) (15,16) (8,0) (10,17) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1322", "image": "data/cycle/graph_visual/medium/graph1322.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (8,17) (12,1) (4,11) (16,7) (16,9) (11,8) (3,7) (4,0) (0,1) (1,4) (11,14) (10,14) (15,0) (7,5) (0,3) (0,6) (10,3) (5,13) (2,0) (6,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph117", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (6,2) (6,5) (4,3) (3,8) (9,11) (10,0) (11,3) (1,2) (5,7) (0,1) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1022", "image": "data/cycle/graph_visual/medium/graph1022.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (2,12) (7,3) (11,8) (3,1) (10,5) (1,9) (0,1) (8,2) (2,5) (4,10) (0,9) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph831", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (10,1) (20,21) (18,23) (4,15) (23,17) (4,1) (19,1) (3,12) (5,3) (7,17) (17,3) (21,1) (7,13) (2,0) (23,22) (8,4) (4,7) (15,0) (4,16) (6,12) (4,11) (22,14) (9,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph874", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (8,23) (1,16) (16,17) (19,22) (11,12) (23,14) (18,10) (24,12) (16,20) (18,21) (13,17) (21,11) (2,17) (6,17) (9,12) (14,15) (22,17) (0,7) (12,8) (7,5) (8,7) (7,4) (20,10) (3,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1713", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (21,15) (0,2) (7,16) (5,9) (3,6) (2,4) (1,0) (8,14) (15,22) (6,0) (15,19) (0,11) (13,23) (23,7) (17,7) (14,5) (4,20) (10,11) (2,11) (13,5) (12,19) (18,22) (23,3) (22,9) (1,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph720", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (6,2) (3,9) (17,15) (0,19) (4,3) (7,12) (13,18) (2,21) (18,20) (6,7) (0,22) (11,8) (8,7) (2,17) (20,5) (0,10) (21,3) (1,13) (16,19) (16,7) (0,1) (14,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph268", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (5,4) (13,2) (4,6) (8,14) (3,11) (1,5) (5,12) (7,11) (13,3) (8,1) (14,10) (9,10) (7,0) (7,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph57", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (7,3) (0,1) (4,2) (4,8) (7,4) (6,5) (9,4) (10,1) (1,8) (6,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1246", "image": "data/cycle/graph_visual/medium/graph1246.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (6,4) (14,3) (13,5) (3,0) (15,3) (1,0) (0,4) (5,0) (11,6) (11,8) (15,13) (9,0) (6,0) (11,0) (14,2) (10,1) (12,8) (1,7) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1067", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (1,6) (1,0) (12,10) (0,5) (5,12) (3,0) (2,11) (5,11) (7,12) (0,4) (9,4) (8,3) (2,0) (3,7) (9,3) (5,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1459", "image": "data/cycle/graph_visual/medium/graph1459.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,12) (0,3) (6,18) (4,15) (0,1) (10,14) (12,16) (6,19) (8,5) (13,6) (4,5) (19,3) (6,14) (13,11) (7,9) (6,17) (7,4) (2,17) (2,0) (4,1) (4,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1419", "image": "data/cycle/graph_visual/medium/graph1419.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (15,2) (7,8) (15,13) (18,4) (14,0) (9,5) (0,2) (10,9) (11,7) (0,9) (3,15) (4,10) (9,17) (3,0) (1,11) (7,0) (12,14) (0,4) (13,6) (16,7) (8,13) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph309", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (3,0) (10,5) (12,5) (7,9) (0,15) (7,2) (11,5) (8,5) (5,3) (14,6) (2,4) (1,5) (14,8) (9,11) (13,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph238", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (12,1) (8,13) (6,9) (11,4) (13,3) (10,5) (8,7) (9,1) (4,2) (2,13) (3,12) (0,13) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph397", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (12,6) (4,2) (15,16) (11,5) (12,8) (7,16) (10,6) (9,4) (14,15) (12,0) (7,3) (14,0) (7,4) (11,1) (13,6) (1,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph621", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (13,3) (2,20) (11,0) (9,10) (16,17) (0,7) (18,11) (20,8) (16,5) (13,18) (16,7) (15,9) (6,15) (13,2) (4,13) (14,16) (12,6) (5,1) (15,5) (19,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph639", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (20,8) (18,15) (7,8) (12,18) (10,15) (5,16) (0,13) (19,2) (14,13) (18,14) (2,3) (4,1) (3,9) (10,4) (13,6) (20,6) (17,13) (4,3) (0,5) (11,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1550", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (10,0) (16,0) (5,14) (9,6) (17,11) (17,2) (5,7) (13,16) (13,11) (8,17) (1,0) (9,2) (20,15) (12,20) (1,4) (2,0) (8,19) (18,2) (20,18) (3,10) (8,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph867", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (21,1) (21,10) (9,4) (22,1) (24,6) (4,12) (23,20) (13,3) (0,2) (8,12) (19,4) (23,21) (0,15) (4,18) (16,24) (17,7) (11,1) (24,17) (5,3) (14,7) (15,22) (4,7) (4,1) (3,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph17", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (5,3) (6,2) (0,5) (7,0) (9,8) (5,10) (6,1) (0,8) (10,2) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph237", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (1,5) (13,0) (3,12) (5,10) (2,13) (9,6) (13,3) (1,9) (4,11) (7,8) (13,8) (2,4) (1,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph588", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (9,14) (4,19) (6,7) (8,19) (2,3) (17,3) (12,11) (6,12) (18,13) (16,8) (13,10) (8,3) (8,10) (5,16) (16,1) (4,15) (9,18) (16,11) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1457", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (16,6) (3,15) (17,12) (19,13) (12,13) (12,11) (15,0) (5,2) (3,0) (18,0) (10,15) (8,15) (0,14) (4,1) (18,4) (6,3) (3,7) (14,19) (1,0) (9,14) (2,0) (2,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph652", "image": "data/cycle/graph_visual/medium/graph652.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (11,6) (16,18) (13,9) (17,14) (19,17) (4,20) (15,14) (1,3) (13,18) (5,2) (19,2) (8,17) (10,16) (10,17) (3,5) (4,14) (0,1) (13,12) (10,7) (11,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph2", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (0,6) (4,8) (1,5) (7,2) (0,7) (3,7) (7,5) (4,6) (3,9) (10,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1119", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (1,0) (4,12) (2,0) (7,3) (5,1) (0,9) (4,3) (3,10) (6,5) (3,0) (4,11) (8,4) (6,0) (6,13) (12,13) (7,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph889", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (20,12) (15,9) (4,24) (18,11) (19,5) (9,14) (0,21) (8,22) (13,18) (23,7) (15,6) (7,24) (1,5) (7,16) (13,10) (11,0) (16,5) (4,2) (17,6) (2,13) (22,0) (15,16) (13,3) (16,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1436", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (1,15) (10,17) (6,12) (2,0) (1,0) (11,10) (8,2) (9,10) (13,5) (11,7) (0,4) (6,0) (11,8) (16,2) (12,14) (5,0) (3,0) (13,10) (4,18) (3,6) (4,8) (10,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1134", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (1,0) (0,2) (5,0) (12,10) (0,3) (11,0) (12,6) (9,8) (8,10) (7,4) (11,13) (7,10) (2,9) (1,7) (6,3) (13,7) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1709", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (0,2) (1,7) (5,22) (7,16) (0,12) (5,3) (21,9) (23,14) (8,11) (0,4) (19,15) (1,0) (17,12) (15,4) (17,11) (3,0) (3,8) (23,8) (18,12) (3,13) (2,4) (17,16) (2,20) (7,6) (10,9) (1,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1612", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (3,2) (1,0) (7,10) (7,5) (7,16) (19,18) (19,1) (19,20) (14,6) (18,17) (9,18) (13,12) (11,8) (21,11) (12,17) (6,0) (6,4) (14,18) (3,10) (21,14) (21,7) (15,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph278", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (4,8) (8,5) (9,14) (8,1) (3,6) (8,11) (0,12) (9,4) (2,10) (5,6) (13,3) (1,12) (7,0) (10,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph154", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (3,0) (6,1) (11,2) (5,11) (9,4) (1,5) (8,3) (12,7) (5,12) (9,3) (12,10) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1498", "image": "data/cycle/graph_visual/medium/graph1498.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,2) (16,1) (19,8) (10,8) (6,11) (10,5) (6,13) (9,12) (2,0) (0,19) (5,14) (8,16) (15,14) (10,4) (14,18) (3,7) (5,9) (14,3) (11,3) (1,0) (16,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph511", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (1,5) (17,0) (10,1) (2,16) (9,17) (12,1) (1,11) (11,0) (15,2) (4,18) (14,9) (6,15) (11,3) (12,6) (0,18) (15,13) (11,7) (8,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph853", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (4,7) (24,9) (15,7) (11,17) (3,20) (17,19) (12,16) (9,14) (14,15) (5,13) (16,22) (20,5) (1,5) (8,6) (10,19) (18,16) (16,15) (2,9) (8,20) (20,21) (18,0) (10,21) (21,23) (20,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph169", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (1,5) (10,12) (1,2) (0,11) (1,6) (6,4) (12,8) (10,0) (12,5) (5,3) (9,8) (7,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph30", "image": "data/cycle/graph_visual/medium/graph30.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,7) (10,8) (6,0) (9,1) (9,10) (2,10) (5,3) (6,2) (4,2) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1789", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (7,0) (8,3) (2,20) (0,2) (0,1) (0,4) (0,24) (4,24) (7,15) (3,10) (16,18) (0,19) (2,13) (12,17) (18,6) (3,22) (12,11) (11,5) (16,1) (18,21) (11,8) (3,0) (4,23) (16,4) (9,13) (9,10) (0,14) (11,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1711", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (23,2) (17,15) (6,14) (23,12) (16,8) (19,11) (12,14) (10,13) (0,7) (3,9) (9,21) (18,15) (15,1) (1,0) (8,22) (22,17) (16,14) (2,0) (0,16) (17,4) (4,19) (21,11) (10,6) (5,1) (23,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1723", "image": "data/cycle/graph_visual/medium/graph1723.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,20) (8,22) (10,19) (13,4) (14,11) (10,11) (18,11) (18,5) (2,0) (17,5) (0,1) (6,13) (7,23) (23,22) (8,20) (15,1) (2,11) (14,13) (23,19) (3,2) (3,9) (10,21) (21,16) (12,22) (1,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph491", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (7,13) (0,16) (6,3) (17,12) (8,1) (0,15) (7,10) (0,8) (18,15) (9,15) (14,16) (2,10) (17,4) (6,11) (7,4) (9,3) (6,5) (8,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph563", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (12,15) (7,5) (5,19) (11,14) (17,10) (12,13) (11,8) (3,12) (19,17) (12,7) (9,11) (16,7) (2,8) (17,0) (0,11) (1,18) (12,1) (6,13) (17,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph825", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (10,17) (16,9) (7,9) (0,21) (2,10) (12,13) (4,14) (11,1) (3,11) (19,14) (2,20) (22,9) (7,10) (9,6) (6,8) (13,7) (14,15) (17,1) (1,0) (18,9) (12,5) (23,21) (7,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph928", "image": "data/cycle/graph_visual/medium/graph928.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (8,4) (7,2) (3,0) (0,1) (4,6) (3,9) (8,1) (2,0) (3,8) (6,10) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1206", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (4,7) (0,1) (11,2) (2,7) (1,8) (7,8) (14,0) (14,3) (1,10) (13,5) (4,6) (5,10) (0,9) (13,15) (3,11) (12,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1507", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (17,7) (11,8) (13,6) (5,16) (2,0) (1,12) (12,15) (11,14) (9,11) (3,12) (13,12) (7,5) (12,7) (20,16) (4,17) (10,17) (1,0) (17,0) (2,8) (1,19) (19,18) (11,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph911", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (0,1) (2,0) (4,8) (8,1) (0,5) (9,4) (10,3) (8,6) (3,6) (0,7) (8,7) (4,0) (3,0) (10,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph941", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (5,7) (9,6) (5,2) (7,10) (0,2) (9,4) (0,3) (0,1) (8,3) (8,5) (9,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph218", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (3,6) (7,11) (1,5) (5,7) (1,9) (1,10) (6,12) (6,4) (12,11) (5,0) (10,2) (0,13) (8,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph687", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (13,7) (2,17) (13,19) (10,18) (11,14) (20,10) (3,9) (6,8) (4,16) (17,16) (1,9) (8,14) (16,12) (9,14) (14,17) (15,14) (5,7) (0,13) (21,20) (7,2) (20,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1464", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (12,2) (15,1) (4,16) (6,0) (6,8) (3,0) (3,19) (15,8) (3,5) (17,9) (0,2) (12,7) (18,2) (2,4) (0,19) (6,14) (14,13) (0,1) (12,0) (6,11) (13,17) (10,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1189", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (0,1) (8,5) (2,11) (2,13) (7,14) (3,9) (10,0) (1,7) (6,5) (5,0) (7,8) (13,14) (10,12) (2,4) (4,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1203", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (0,1) (6,2) (6,13) (7,12) (0,3) (1,5) (6,3) (2,0) (0,4) (1,9) (13,14) (15,4) (8,13) (1,11) (10,4) (7,15) (5,13) (0,7) (6,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph304", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (7,12) (8,2) (10,11) (1,14) (7,13) (1,12) (0,11) (0,12) (5,7) (12,3) (11,8) (15,5) (9,12) (6,11) (4,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1389", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (7,8) (2,18) (0,10) (5,13) (0,3) (13,2) (4,8) (9,1) (9,3) (2,8) (1,0) (4,0) (2,0) (9,11) (2,1) (15,14) (16,9) (17,3) (6,15) (12,10) (0,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1749", "image": "data/cycle/graph_visual/medium/graph1749.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (2,20) (8,24) (7,16) (0,2) (17,12) (13,3) (8,11) (4,15) (24,9) (0,12) (23,14) (1,22) (3,0) (24,3) (21,9) (0,1) (16,17) (6,7) (9,10) (12,18) (7,1) (15,19) (3,5) (0,4) (0,5) (4,2) (17,11) (23,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1312", "image": "data/cycle/graph_visual/medium/graph1312.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (14,10) (1,0) (16,12) (0,2) (9,6) (13,9) (15,8) (15,5) (6,0) (8,11) (1,12) (8,9) (15,14) (1,4) (0,3) (11,2) (4,2) (2,3) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1500", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (4,5) (1,10) (9,11) (1,0) (17,0) (19,17) (17,10) (16,6) (6,7) (8,17) (12,6) (7,18) (4,3) (20,15) (5,13) (4,2) (17,16) (9,16) (3,15) (20,16) (14,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph7", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (7,10) (7,1) (4,5) (2,8) (4,9) (3,5) (3,8) (0,7) (6,2) (5,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph340", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (15,9) (10,15) (8,2) (14,12) (4,3) (10,12) (2,0) (2,11) (9,4) (1,6) (2,6) (5,9) (12,11) (7,5) (13,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph565", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (6,3) (5,18) (1,19) (4,13) (17,8) (9,18) (12,11) (19,10) (11,16) (1,13) (9,15) (3,2) (13,0) (19,15) (8,10) (2,11) (7,14) (11,10) (14,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph788", "image": "data/cycle/graph_visual/medium/graph788.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (18,22) (0,16) (14,3) (13,12) (17,13) (21,8) (16,13) (12,23) (2,1) (19,11) (19,15) (15,20) (11,7) (22,5) (21,0) (4,6) (9,1) (17,19) (22,9) (14,4) (3,10) (18,11) (14,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph206", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (6,3) (6,8) (0,1) (1,12) (4,10) (4,9) (6,12) (11,9) (13,4) (2,1) (7,9) (7,6) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1669", "image": "data/cycle/graph_visual/medium/graph1669.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (2,8) (22,17) (7,1) (14,21) (13,5) (15,8) (2,0) (16,1) (8,20) (15,13) (21,15) (9,21) (14,0) (3,22) (0,1) (14,6) (16,21) (18,4) (10,19) (10,2) (21,12) (11,18) (22,21) (3,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph334", "image": "data/cycle/graph_visual/medium/graph334.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (0,7) (3,10) (2,6) (12,4) (8,9) (13,8) (1,11) (15,6) (9,3) (12,0) (15,5) (12,14) (4,1) (13,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1746", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (9,3) (20,15) (19,22) (2,7) (10,21) (1,9) (0,13) (2,0) (6,8) (10,20) (15,19) (0,1) (7,13) (14,9) (14,11) (17,14) (23,13) (16,14) (2,17) (16,4) (22,24) (18,17) (5,7) (8,14) (12,16) (6,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1182", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (5,14) (1,4) (7,10) (2,4) (7,11) (6,4) (12,3) (1,0) (2,0) (14,7) (8,9) (14,0) (13,0) (3,4) (12,5) (2,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1333", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (3,14) (2,0) (7,15) (0,13) (14,12) (16,6) (5,16) (11,15) (1,17) (1,5) (6,2) (8,1) (0,3) (16,9) (0,1) (4,8) (14,5) (11,4) (11,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph88", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (4,3) (6,1) (11,2) (0,11) (10,1) (5,10) (9,3) (1,11) (0,7) (8,4) (2,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1200", "image": "data/cycle/graph_visual/medium/graph1200.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (13,9) (0,15) (0,2) (11,10) (5,13) (1,5) (4,9) (3,0) (0,8) (3,2) (13,14) (15,7) (11,9) (3,8) (6,0) (1,0) (13,0) (8,12) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1795", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (22,5) (14,22) (12,5) (17,19) (15,16) (5,4) (11,7) (8,4) (0,2) (21,11) (1,0) (20,2) (10,2) (0,10) (19,6) (23,12) (14,24) (14,3) (9,8) (1,23) (17,10) (18,19) (14,16) (21,1) (13,0) (22,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph53", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (10,3) (10,8) (7,5) (2,1) (4,0) (1,0) (1,9) (2,6) (5,8) (9,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1343", "image": "data/cycle/graph_visual/medium/graph1343.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (4,10) (17,3) (16,1) (13,4) (17,7) (4,0) (4,1) (15,1) (4,14) (8,4) (2,0) (12,7) (6,12) (15,0) (3,11) (3,0) (9,1) (5,3) (0,1) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1771", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (0,2) (10,2) (10,4) (11,3) (22,21) (11,20) (1,0) (4,6) (17,16) (18,24) (1,23) (5,24) (8,13) (16,24) (18,14) (4,9) (24,11) (23,3) (19,8) (15,1) (22,18) (23,7) (12,10) (17,0) (13,9) (20,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1606", "image": "data/cycle/graph_visual/medium/graph1606.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (8,4) (1,5) (16,19) (1,0) (12,5) (14,9) (15,14) (10,21) (0,18) (6,15) (7,3) (17,16) (9,21) (2,0) (16,11) (8,17) (21,20) (20,7) (13,19) (10,18) (2,20) (20,5) (15,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1796", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (15,8) (20,22) (15,1) (17,7) (11,9) (0,3) (11,15) (14,18) (24,14) (11,16) (5,16) (10,4) (4,14) (7,23) (21,0) (0,1) (8,2) (21,6) (0,2) (0,12) (4,19) (19,22) (21,19) (8,20) (17,0) (21,3) (13,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph837", "image": "data/cycle/graph_visual/medium/graph837.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (21,15) (20,6) (9,3) (15,12) (0,17) (18,12) (6,2) (7,0) (21,9) (17,12) (23,10) (8,23) (3,5) (6,22) (16,4) (4,20) (1,20) (21,19) (11,8) (1,13) (23,22) (23,7) (13,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph549", "image": "data/cycle/graph_visual/medium/graph549.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (1,14) (12,3) (19,7) (10,0) (11,3) (17,13) (18,11) (2,7) (16,6) (18,13) (1,2) (15,16) (5,4) (6,1) (8,1) (12,4) (13,2) (10,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph985", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (11,10) (0,10) (2,0) (1,0) (1,10) (0,7) (0,3) (9,0) (2,8) (7,6) (1,3) (11,4) (5,3) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1715", "image": "data/cycle/graph_visual/medium/graph1715.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (21,11) (1,4) (3,0) (2,17) (2,0) (13,15) (14,5) (0,1) (18,13) (2,9) (9,6) (4,0) (20,12) (16,23) (19,20) (15,23) (17,11) (0,10) (0,16) (3,10) (2,18) (7,8) (5,7) (5,0) (17,8) (22,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph883", "image": "data/cycle/graph_visual/medium/graph883.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (14,22) (16,5) (11,24) (1,15) (8,12) (0,6) (10,3) (12,23) (21,11) (2,6) (10,14) (0,1) (22,8) (19,11) (7,20) (16,9) (22,4) (8,11) (13,23) (17,0) (3,7) (1,21) (4,18) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph820", "image": "data/cycle/graph_visual/medium/graph820.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (9,8) (10,14) (11,19) (14,12) (7,6) (22,23) (15,11) (5,3) (0,20) (6,10) (0,16) (16,22) (15,1) (10,9) (21,5) (5,10) (12,2) (17,0) (4,17) (22,13) (11,2) (10,20) (18,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1220", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (0,9) (12,4) (2,6) (4,3) (14,15) (1,12) (11,0) (1,0) (5,4) (6,10) (10,14) (7,3) (5,8) (13,7) (5,14) (10,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph755", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (16,0) (14,6) (9,10) (0,5) (15,18) (4,19) (17,22) (21,7) (10,12) (8,21) (14,16) (1,3) (17,15) (8,16) (1,15) (12,14) (10,22) (9,2) (17,4) (20,11) (19,11) (6,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1676", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (21,14) (22,4) (15,21) (22,2) (19,14) (22,0) (0,2) (13,6) (16,2) (17,4) (5,12) (9,0) (22,1) (3,0) (11,6) (7,12) (10,5) (8,18) (3,20) (21,5) (9,18) (6,5) (0,1) (20,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1278", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (0,16) (13,4) (2,1) (0,1) (2,10) (14,0) (7,4) (13,10) (11,2) (12,4) (6,9) (6,15) (14,5) (5,2) (4,0) (0,2) (9,10) (3,8) (11,8) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph537", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (5,7) (18,13) (11,2) (11,17) (15,12) (14,12) (2,8) (16,12) (6,1) (16,17) (10,12) (0,2) (4,3) (5,9) (9,4) (13,10) (15,9) (2,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph902", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (5,0) (0,10) (9,10) (1,3) (5,8) (0,4) (3,0) (2,7) (0,6) (0,8) (2,0) (7,0) (1,0) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1032", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (12,0) (8,7) (4,1) (11,3) (8,9) (6,5) (9,12) (7,4) (1,3) (4,0) (3,5) (10,3) (4,2) (0,2) (1,0) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph111", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (3,2) (9,3) (8,1) (7,0) (9,10) (11,7) (8,7) (7,5) (2,8) (6,8) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1460", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (15,18) (4,14) (11,19) (1,0) (17,18) (19,13) (6,11) (5,4) (8,19) (17,13) (1,9) (1,2) (0,16) (12,0) (13,14) (19,10) (11,16) (9,15) (3,7) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph153", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (2,4) (9,11) (3,12) (5,7) (12,2) (4,5) (12,8) (11,8) (0,8) (10,11) (4,6) (6,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1076", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (4,2) (3,12) (0,1) (12,1) (7,9) (0,3) (8,11) (0,2) (7,4) (5,6) (4,10) (6,3) (1,8) (12,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1302", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (1,2) (14,13) (2,8) (3,0) (0,1) (6,12) (2,13) (11,16) (5,4) (4,0) (7,1) (11,3) (0,2) (15,13) (12,4) (10,0) (9,3) (2,16) (10,1) (6,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph628", "image": "data/cycle/graph_visual/medium/graph628.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (1,11) (16,19) (0,18) (10,14) (12,20) (9,15) (19,4) (5,0) (13,9) (7,8) (10,15) (16,5) (16,7) (0,6) (19,11) (3,18) (1,2) (13,20) (12,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph763", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (14,16) (19,22) (12,0) (7,20) (11,15) (18,19) (3,21) (9,11) (0,21) (10,4) (15,1) (22,14) (8,20) (5,16) (6,21) (7,17) (13,11) (8,15) (4,12) (2,8) (17,0) (19,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1228", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (8,6) (14,15) (3,4) (10,8) (4,10) (3,2) (10,15) (1,4) (1,0) (14,13) (3,7) (13,0) (3,0) (0,5) (9,5) (2,12) (11,13) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph119", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (0,11) (3,5) (9,6) (4,3) (2,1) (1,10) (6,7) (8,11) (2,7) (0,1) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1691", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (15,14) (1,11) (9,7) (20,2) (12,13) (15,7) (8,6) (17,1) (13,7) (0,3) (21,23) (17,10) (19,14) (5,12) (4,14) (10,7) (9,6) (2,10) (0,1) (3,11) (9,16) (0,2) (0,21) (22,9) (18,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1380", "image": "data/cycle/graph_visual/medium/graph1380.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,13) (13,2) (9,16) (14,15) (8,7) (4,0) (3,0) (9,11) (3,17) (9,3) (0,1) (15,0) (8,4) (10,12) (2,0) (1,2) (10,0) (18,2) (15,6) (2,8) (9,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph283", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (2,4) (11,5) (0,7) (4,8) (6,3) (4,1) (6,7) (5,0) (1,9) (12,1) (4,10) (4,14) (1,0) (7,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1738", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (2,20) (14,15) (10,2) (6,8) (12,5) (3,0) (0,21) (19,14) (12,13) (9,16) (6,9) (23,21) (7,15) (2,0) (5,0) (9,22) (9,18) (10,7) (13,7) (7,9) (10,17) (0,1) (17,1) (14,4) (4,0) (1,11) (3,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph803", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (16,20) (5,21) (14,3) (20,23) (12,10) (9,17) (20,15) (1,13) (12,1) (2,22) (14,1) (19,6) (2,7) (13,4) (4,8) (15,6) (2,1) (6,18) (15,0) (9,5) (11,9) (4,11) (17,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph602", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (6,12) (13,2) (15,5) (6,5) (3,19) (18,7) (2,4) (14,18) (5,8) (0,9) (10,6) (11,5) (1,12) (14,17) (14,20) (16,5) (4,9) (15,20) (0,3) (0,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1292", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (11,10) (11,7) (16,2) (6,8) (0,5) (0,3) (13,3) (0,1) (12,15) (14,9) (0,4) (2,0) (1,6) (4,3) (7,6) (5,10) (14,7) (7,12) (14,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph546", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (2,7) (11,2) (3,11) (10,16) (5,14) (17,5) (9,0) (19,10) (14,12) (7,4) (1,8) (1,13) (0,19) (15,3) (5,18) (1,19) (17,13) (7,8) (6,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1230", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (4,14) (1,2) (13,11) (1,9) (13,12) (12,5) (0,10) (9,15) (4,6) (3,14) (11,7) (0,13) (3,8) (5,15) (14,11) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1370", "image": "data/cycle/graph_visual/medium/graph1370.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,3) (5,0) (9,15) (0,1) (3,1) (6,7) (10,4) (5,13) (11,15) (6,8) (0,2) (8,14) (15,12) (8,3) (4,0) (14,9) (2,14) (3,0) (15,5) (7,10) (6,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph523", "image": "data/cycle/graph_visual/medium/graph523.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (18,1) (8,12) (16,10) (2,5) (11,18) (6,18) (15,5) (1,10) (15,14) (2,18) (17,7) (8,3) (16,13) (9,17) (3,18) (16,4) (0,13) (17,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph51", "image": "data/cycle/graph_visual/medium/graph51.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (9,0) (5,10) (6,5) (9,3) (4,2) (4,7) (10,2) (1,7) (5,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph616", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (0,16) (14,8) (16,5) (2,14) (13,6) (1,20) (1,10) (4,15) (19,20) (6,18) (17,11) (16,4) (12,7) (8,11) (9,7) (19,6) (20,9) (1,4) (0,14) (18,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph850", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (3,2) (6,10) (17,22) (3,17) (11,19) (23,12) (4,14) (21,20) (16,13) (14,8) (22,5) (21,1) (7,14) (24,9) (0,4) (2,23) (10,24) (5,15) (11,13) (3,16) (8,1) (20,6) (14,23) (18,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph774", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (16,21) (1,19) (2,15) (12,14) (1,7) (18,2) (6,17) (14,3) (9,20) (9,5) (22,4) (21,4) (8,10) (0,14) (21,7) (8,15) (13,2) (6,9) (2,20) (12,2) (21,11) (9,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph595", "image": "data/cycle/graph_visual/medium/graph595.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (9,13) (3,4) (11,5) (0,7) (11,2) (18,17) (14,0) (16,4) (6,18) (10,3) (12,0) (9,10) (1,16) (16,18) (7,15) (8,19) (13,2) (3,8) (12,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph473", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (12,17) (1,5) (2,8) (8,0) (14,0) (9,7) (3,16) (17,7) (12,15) (11,4) (16,6) (7,14) (3,7) (11,15) (3,5) (11,13) (1,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1502", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (1,19) (18,5) (14,1) (2,0) (13,6) (0,1) (11,17) (12,14) (3,7) (2,11) (19,10) (13,11) (3,0) (0,4) (9,19) (10,11) (3,2) (20,15) (0,20) (4,13) (8,18) (5,16) (15,9) (10,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1002", "image": "data/cycle/graph_visual/medium/graph1002.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (3,5) (7,3) (6,7) (0,9) (8,10) (1,0) (0,2) (0,8) (11,1) (5,10) (2,4) (11,7) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1213", "image": "data/cycle/graph_visual/medium/graph1213.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (13,3) (2,0) (3,12) (12,5) (7,14) (8,1) (8,14) (10,11) (1,0) (9,5) (6,15) (2,3) (4,14) (2,14) (13,11) (1,6) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1780", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (3,23) (15,10) (20,7) (14,24) (2,17) (20,8) (22,21) (1,0) (17,21) (6,24) (3,11) (7,9) (6,7) (19,10) (1,8) (17,18) (13,15) (2,16) (12,22) (4,2) (10,11) (15,0) (5,11) (7,10) (11,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph209", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (10,0) (6,2) (7,1) (11,0) (7,4) (9,7) (3,12) (6,0) (13,5) (10,3) (2,1) (13,8) (3,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1515", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (0,2) (16,4) (17,14) (14,9) (1,9) (2,17) (2,7) (1,0) (13,0) (7,13) (15,14) (7,5) (20,6) (17,16) (18,10) (8,14) (13,19) (12,16) (9,3) (6,8) (20,10) (14,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1122", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (13,8) (2,1) (0,1) (1,4) (10,6) (0,2) (5,0) (11,7) (2,7) (3,4) (1,12) (9,11) (8,6) (5,3) (0,3) (6,0) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1038", "image": "data/cycle/graph_visual/medium/graph1038.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,1) (8,11) (3,2) (10,7) (0,2) (11,3) (0,3) (2,10) (6,9) (9,2) (12,7) (2,4) (1,11) (5,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1071", "image": "data/cycle/graph_visual/medium/graph1071.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (10,11) (12,7) (0,3) (7,6) (2,0) (1,9) (0,5) (0,1) (0,4) (2,3) (2,6) (7,11) (12,9) (2,8) (5,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph714", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (7,16) (12,1) (19,9) (9,21) (19,7) (11,16) (4,8) (14,1) (5,13) (6,3) (13,21) (3,10) (20,1) (20,17) (11,2) (14,4) (1,15) (17,16) (18,8) (0,2) (10,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1108", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (5,10) (0,2) (13,0) (2,6) (13,7) (6,8) (8,12) (0,5) (3,0) (6,9) (6,5) (8,3) (1,0) (4,0) (11,4) (11,5) (1,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph809", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (11,16) (14,8) (22,17) (5,19) (20,1) (5,6) (17,7) (20,15) (6,13) (12,18) (4,9) (14,9) (10,14) (0,14) (16,18) (3,14) (4,2) (16,15) (19,21) (17,2) (5,3) (22,20) (23,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph655", "image": "data/cycle/graph_visual/medium/graph655.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (18,8) (3,2) (11,16) (1,0) (12,6) (3,20) (13,10) (10,8) (16,5) (13,19) (1,16) (17,3) (11,12) (19,4) (9,18) (7,6) (4,15) (8,16) (14,9) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph129", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (8,1) (10,6) (4,2) (0,9) (7,0) (6,2) (1,5) (0,12) (5,3) (10,1) (5,9) (8,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph890", "image": "data/cycle/graph_visual/medium/graph890.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (24,4) (18,3) (18,19) (10,15) (7,2) (10,2) (16,15) (12,13) (23,11) (0,18) (13,4) (17,15) (5,20) (11,1) (8,20) (14,6) (1,9) (8,21) (0,6) (1,13) (23,7) (14,15) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph818", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (17,5) (21,9) (4,5) (1,18) (3,0) (10,9) (18,0) (16,15) (21,15) (6,2) (8,19) (7,14) (20,8) (5,14) (7,2) (0,23) (20,5) (5,11) (16,0) (5,3) (22,15) (12,11) (16,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1631", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (0,14) (5,11) (5,13) (19,20) (9,11) (8,2) (14,11) (10,13) (0,1) (22,7) (14,12) (20,0) (7,0) (8,15) (12,17) (16,4) (1,17) (1,21) (4,5) (6,16) (1,15) (3,1) (13,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph959", "image": "data/cycle/graph_visual/medium/graph959.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,1) (9,10) (0,7) (9,3) (6,4) (0,4) (0,2) (10,2) (1,7) (8,9) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1196", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (0,2) (0,1) (13,7) (9,1) (7,3) (13,11) (10,14) (12,7) (0,9) (8,9) (4,13) (0,5) (4,10) (0,3) (5,6) (4,0) (6,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph359", "image": "data/cycle/graph_visual/medium/graph359.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,1) (11,2) (0,13) (7,11) (10,12) (14,7) (6,9) (12,13) (0,1) (11,9) (3,14) (11,5) (2,4) (2,8) (2,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph719", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (14,15) (5,9) (21,0) (2,4) (6,16) (1,3) (18,12) (4,17) (13,14) (0,6) (19,6) (8,19) (7,4) (5,12) (4,19) (13,6) (3,17) (4,5) (11,20) (20,6) (10,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1171", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (4,3) (4,5) (0,4) (14,6) (1,8) (2,0) (5,0) (11,9) (2,12) (13,6) (7,9) (8,0) (13,10) (0,1) (3,12) (0,3) (10,9) (6,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph409", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (5,13) (0,14) (7,2) (10,15) (3,11) (12,5) (3,14) (1,16) (0,9) (10,5) (7,4) (8,1) (4,6) (7,8) (11,2) (1,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1396", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (18,4) (13,18) (17,2) (0,1) (2,11) (8,15) (9,8) (14,9) (1,2) (10,11) (6,18) (18,5) (11,8) (3,15) (4,17) (7,9) (0,6) (12,14) (16,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph996", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (10,7) (4,9) (11,9) (0,1) (11,2) (5,1) (1,6) (10,4) (8,4) (0,2) (4,0) (2,5) (3,0) (5,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1387", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (8,4) (9,13) (16,5) (17,7) (9,2) (16,8) (11,5) (10,12) (18,0) (17,2) (18,13) (6,15) (14,9) (15,14) (0,1) (16,10) (1,5) (16,15) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph767", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (13,3) (0,2) (7,1) (18,15) (9,1) (14,12) (5,21) (2,19) (3,8) (6,7) (10,9) (17,12) (4,2) (8,11) (16,7) (11,17) (15,4) (22,8) (17,16) (20,9) (12,0) (3,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1523", "image": "data/cycle/graph_visual/medium/graph1523.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (16,15) (6,4) (16,11) (7,19) (1,0) (19,0) (14,20) (6,18) (11,14) (5,16) (3,10) (2,8) (9,0) (1,17) (8,10) (6,2) (16,6) (4,12) (19,1) (13,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph123", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (0,5) (0,12) (1,4) (4,6) (9,8) (7,10) (3,12) (11,7) (9,2) (4,3) (7,5) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph698", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (16,4) (10,18) (2,7) (19,13) (15,14) (14,11) (17,2) (21,20) (3,9) (17,14) (10,20) (9,14) (16,12) (0,13) (20,6) (6,8) (5,7) (13,7) (1,9) (17,16) (8,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph982", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (8,1) (3,9) (5,7) (0,1) (1,5) (9,1) (10,2) (2,5) (3,0) (2,6) (4,0) (4,11) (0,2) (0,7) (6,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1127", "image": "data/cycle/graph_visual/medium/graph1127.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (12,3) (10,9) (8,1) (1,0) (3,4) (9,11) (0,6) (0,4) (4,5) (0,2) (6,13) (0,8) (0,3) (13,10) (2,12) (5,0) (9,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph949", "image": "data/cycle/graph_visual/medium/graph949.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (9,0) (4,0) (0,2) (8,2) (3,8) (3,0) (10,9) (8,4) (7,0) (2,5) (0,1) (1,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph102", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (7,5) (11,4) (4,1) (2,11) (0,6) (2,10) (3,0) (5,6) (0,2) (7,8) (9,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1383", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (13,15) (2,0) (8,14) (5,0) (12,5) (2,15) (5,11) (0,3) (9,10) (18,4) (5,1) (3,6) (1,13) (18,15) (16,7) (9,6) (1,0) (4,0) (16,3) (17,9) (17,4) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph499", "image": "data/cycle/graph_visual/medium/graph499.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (7,17) (2,6) (1,0) (11,8) (15,5) (7,3) (9,16) (10,14) (14,11) (18,12) (8,12) (0,6) (0,16) (13,1) (4,11) (7,5) (1,4) (3,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph713", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (9,1) (17,16) (19,2) (3,5) (3,13) (4,2) (11,17) (12,17) (7,16) (12,0) (3,21) (18,15) (20,9) (11,8) (0,2) (10,9) (15,4) (1,7) (14,12) (6,7) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1181", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (0,2) (1,0) (1,13) (5,10) (6,3) (9,13) (2,11) (0,4) (12,5) (3,14) (0,3) (5,0) (7,13) (12,4) (8,11) (8,14) (8,10) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph43", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (0,3) (1,9) (5,7) (7,10) (3,7) (8,0) (6,9) (2,0) (4,6) (9,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1382", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (12,2) (1,9) (17,2) (2,15) (2,0) (10,4) (11,8) (4,0) (13,2) (15,8) (6,16) (2,9) (9,5) (12,14) (10,18) (1,0) (7,1) (0,3) (9,6) (0,14) (7,4) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1533", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (17,7) (14,15) (1,15) (14,4) (0,2) (10,0) (7,18) (19,0) (14,20) (0,1) (19,4) (11,15) (8,20) (13,8) (11,5) (12,11) (9,12) (16,3) (19,16) (8,2) (6,4) (17,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph320", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (12,2) (15,11) (15,8) (13,10) (10,9) (5,11) (3,14) (7,2) (7,6) (15,0) (2,4) (10,7) (11,3) (11,4) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph331", "image": "data/cycle/graph_visual/medium/graph331.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (6,14) (5,10) (14,5) (2,15) (3,4) (3,14) (7,15) (13,12) (0,3) (11,9) (8,1) (6,12) (8,15) (8,0) (9,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph156", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (6,0) (10,11) (8,3) (9,7) (9,2) (8,5) (12,4) (6,12) (12,9) (8,1) (12,10) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph766", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (12,11) (17,19) (5,7) (7,15) (13,9) (18,22) (8,10) (22,3) (17,10) (8,11) (0,20) (7,21) (1,15) (4,8) (2,6) (20,18) (12,5) (2,20) (9,6) (14,2) (8,16) (15,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1040", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (4,10) (0,5) (7,5) (7,1) (6,2) (8,10) (12,7) (3,4) (10,5) (11,2) (2,0) (9,8) (1,0) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph975", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (4,7) (8,10) (9,2) (10,9) (1,7) (3,11) (3,10) (8,5) (0,1) (6,0) (0,3) (4,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1051", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (5,12) (2,0) (3,0) (6,3) (1,8) (1,9) (0,4) (6,2) (10,11) (1,5) (4,12) (11,6) (0,1) (10,0) (11,7) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph396", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (12,2) (8,6) (8,10) (2,0) (3,5) (0,7) (12,3) (6,14) (11,4) (16,12) (15,1) (4,2) (6,9) (14,13) (15,13) (6,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph101", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (7,8) (0,6) (4,5) (5,11) (1,11) (11,10) (2,0) (9,10) (0,1) (11,8) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1049", "image": "data/cycle/graph_visual/medium/graph1049.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (1,12) (7,1) (0,9) (4,2) (5,1) (6,8) (8,5) (0,3) (0,2) (4,11) (3,5) (1,0) (2,3) (0,4) (12,10) (9,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph635", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (14,7) (1,9) (10,7) (11,2) (0,2) (3,17) (14,20) (14,13) (14,18) (5,15) (8,9) (11,5) (8,17) (5,13) (4,2) (9,12) (19,16) (3,15) (13,6) (16,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph10", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (6,2) (4,8) (1,0) (7,10) (9,5) (7,9) (3,2) (2,1) (8,3) (2,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph428", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (4,7) (1,12) (3,6) (2,15) (14,17) (11,8) (8,12) (5,7) (2,16) (2,4) (7,10) (12,16) (13,6) (15,6) (12,0) (9,5) (17,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph4", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (9,6) (6,3) (10,7) (1,7) (2,8) (7,4) (2,0) (4,5) (7,8) (3,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph424", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (14,15) (6,10) (0,12) (7,4) (12,8) (17,14) (2,1) (0,14) (7,3) (6,12) (2,4) (16,15) (11,5) (16,7) (11,1) (13,6) (4,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1136", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (0,12) (0,2) (5,9) (8,1) (6,13) (2,10) (12,3) (9,13) (11,4) (0,5) (0,4) (0,3) (1,7) (1,0) (12,7) (10,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1361", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (0,11) (9,12) (3,14) (10,9) (7,15) (2,0) (1,8) (9,13) (1,0) (1,13) (2,10) (2,7) (6,9) (14,15) (12,4) (9,17) (14,16) (0,3) (4,0) (7,11) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1528", "image": "data/cycle/graph_visual/medium/graph1528.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (11,0) (8,5) (7,3) (0,4) (10,6) (4,19) (5,14) (9,20) (4,17) (1,12) (15,0) (10,0) (1,0) (14,16) (14,13) (3,0) (0,2) (7,18) (10,20) (16,12) (2,6) (3,4) (19,5) (13,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph644", "image": "data/cycle/graph_visual/medium/graph644.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,6) (13,20) (11,0) (16,15) (20,2) (1,4) (17,14) (10,3) (10,9) (11,3) (12,2) (15,18) (10,17) (19,2) (8,0) (8,7) (5,17) (6,4) (19,16) (12,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph743", "image": "data/cycle/graph_visual/medium/graph743.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (16,14) (10,2) (20,10) (9,17) (19,2) (21,6) (11,3) (17,1) (11,19) (22,13) (15,9) (18,22) (13,16) (18,0) (20,8) (0,4) (3,7) (0,6) (8,18) (20,12) (5,15) (17,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1759", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (9,10) (1,0) (2,22) (16,22) (13,22) (20,10) (15,18) (5,10) (10,6) (8,9) (4,17) (15,1) (11,2) (11,19) (3,5) (17,0) (2,0) (0,16) (2,24) (10,14) (20,0) (14,12) (23,5) (7,6) (11,15) (12,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph512", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (1,10) (12,15) (2,8) (14,0) (3,16) (11,4) (7,18) (15,11) (17,7) (5,3) (17,12) (18,3) (1,5) (7,9) (11,13) (14,7) (16,6) (8,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1794", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (14,16) (2,22) (6,13) (7,10) (23,3) (13,23) (0,5) (5,15) (4,0) (2,0) (1,0) (2,20) (7,14) (3,17) (18,15) (9,1) (14,19) (17,8) (3,0) (13,5) (4,16) (11,21) (24,23) (5,22) (22,4) (23,11) (12,9) (8,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1443", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (6,9) (8,15) (1,18) (2,17) (4,10) (15,2) (1,0) (1,7) (2,0) (8,11) (14,3) (10,19) (16,6) (2,13) (7,4) (9,19) (5,9) (12,2) (14,0) (12,14) (2,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1615", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (16,3) (9,19) (21,6) (1,10) (21,14) (20,7) (17,16) (18,14) (2,19) (11,15) (20,19) (8,16) (2,0) (12,13) (5,2) (3,21) (12,9) (19,4) (0,21) (13,14) (1,0) (0,3) (1,20) (14,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph239", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (0,6) (5,1) (3,7) (4,6) (11,13) (13,6) (2,7) (12,10) (8,4) (11,10) (3,9) (7,5) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph620", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (15,2) (15,12) (14,6) (19,16) (8,0) (0,3) (5,13) (17,9) (14,5) (16,12) (2,18) (4,3) (20,8) (14,3) (10,15) (9,18) (1,8) (16,6) (11,18) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1542", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (16,6) (20,14) (17,1) (19,0) (16,13) (15,7) (14,12) (12,17) (2,8) (4,15) (5,4) (11,5) (3,1) (18,20) (10,1) (14,11) (13,9) (13,5) (8,11) (0,2) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph361", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (3,0) (5,7) (11,6) (12,14) (5,10) (12,1) (9,0) (5,2) (4,9) (2,4) (14,3) (0,16) (13,14) (6,8) (15,16) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1462", "image": "data/cycle/graph_visual/medium/graph1462.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (19,10) (6,18) (6,2) (12,17) (0,1) (11,5) (8,9) (8,13) (7,5) (11,13) (15,12) (6,15) (12,4) (0,3) (0,7) (1,4) (13,10) (0,2) (3,9) (16,1) (17,0) (3,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1043", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (7,1) (3,6) (4,5) (1,11) (8,4) (0,1) (7,0) (10,4) (2,4) (0,5) (1,9) (6,7) (0,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph299", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (10,14) (7,2) (1,3) (4,11) (2,13) (2,1) (5,11) (10,12) (0,14) (10,13) (5,1) (7,8) (4,6) (7,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1260", "image": "data/cycle/graph_visual/medium/graph1260.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,13) (0,2) (15,7) (13,0) (11,9) (9,4) (5,1) (13,9) (0,8) (1,0) (8,3) (3,2) (0,6) (15,0) (0,3) (13,14) (11,10) (8,12) (16,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1505", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (16,7) (2,0) (12,11) (19,4) (3,0) (0,1) (16,5) (10,14) (9,15) (11,1) (19,11) (15,10) (13,20) (5,0) (0,18) (0,6) (13,9) (12,17) (3,18) (20,12) (1,2) (16,19) (7,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph413", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (7,5) (10,15) (16,11) (10,13) (16,8) (14,6) (9,3) (2,7) (4,16) (7,13) (1,9) (2,14) (14,8) (9,14) (13,0) (12,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1369", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (4,10) (8,9) (11,17) (16,11) (0,15) (1,14) (3,0) (4,6) (13,16) (1,6) (6,2) (8,2) (12,8) (5,16) (0,7) (3,10) (1,0) (16,0) (0,2) (6,16) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph471", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (3,16) (5,9) (13,11) (8,1) (17,6) (14,2) (12,5) (2,3) (7,14) (6,1) (15,17) (4,14) (10,11) (3,13) (8,14) (0,4) (12,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph172", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (4,8) (6,1) (7,10) (6,10) (7,12) (4,7) (9,3) (6,5) (11,2) (2,0) (3,12) (12,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1450", "image": "data/cycle/graph_visual/medium/graph1450.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,6) (12,17) (13,12) (2,0) (19,14) (19,13) (14,0) (2,5) (18,0) (2,8) (9,14) (15,8) (6,16) (1,4) (0,15) (0,4) (3,0) (1,0) (18,4) (11,12) (3,7) (3,15) (15,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1153", "image": "data/cycle/graph_visual/medium/graph1153.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (8,14) (13,3) (5,12) (1,0) (1,5) (3,0) (11,13) (5,6) (8,10) (4,11) (0,7) (2,9) (0,9) (10,13) (0,6) (7,4) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph220", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (7,0) (2,10) (4,8) (2,12) (3,8) (11,5) (8,12) (1,12) (7,11) (9,13) (6,8) (13,12) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph405", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (8,10) (0,1) (10,13) (6,12) (11,10) (2,15) (11,16) (3,10) (3,6) (2,8) (13,5) (9,12) (0,5) (4,11) (10,7) (1,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph676", "image": "data/cycle/graph_visual/medium/graph676.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (18,4) (16,12) (20,7) (8,5) (20,9) (10,21) (11,0) (10,13) (4,19) (5,19) (5,14) (12,1) (3,4) (2,6) (0,15) (17,14) (0,10) (21,16) (6,10) (3,7) (13,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph0", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (2,5) (2,8) (4,8) (0,7) (8,1) (3,8) (6,7) (0,2) (9,0) (9,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1629", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (11,20) (21,0) (8,13) (12,22) (15,6) (0,2) (13,15) (14,9) (5,1) (12,6) (1,18) (0,11) (7,11) (2,17) (1,10) (0,12) (3,0) (15,2) (16,17) (1,0) (9,21) (11,3) (20,1) (19,22) (18,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph389", "image": "data/cycle/graph_visual/medium/graph389.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (2,5) (10,2) (10,13) (2,1) (8,11) (7,4) (14,0) (3,8) (6,15) (5,14) (12,4) (9,10) (11,2) (0,16) (4,13) (6,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1626", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (10,0) (2,21) (3,9) (2,0) (7,12) (11,8) (18,20) (16,7) (13,18) (2,17) (2,6) (3,4) (7,8) (0,4) (3,0) (20,5) (19,16) (21,3) (14,4) (1,13) (0,22) (1,0) (6,7) (17,15) (0,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph367", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (5,8) (9,11) (3,5) (11,16) (12,5) (0,3) (4,2) (5,13) (7,2) (8,15) (9,7) (0,14) (6,14) (5,1) (5,10) (16,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph804", "image": "data/cycle/graph_visual/medium/graph804.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (22,6) (7,13) (10,16) (17,14) (15,1) (23,21) (11,12) (10,18) (17,15) (6,1) (5,9) (0,4) (14,7) (2,23) (20,12) (14,3) (23,18) (14,19) (6,12) (19,2) (15,9) (17,4) (8,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1478", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (4,2) (10,11) (9,5) (15,3) (12,19) (4,1) (0,4) (6,3) (19,13) (4,18) (14,8) (15,9) (0,11) (11,2) (0,3) (5,14) (16,7) (1,0) (7,17) (0,2) (7,15) (5,13) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph725", "image": "data/cycle/graph_visual/medium/graph725.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (19,17) (13,11) (15,5) (4,14) (3,17) (3,2) (4,0) (3,16) (18,12) (5,22) (2,14) (21,20) (13,16) (1,8) (22,7) (10,6) (14,9) (14,8) (11,12) (20,6) (1,21) (10,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1435", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (14,0) (2,14) (16,5) (13,12) (0,10) (10,3) (8,17) (12,15) (7,11) (3,0) (9,7) (10,9) (18,9) (14,4) (2,0) (15,0) (0,1) (16,1) (6,17) (4,5) (11,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1424", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (11,4) (1,9) (6,8) (0,14) (1,0) (2,3) (0,16) (9,13) (9,10) (4,6) (18,5) (14,7) (2,0) (13,12) (11,15) (12,16) (17,7) (18,0) (14,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1511", "image": "data/cycle/graph_visual/medium/graph1511.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (17,14) (1,19) (20,16) (14,16) (13,4) (3,5) (4,1) (0,15) (15,4) (0,2) (17,3) (3,11) (7,12) (10,4) (3,0) (6,12) (9,1) (17,7) (4,0) (0,1) (7,4) (8,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1034", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (3,0) (11,4) (2,4) (5,1) (0,4) (3,7) (10,11) (1,12) (6,3) (0,1) (7,0) (2,8) (0,11) (2,0) (9,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1548", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (8,17) (0,19) (1,17) (13,0) (13,11) (15,19) (10,15) (20,11) (5,9) (16,8) (11,12) (4,3) (9,14) (0,17) (13,18) (1,0) (13,6) (7,0) (8,3) (2,5) (13,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph961", "image": "data/cycle/graph_visual/medium/graph961.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (0,2) (2,6) (5,1) (4,7) (3,0) (11,2) (5,9) (10,4) (0,11) (10,8) (10,1) (1,0) (0,4) (9,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph386", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (5,3) (0,12) (4,7) (8,15) (8,12) (7,5) (11,12) (11,10) (2,16) (1,7) (12,7) (6,8) (9,14) (16,0) (16,13) (14,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph456", "image": "data/cycle/graph_visual/medium/graph456.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (1,12) (4,1) (5,15) (10,14) (3,2) (15,8) (9,8) (9,13) (6,9) (11,8) (16,4) (2,17) (17,12) (11,2) (14,15) (11,7) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph398", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (15,0) (10,9) (4,2) (11,10) (11,5) (10,16) (6,7) (13,10) (8,1) (4,11) (15,3) (15,8) (2,12) (7,2) (3,11) (7,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1444", "image": "data/cycle/graph_visual/medium/graph1444.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (8,4) (10,17) (13,19) (11,5) (9,2) (16,10) (6,15) (17,7) (5,1) (7,3) (18,0) (15,14) (12,16) (0,2) (5,19) (0,1) (2,18) (9,14) (8,16) (15,16) (9,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1605", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (19,13) (2,5) (20,12) (19,0) (8,21) (14,10) (1,4) (8,14) (0,1) (15,11) (6,3) (8,2) (14,0) (16,20) (0,2) (4,18) (7,3) (13,12) (3,15) (0,15) (17,12) (6,18) (9,15) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph205", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (13,11) (3,2) (2,8) (1,12) (3,10) (11,4) (3,6) (4,1) (9,3) (0,6) (6,5) (12,2) (7,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1186", "image": "data/cycle/graph_visual/medium/graph1186.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (4,3) (1,10) (0,11) (3,2) (2,11) (13,14) (0,3) (0,7) (0,2) (10,11) (1,12) (8,4) (11,14) (10,5) (0,1) (6,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph430", "image": "data/cycle/graph_visual/medium/graph430.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,4) (1,7) (1,2) (13,15) (13,16) (2,13) (10,3) (1,11) (4,12) (2,17) (6,1) (3,11) (8,2) (10,0) (6,14) (9,17) (12,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph282", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (13,1) (6,14) (5,14) (9,6) (8,7) (0,4) (6,2) (12,3) (11,12) (7,6) (4,8) (10,0) (13,14) (12,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1118", "image": "data/cycle/graph_visual/medium/graph1118.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (12,3) (7,1) (7,13) (0,1) (0,7) (4,5) (11,0) (11,12) (4,10) (9,5) (5,12) (8,2) (2,6) (8,3) (0,3) (2,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1758", "image": "data/cycle/graph_visual/medium/graph1758.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (18,22) (7,16) (4,1) (9,22) (14,8) (2,4) (0,1) (0,2) (19,12) (2,11) (14,5) (7,17) (15,19) (23,22) (7,23) (24,15) (10,11) (15,13) (6,0) (11,0) (5,13) (6,3) (23,3) (4,20) (21,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph744", "image": "data/cycle/graph_visual/medium/graph744.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (15,18) (22,6) (5,19) (11,20) (20,13) (4,7) (2,21) (4,10) (10,16) (15,10) (4,3) (3,12) (13,6) (21,8) (5,0) (14,13) (14,18) (8,9) (17,18) (13,0) (21,1) (2,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1201", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (0,13) (11,12) (9,7) (7,5) (1,0) (14,15) (6,1) (1,3) (4,0) (14,8) (4,1) (8,11) (9,6) (2,14) (10,4) (6,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph882", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (1,19) (18,0) (6,22) (2,8) (4,17) (23,19) (12,1) (16,18) (24,0) (11,0) (13,8) (11,9) (7,22) (12,7) (17,20) (24,17) (14,12) (16,5) (12,3) (11,10) (13,17) (7,5) (11,15) (21,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph255", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (2,5) (2,8) (1,5) (14,6) (9,8) (3,11) (13,8) (6,12) (3,8) (8,0) (4,10) (4,12) (11,12) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1481", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (15,14) (7,13) (17,16) (5,7) (14,11) (8,14) (9,14) (13,0) (18,10) (17,14) (16,12) (7,2) (16,4) (3,9) (0,1) (1,9) (17,2) (2,0) (6,19) (13,10) (6,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph401", "image": "data/cycle/graph_visual/medium/graph401.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (16,10) (9,15) (6,1) (7,11) (3,14) (16,2) (11,3) (2,0) (5,16) (13,14) (9,12) (1,2) (1,4) (4,14) (14,8) (13,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph534", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (13,8) (13,6) (0,14) (8,7) (5,9) (9,10) (10,4) (1,11) (15,2) (9,0) (18,4) (12,14) (11,7) (13,15) (17,9) (3,15) (7,0) (7,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1060", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (9,10) (1,7) (6,8) (2,0) (7,0) (10,4) (4,0) (9,5) (12,2) (10,3) (3,2) (4,8) (5,0) (1,0) (3,0) (11,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1019", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (4,5) (5,0) (1,3) (3,6) (0,3) (10,0) (10,7) (0,1) (11,0) (1,5) (11,9) (5,2) (2,0) (8,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph502", "image": "data/cycle/graph_visual/medium/graph502.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (15,7) (5,17) (4,16) (13,0) (0,1) (15,11) (14,3) (12,14) (16,6) (1,5) (1,8) (5,14) (16,9) (11,1) (11,18) (2,6) (8,4) (11,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph609", "image": "data/cycle/graph_visual/medium/graph609.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (13,1) (17,5) (0,19) (18,10) (0,9) (10,19) (11,2) (14,12) (6,4) (3,20) (17,13) (3,15) (7,8) (7,2) (16,11) (19,5) (5,14) (8,1) (20,1) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1427", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (0,1) (17,3) (5,3) (8,7) (13,17) (2,0) (3,0) (1,13) (18,15) (2,14) (0,9) (18,16) (7,16) (7,11) (4,3) (6,7) (12,4) (2,6) (8,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph908", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (8,1) (7,10) (0,10) (4,6) (1,5) (2,10) (4,10) (9,2) (1,0) (3,2) (5,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph297", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (7,13) (12,10) (14,10) (3,6) (9,2) (13,11) (8,10) (8,9) (0,5) (11,0) (1,7) (4,7) (7,14) (6,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph326", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (1,8) (6,15) (4,11) (4,8) (5,12) (14,5) (11,7) (13,11) (9,14) (10,0) (14,3) (0,1) (15,1) (1,5) (2,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1135", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (5,13) (7,9) (3,10) (10,0) (2,0) (1,2) (7,1) (7,4) (8,13) (12,3) (6,2) (3,13) (6,0) (3,0) (0,11) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1486", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (5,7) (13,19) (2,9) (6,9) (4,1) (11,17) (0,16) (1,0) (8,17) (8,7) (4,0) (0,5) (2,17) (0,3) (13,14) (2,18) (16,8) (0,2) (13,18) (3,10) (0,10) (5,12) (15,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1216", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (6,1) (11,12) (5,9) (0,4) (14,12) (4,9) (13,12) (0,1) (2,6) (10,15) (2,8) (0,3) (4,3) (15,9) (10,12) (5,7) (0,2) (11,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph758", "image": "data/cycle/graph_visual/medium/graph758.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (8,3) (14,22) (8,19) (0,13) (0,17) (2,5) (11,14) (20,13) (18,19) (9,13) (7,0) (10,21) (12,15) (17,8) (15,11) (9,5) (13,11) (17,1) (13,6) (21,0) (16,9) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph770", "image": "data/cycle/graph_visual/medium/graph770.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (20,12) (1,0) (21,10) (20,13) (13,5) (17,22) (21,18) (6,15) (18,1) (12,16) (8,19) (1,19) (3,2) (5,7) (14,9) (2,11) (9,8) (4,2) (21,5) (19,6) (17,11) (16,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph131", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (8,9) (11,4) (3,6) (12,2) (6,1) (12,6) (7,8) (7,4) (7,12) (0,4) (0,5) (10,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1653", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (1,19) (12,14) (17,12) (17,0) (16,5) (8,13) (22,6) (7,20) (9,11) (10,11) (16,18) (0,1) (12,1) (17,13) (11,0) (5,7) (12,7) (17,4) (8,2) (0,2) (19,21) (0,3) (15,11) (22,18) (3,12) (4,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph999", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (8,10) (1,8) (2,0) (0,1) (6,10) (0,4) (0,7) (11,9) (2,4) (1,5) (3,5) (2,6) (0,3) (5,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph420", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (10,9) (16,14) (1,6) (1,5) (2,3) (11,17) (9,8) (7,5) (8,6) (2,11) (12,16) (5,13) (17,14) (13,12) (0,1) (15,11) (2,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph261", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (13,12) (3,6) (14,4) (8,9) (11,10) (11,1) (14,7) (2,0) (2,12) (6,9) (12,7) (3,5) (10,3) (0,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph447", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (17,13) (14,3) (2,0) (1,2) (16,5) (14,8) (2,13) (12,13) (14,16) (1,4) (7,11) (9,15) (10,16) (1,6) (3,11) (14,4) (9,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph178", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (0,2) (12,7) (1,5) (10,11) (1,2) (6,2) (8,12) (0,10) (9,6) (3,0) (7,4) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph962", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (1,5) (5,2) (4,6) (0,2) (8,0) (4,2) (4,9) (11,7) (1,0) (0,3) (8,5) (3,2) (10,6) (9,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1133", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (1,4) (8,6) (11,4) (5,10) (13,0) (9,6) (13,7) (0,5) (6,5) (8,3) (6,2) (1,0) (8,12) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph322", "image": "data/cycle/graph_visual/medium/graph322.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (9,10) (1,8) (9,6) (4,11) (5,14) (2,10) (8,2) (10,12) (13,6) (2,0) (15,14) (2,5) (7,11) (4,13) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1578", "image": "data/cycle/graph_visual/medium/graph1578.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (11,10) (9,10) (2,0) (1,0) (8,4) (1,17) (2,8) (5,0) (8,11) (18,10) (11,7) (12,6) (13,20) (12,15) (19,2) (5,13) (20,10) (0,3) (10,3) (6,3) (16,4) (21,14) (21,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1000", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (2,4) (4,5) (1,9) (10,4) (1,7) (8,4) (3,6) (0,1) (2,0) (11,7) (6,7) (5,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph630", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (8,2) (18,7) (14,20) (5,11) (19,16) (11,15) (3,16) (14,4) (15,1) (19,0) (12,11) (7,17) (6,4) (14,15) (17,0) (8,13) (19,4) (8,20) (12,9) (0,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1730", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (0,4) (4,14) (17,4) (23,16) (20,10) (21,0) (0,6) (3,0) (15,18) (16,9) (1,6) (8,18) (2,22) (0,5) (18,17) (10,2) (5,12) (2,3) (19,1) (16,13) (1,0) (12,7) (1,20) (2,0) (20,7) (17,9) (11,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph228", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (10,0) (3,8) (2,8) (13,6) (10,7) (0,12) (5,13) (4,6) (4,11) (9,4) (5,7) (1,13) (2,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph932", "image": "data/cycle/graph_visual/medium/graph932.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,2) (3,4) (8,0) (5,8) (1,4) (4,0) (9,7) (5,6) (0,2) (1,10) (2,9) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph377", "image": "data/cycle/graph_visual/medium/graph377.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (6,7) (15,0) (3,11) (10,11) (15,3) (10,16) (11,5) (8,15) (4,11) (13,10) (2,4) (2,7) (1,8) (14,7) (10,9) (2,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph66", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (11,10) (7,3) (7,5) (7,0) (5,1) (6,4) (4,8) (0,6) (3,9) (7,2) (6,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph514", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (5,18) (1,12) (17,16) (7,16) (15,14) (2,5) (8,6) (8,1) (9,10) (0,14) (13,12) (2,0) (2,4) (3,17) (0,9) (4,12) (7,0) (11,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph191", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (13,3) (6,11) (2,6) (12,10) (0,4) (5,7) (1,8) (1,2) (0,2) (7,1) (12,9) (8,3) (10,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1489", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (0,1) (5,7) (10,17) (12,3) (0,2) (16,7) (9,11) (7,12) (0,11) (5,19) (13,12) (19,17) (11,14) (12,1) (17,4) (18,1) (2,8) (8,11) (0,17) (15,12) (13,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1162", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (4,6) (0,2) (3,12) (4,10) (6,1) (11,13) (2,9) (4,5) (0,8) (1,0) (7,5) (12,2) (8,11) (4,14) (8,10) (0,4) (0,3) (11,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1565", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (6,1) (17,14) (16,12) (9,21) (13,17) (0,2) (18,12) (0,4) (15,12) (10,12) (0,1) (13,10) (17,20) (3,4) (2,11) (20,21) (7,5) (2,6) (0,3) (8,2) (5,9) (16,19) (9,4) (0,5) (11,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1126", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (11,3) (3,0) (9,2) (7,10) (13,12) (3,2) (2,10) (1,11) (12,7) (5,8) (9,6) (4,2) (8,11) (0,2) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1589", "image": "data/cycle/graph_visual/medium/graph1589.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,21) (21,7) (0,1) (18,12) (12,8) (14,4) (9,17) (12,1) (14,0) (15,9) (7,3) (2,0) (18,7) (18,13) (10,5) (16,8) (0,17) (11,12) (19,0) (20,4) (10,4) (6,5) (2,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1429", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (11,7) (8,3) (1,2) (12,5) (0,2) (4,14) (1,0) (0,3) (17,13) (15,9) (18,15) (10,0) (11,16) (14,13) (0,16) (17,11) (18,5) (9,1) (14,3) (12,13) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph789", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (4,17) (15,2) (9,11) (9,17) (18,21) (13,1) (3,18) (16,21) (15,7) (15,3) (23,20) (9,6) (0,4) (8,19) (16,10) (5,14) (5,8) (13,15) (4,3) (12,5) (1,5) (22,6) (2,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1093", "image": "data/cycle/graph_visual/medium/graph1093.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (3,13) (11,4) (6,0) (13,11) (12,10) (1,0) (4,0) (1,5) (5,6) (4,7) (8,0) (9,5) (2,0) (10,13) (7,0) (9,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph39", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (5,10) (1,8) (3,6) (8,6) (0,2) (3,10) (7,8) (9,4) (0,7) (4,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph969", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (10,1) (10,5) (11,7) (0,6) (0,3) (1,7) (9,11) (1,0) (2,7) (5,0) (2,6) (2,0) (0,4) (8,5) (4,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph176", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (7,10) (5,9) (1,7) (4,8) (0,2) (7,5) (8,2) (11,6) (3,7) (6,3) (12,9) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph863", "image": "data/cycle/graph_visual/medium/graph863.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (14,21) (20,15) (7,0) (7,23) (19,9) (3,17) (5,19) (16,22) (17,6) (12,20) (1,12) (11,0) (16,24) (8,1) (2,0) (2,4) (6,8) (13,19) (19,16) (4,20) (18,12) (14,0) (9,10) (2,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph591", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (8,14) (10,18) (17,2) (6,8) (7,5) (19,6) (9,1) (10,13) (13,7) (16,17) (14,15) (9,14) (16,4) (3,9) (14,17) (14,11) (12,16) (0,13) (7,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1080", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (0,1) (0,2) (9,3) (2,12) (6,3) (1,4) (0,6) (3,10) (3,2) (3,0) (2,8) (5,6) (7,9) (0,4) (1,12) (13,11) (4,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph139", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (2,0) (8,10) (7,1) (11,8) (1,4) (9,5) (3,6) (10,5) (4,12) (11,12) (8,3) (2,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph189", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (0,5) (7,5) (2,9) (12,0) (7,11) (13,12) (6,4) (4,3) (1,4) (10,7) (9,8) (2,4) (12,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph493", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (17,18) (18,11) (2,17) (8,14) (9,14) (3,5) (10,16) (16,13) (4,2) (3,14) (17,1) (4,9) (14,0) (7,14) (16,15) (5,6) (5,15) (6,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph136", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (10,6) (7,12) (7,4) (2,11) (1,6) (3,12) (8,4) (7,10) (12,11) (3,9) (0,2) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1018", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (8,2) (8,5) (0,2) (3,0) (1,2) (7,3) (4,6) (1,0) (10,9) (2,7) (0,11) (10,4) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1628", "image": "data/cycle/graph_visual/medium/graph1628.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (1,7) (15,8) (13,2) (15,2) (0,14) (22,4) (2,18) (2,12) (21,7) (14,3) (19,9) (0,1) (9,6) (1,19) (9,20) (11,21) (0,3) (2,0) (14,12) (10,8) (0,4) (21,4) (20,2) (9,5) (17,6) (21,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph851", "image": "data/cycle/graph_visual/medium/graph851.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (0,16) (13,16) (1,18) (8,20) (11,12) (2,6) (8,19) (14,7) (24,23) (9,10) (0,24) (0,18) (5,3) (11,5) (7,2) (5,20) (15,21) (5,17) (16,15) (5,4) (3,0) (5,14) (9,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph251", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (10,13) (2,1) (11,9) (4,1) (3,5) (0,8) (4,9) (5,6) (8,14) (8,1) (5,12) (9,7) (13,6) (14,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph224", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (2,4) (2,12) (4,5) (5,7) (6,4) (11,9) (3,12) (1,6) (8,11) (13,10) (8,10) (12,11) (0,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph842", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (17,4) (5,10) (2,11) (22,13) (20,0) (5,23) (18,15) (0,17) (15,11) (10,9) (7,6) (21,12) (10,14) (0,16) (24,2) (19,11) (5,3) (12,14) (6,10) (22,16) (2,22) (8,9) (10,20) (1,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph234", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (5,12) (8,10) (12,13) (7,13) (4,5) (0,13) (11,9) (0,8) (1,9) (11,3) (10,11) (2,4) (6,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph674", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (1,13) (2,17) (2,0) (7,12) (6,2) (19,16) (19,21) (3,9) (20,5) (17,15) (7,16) (10,0) (11,8) (3,21) (7,8) (13,18) (3,4) (1,0) (18,20) (6,7) (4,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1384", "image": "data/cycle/graph_visual/medium/graph1384.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (1,7) (17,2) (18,9) (2,5) (11,4) (6,9) (0,1) (9,3) (18,0) (14,15) (1,12) (0,2) (8,7) (4,5) (10,14) (8,13) (4,12) (16,15) (10,1) (0,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph569", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (11,7) (8,0) (0,18) (7,5) (17,2) (4,12) (1,8) (9,3) (14,7) (5,10) (0,9) (16,6) (9,6) (4,19) (5,4) (4,13) (15,2) (19,8) (13,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1417", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (6,14) (11,12) (2,10) (15,9) (7,1) (14,8) (17,11) (0,1) (5,13) (15,16) (14,0) (8,2) (2,0) (11,15) (3,13) (8,18) (15,8) (10,3) (1,16) (4,18) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1661", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (2,0) (5,2) (8,17) (10,21) (17,0) (8,19) (11,13) (9,5) (3,0) (4,3) (0,4) (0,21) (22,14) (13,9) (14,11) (15,11) (15,12) (9,16) (17,1) (20,13) (7,0) (1,0) (13,6) (19,18) (0,13) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph481", "image": "data/cycle/graph_visual/medium/graph481.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,9) (6,16) (5,6) (14,1) (6,15) (4,8) (1,13) (2,1) (9,18) (10,12) (2,17) (2,7) (3,14) (13,4) (15,0) (12,1) (4,11) (9,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1358", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (16,11) (14,9) (13,16) (12,11) (0,2) (3,15) (8,17) (1,16) (13,10) (3,8) (1,0) (3,2) (5,16) (4,9) (8,10) (6,7) (6,12) (8,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph483", "image": "data/cycle/graph_visual/medium/graph483.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (15,4) (14,13) (10,6) (2,12) (2,17) (14,6) (8,6) (2,4) (1,15) (7,17) (0,18) (0,12) (0,9) (3,5) (11,8) (3,12) (13,16) (6,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1031", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (0,1) (4,2) (5,8) (5,1) (6,8) (2,3) (12,1) (1,7) (0,9) (4,11) (3,5) (1,9) (12,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1613", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (9,21) (12,13) (20,21) (4,14) (5,16) (3,10) (10,0) (7,9) (6,17) (21,14) (0,1) (15,0) (2,0) (5,4) (17,19) (15,12) (10,9) (17,8) (14,2) (19,11) (0,18) (11,7) (1,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1354", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (13,12) (17,4) (14,2) (15,8) (7,4) (8,10) (16,2) (14,0) (1,9) (0,1) (14,3) (15,6) (9,6) (7,1) (2,11) (9,2) (9,5) (2,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph638", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (16,5) (3,9) (0,13) (10,4) (6,20) (5,0) (1,4) (12,18) (13,6) (4,3) (13,14) (14,18) (15,18) (20,8) (2,3) (19,2) (17,13) (7,8) (10,11) (10,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph460", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (1,10) (3,9) (10,14) (4,12) (4,9) (2,16) (17,0) (1,7) (12,1) (7,0) (8,7) (9,6) (4,5) (5,2) (15,14) (11,8) (15,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph901", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (9,7) (1,8) (1,7) (2,7) (0,2) (5,10) (5,0) (2,4) (0,4) (10,9) (1,0) (6,5) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph145", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (12,1) (1,9) (7,1) (9,0) (10,12) (1,5) (4,11) (3,2) (8,5) (6,8) (5,3) (4,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph960", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (3,1) (0,5) (1,0) (4,2) (10,9) (0,11) (8,3) (6,3) (9,0) (7,3) (6,4) (11,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph802", "image": "data/cycle/graph_visual/medium/graph802.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (9,11) (13,8) (14,22) (16,1) (20,21) (13,22) (3,19) (8,18) (2,13) (11,6) (5,9) (22,5) (10,16) (4,9) (7,12) (15,17) (3,0) (20,10) (12,23) (0,7) (23,21) (17,21) (8,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph847", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (9,3) (23,8) (0,23) (24,20) (5,17) (24,22) (13,15) (4,23) (20,17) (19,10) (3,19) (23,24) (16,6) (10,14) (14,1) (8,15) (12,18) (16,7) (11,21) (7,13) (22,2) (14,17) (11,5) (18,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1724", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (5,22) (1,0) (8,11) (15,19) (20,2) (12,18) (17,11) (7,6) (13,3) (2,0) (10,9) (0,12) (14,23) (1,9) (23,8) (16,17) (16,7) (12,17) (3,8) (15,4) (1,7) (2,4) (5,3) (21,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph733", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (17,13) (18,12) (14,15) (21,16) (6,3) (1,22) (9,5) (7,2) (13,10) (12,16) (6,4) (2,11) (2,0) (9,2) (5,8) (20,17) (17,15) (11,21) (9,4) (19,12) (1,20) (10,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1178", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (2,1) (14,10) (9,7) (6,4) (11,5) (0,3) (4,11) (1,3) (2,0) (0,4) (2,7) (10,13) (2,13) (12,10) (1,5) (8,7) (0,14) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph769", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (6,11) (7,10) (9,19) (16,15) (14,13) (3,12) (5,17) (1,11) (2,22) (8,0) (10,2) (0,18) (17,20) (9,12) (3,16) (4,0) (6,21) (6,18) (16,20) (3,13) (1,22) (0,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph641", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (16,6) (4,16) (11,18) (8,20) (12,13) (10,15) (3,4) (2,13) (8,1) (5,1) (15,14) (4,9) (7,16) (9,12) (3,19) (11,15) (0,12) (18,9) (19,8) (17,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph248", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (4,1) (13,3) (3,10) (8,13) (9,14) (14,5) (2,10) (10,12) (2,11) (0,4) (6,10) (10,4) (7,12) (14,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph598", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (9,10) (13,14) (15,18) (5,12) (14,18) (4,3) (2,3) (10,15) (16,13) (17,2) (8,3) (8,7) (4,1) (0,5) (6,19) (11,18) (13,6) (4,10) (13,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph993", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (1,0) (1,2) (6,3) (2,8) (9,8) (5,10) (3,4) (8,10) (4,7) (7,10) (0,9) (11,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1597", "image": "data/cycle/graph_visual/medium/graph1597.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (4,0) (17,0) (3,0) (8,14) (3,9) (20,4) (15,12) (20,1) (0,7) (0,1) (18,12) (13,1) (15,6) (11,5) (9,21) (2,6) (19,21) (5,7) (4,16) (17,12) (21,11) (0,2) (20,6) (3,10) (8,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph257", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (11,3) (8,1) (10,0) (2,0) (4,0) (13,10) (9,12) (7,1) (6,2) (1,2) (14,11) (6,12) (5,7) (8,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1355", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (3,10) (15,11) (8,15) (0,14) (0,4) (8,13) (8,2) (5,14) (16,11) (2,0) (13,4) (15,14) (17,8) (1,16) (0,1) (15,7) (12,3) (9,11) (3,0) (10,2) (1,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph905", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (9,8) (4,7) (6,9) (1,5) (0,1) (10,4) (6,0) (8,4) (5,3) (3,2) (2,0) (2,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph355", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (13,15) (15,8) (12,11) (1,0) (9,4) (8,0) (0,10) (2,3) (4,15) (8,5) (6,13) (7,1) (11,10) (15,2) (14,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph987", "image": "data/cycle/graph_visual/medium/graph987.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (2,3) (4,11) (0,2) (6,5) (3,9) (0,6) (0,3) (0,1) (3,6) (0,4) (3,10) (1,4) (7,9) (1,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1636", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (18,5) (20,21) (2,1) (0,19) (19,14) (16,4) (12,8) (2,18) (10,21) (9,22) (22,7) (5,14) (15,11) (6,9) (13,4) (0,22) (8,4) (11,2) (10,13) (3,19) (6,17) (2,10) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph37", "image": "data/cycle/graph_visual/medium/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 10, and the edges are: (7,5) (0,3) (7,10) (6,9) (6,4) (2,0) (7,9) (8,0) (1,9) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph462", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (10,3) (6,14) (5,4) (8,2) (4,12) (1,11) (0,10) (9,17) (2,17) (7,1) (13,16) (15,13) (2,1) (11,3) (16,12) (1,6) (13,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph198", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (3,4) (6,5) (5,8) (12,3) (4,0) (2,13) (4,1) (1,13) (12,8) (9,7) (11,12) (0,9) (10,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1406", "image": "data/cycle/graph_visual/medium/graph1406.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (13,2) (9,2) (18,10) (4,7) (10,4) (5,9) (14,12) (7,1) (2,15) (6,9) (14,0) (0,1) (6,16) (12,2) (3,14) (9,1) (15,8) (17,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph701", "image": "data/cycle/graph_visual/medium/graph701.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,6) (11,18) (15,16) (17,1) (5,3) (17,2) (21,20) (19,18) (10,16) (17,20) (12,6) (13,16) (14,3) (9,4) (14,8) (20,15) (5,19) (2,4) (14,9) (7,14) (0,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1008", "image": "data/cycle/graph_visual/medium/graph1008.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (5,3) (11,7) (7,4) (10,7) (9,10) (3,8) (0,1) (10,1) (5,6) (7,3) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1583", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (2,0) (16,4) (6,12) (0,5) (7,17) (14,21) (1,10) (3,17) (3,12) (20,1) (4,1) (15,0) (13,7) (15,4) (0,4) (17,14) (4,11) (9,21) (3,0) (8,4) (18,1) (4,7) (1,0) (21,19) (5,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph737", "image": "data/cycle/graph_visual/medium/graph737.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (21,3) (11,6) (7,9) (2,0) (0,11) (18,17) (16,0) (10,7) (20,2) (0,1) (8,19) (20,14) (1,17) (14,15) (18,13) (8,11) (12,1) (13,5) (10,3) (21,15) (9,22) (4,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph444", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (12,10) (13,10) (15,1) (17,15) (15,5) (3,17) (15,8) (11,7) (16,17) (14,7) (12,6) (4,9) (4,0) (2,14) (6,1) (14,6) (12,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph345", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (3,11) (3,15) (6,7) (6,8) (10,0) (4,15) (7,12) (10,5) (4,13) (14,6) (9,13) (9,2) (5,4) (15,6) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph878", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (17,20) (13,0) (3,24) (0,11) (9,21) (8,21) (19,11) (23,12) (11,2) (8,18) (10,12) (6,14) (8,4) (7,12) (1,6) (21,2) (0,16) (15,18) (3,0) (0,5) (23,9) (22,5) (7,6) (22,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph824", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (16,21) (6,19) (9,17) (23,18) (4,13) (23,20) (7,23) (18,1) (0,19) (17,1) (14,2) (17,3) (12,0) (2,20) (20,6) (8,15) (4,0) (6,8) (16,19) (20,22) (10,4) (15,11) (16,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1412", "image": "data/cycle/graph_visual/medium/graph1412.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (1,0) (8,4) (10,0) (0,15) (2,8) (14,15) (11,9) (8,7) (9,3) (2,18) (5,13) (2,13) (9,1) (2,1) (15,6) (17,3) (10,12) (9,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1785", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (17,8) (4,0) (16,22) (8,10) (11,14) (23,4) (24,14) (21,0) (3,10) (0,22) (6,19) (1,0) (4,12) (16,6) (1,20) (0,3) (13,24) (16,18) (5,16) (6,2) (15,6) (0,2) (16,11) (7,19) (2,8) (1,19) (24,4) (0,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1091", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (12,6) (12,4) (0,1) (12,3) (10,8) (13,1) (13,4) (6,2) (7,8) (0,4) (0,9) (11,13) (7,6) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1643", "image": "data/cycle/graph_visual/medium/graph1643.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,9) (21,10) (0,3) (10,9) (11,7) (20,18) (17,8) (14,0) (9,0) (4,22) (16,22) (19,7) (15,3) (20,9) (14,12) (2,0) (21,4) (6,13) (7,0) (7,8) (0,4) (15,2) (0,1) (13,15) (11,1) (13,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph170", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (11,9) (2,1) (5,7) (0,1) (6,2) (12,11) (4,3) (3,12) (2,3) (0,10) (5,6) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1518", "image": "data/cycle/graph_visual/medium/graph1518.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (14,8) (5,18) (0,2) (2,14) (8,3) (16,10) (9,14) (15,12) (16,20) (15,17) (1,3) (15,5) (3,0) (7,11) (15,9) (5,0) (20,13) (6,19) (0,1) (4,10) (3,10) (7,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph448", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (6,13) (11,1) (14,0) (15,16) (7,3) (14,17) (6,12) (4,7) (5,11) (0,12) (6,10) (2,1) (4,9) (4,2) (16,7) (8,12) (14,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph896", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (11,19) (15,7) (19,0) (9,10) (16,18) (0,24) (1,16) (14,0) (4,16) (11,5) (0,7) (23,4) (10,3) (13,2) (24,4) (8,3) (3,22) (18,6) (17,12) (8,11) (2,20) (11,12) (13,9) (21,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph364", "image": "data/cycle/graph_visual/medium/graph364.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (11,12) (4,7) (1,11) (15,11) (5,16) (15,8) (10,7) (12,16) (3,0) (1,2) (13,12) (5,0) (10,9) (14,0) (13,9) (6,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph300", "image": "data/cycle/graph_visual/medium/graph300.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (13,14) (15,7) (10,11) (5,13) (2,3) (5,1) (15,0) (13,9) (13,0) (9,4) (0,8) (9,11) (3,8) (0,6) (8,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1602", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (9,13) (9,20) (12,18) (16,2) (13,1) (12,20) (18,21) (7,3) (18,17) (16,9) (5,3) (5,16) (17,4) (2,0) (14,0) (7,15) (8,5) (0,1) (3,0) (0,19) (12,10) (6,3) (11,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1167", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (1,0) (14,7) (14,10) (12,5) (12,7) (4,10) (6,10) (3,1) (7,1) (9,8) (0,2) (9,11) (13,5) (0,3) (9,4) (2,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1751", "image": "data/cycle/graph_visual/medium/graph1751.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (2,6) (9,20) (22,4) (13,10) (10,0) (10,6) (16,12) (16,22) (0,11) (2,0) (21,4) (22,3) (5,19) (1,0) (15,24) (5,14) (4,19) (14,13) (21,18) (10,24) (14,20) (17,0) (12,1) (8,5) (7,3) (7,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1556", "image": "data/cycle/graph_visual/medium/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 20, and the edges are: (0,1) (14,8) (12,5) (9,14) (1,8) (14,2) (18,17) (11,12) (2,0) (10,6) (7,10) (19,6) (3,16) (4,14) (16,13) (20,7) (1,20) (3,17) (11,13) (5,15) (2,3) (4,0) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph245", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (14,8) (6,7) (11,9) (7,2) (4,13) (6,8) (12,2) (1,3) (1,9) (4,0) (1,7) (7,10) (5,8) (4,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1006", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (5,0) (2,11) (9,4) (4,0) (1,5) (5,9) (0,3) (7,3) (11,9) (6,1) (7,5) (3,10) (0,1) (2,0) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1107", "image": "data/cycle/graph_visual/medium/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 13, and the edges are: (0,3) (5,6) (2,1) (6,2) (11,1) (3,6) (11,8) (9,8) (10,13) (8,7) (4,12) (13,3) (4,0) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1680", "image": "data/cycle/graph_visual/medium/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 23, and the edges are: (18,15) (2,0) (13,23) (15,5) (9,12) (10,7) (13,5) (14,7) (13,6) (23,3) (16,14) (16,4) (0,1) (22,5) (14,19) (0,4) (11,21) (9,8) (2,22) (17,8) (17,3) (20,2) (11,23) (22,4) (9,1) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1248", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (3,4) (0,2) (5,7) (2,11) (9,5) (10,12) (5,0) (1,0) (4,9) (0,4) (14,12) (11,12) (2,8) (2,6) (15,9) (0,3) (15,10) (13,12) (6,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph421", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (8,17) (15,12) (9,10) (4,5) (14,2) (1,16) (15,0) (14,4) (7,17) (13,12) (0,14) (5,16) (0,10) (11,9) (6,17) (7,11) (3,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph497", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (13,16) (6,18) (18,11) (1,18) (16,10) (7,17) (3,18) (12,8) (10,1) (2,5) (1,17) (9,17) (3,8) (13,0) (15,14) (5,15) (2,18) (16,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph773", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (17,22) (17,8) (20,15) (7,19) (2,14) (20,12) (3,18) (6,7) (18,8) (0,15) (22,6) (13,18) (7,1) (21,17) (9,4) (17,5) (2,19) (10,19) (11,15) (4,11) (17,15) (16,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1286", "image": "data/cycle/graph_visual/medium/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 16, and the edges are: (11,16) (15,12) (0,7) (3,0) (12,4) (3,10) (1,0) (5,7) (2,0) (13,8) (2,6) (0,12) (0,4) (3,9) (4,1) (9,8) (5,11) (1,13) (6,14) (6,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph575", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (17,3) (7,12) (18,13) (12,10) (13,8) (14,11) (4,19) (5,17) (11,9) (9,6) (15,8) (0,7) (8,16) (0,3) (4,12) (13,2) (1,16) (9,5) (10,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph746", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (13,9) (10,8) (19,16) (3,11) (19,1) (10,7) (6,15) (3,14) (16,18) (4,3) (16,2) (5,10) (5,9) (20,8) (22,0) (5,14) (21,14) (19,0) (6,11) (3,12) (8,16) (17,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph63", "image": "data/cycle/graph_visual/medium/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 11, and the edges are: (1,9) (11,6) (9,3) (0,3) (10,0) (3,7) (10,8) (6,7) (3,4) (11,5) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph593", "image": "data/cycle/graph_visual/medium/graph593.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (15,10) (6,13) (7,0) (17,8) (18,0) (14,19) (9,5) (8,3) (17,13) (5,2) (12,11) (3,4) (9,11) (13,19) (1,17) (9,13) (0,16) (15,8) (13,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1463", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (0,3) (13,15) (1,8) (19,3) (4,3) (9,12) (6,16) (16,4) (11,14) (5,1) (12,0) (2,0) (18,11) (17,9) (0,4) (7,16) (6,15) (12,10) (18,19) (4,9) (1,0) (2,13) (15,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph125", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (8,12) (2,1) (4,7) (6,2) (5,1) (6,9) (8,1) (0,3) (11,10) (12,7) (2,0) (0,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1184", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (3,6) (10,14) (9,2) (7,13) (12,10) (0,1) (14,7) (0,11) (10,8) (0,2) (11,13) (4,0) (9,8) (7,4) (7,1) (6,12) (0,5) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph290", "image": "data/cycle/graph_visual/medium/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 14, and the edges are: (8,5) (3,0) (11,9) (3,8) (9,0) (6,10) (7,5) (0,1) (9,12) (4,6) (4,7) (10,13) (14,13) (5,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1665", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (0,2) (8,18) (18,1) (22,9) (20,1) (0,5) (2,21) (14,4) (7,12) (11,18) (16,13) (19,0) (2,3) (4,0) (3,0) (9,17) (7,20) (15,18) (2,10) (4,17) (17,16) (6,1) (10,20) (5,12) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph142", "image": "data/cycle/graph_visual/medium/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 12, and the edges are: (6,2) (3,12) (1,0) (7,5) (8,3) (6,5) (3,4) (2,3) (11,9) (11,12) (1,2) (10,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1416", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (18,5) (12,15) (0,17) (0,11) (7,16) (8,2) (17,1) (9,11) (13,12) (12,7) (2,0) (6,13) (14,11) (12,1) (5,7) (17,4) (3,12) (17,10) (0,1) (8,11) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph580", "image": "data/cycle/graph_visual/medium/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 19, and the edges are: (18,1) (6,13) (13,12) (8,2) (17,10) (14,11) (9,11) (1,12) (3,12) (0,17) (4,17) (15,12) (7,5) (8,11) (19,5) (7,16) (12,7) (19,17) (11,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph877", "image": "data/cycle/graph_visual/medium/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 24, and the edges are: (16,19) (6,16) (24,19) (18,20) (12,1) (24,4) (14,24) (6,23) (1,8) (22,3) (12,2) (7,9) (13,17) (0,6) (18,21) (3,18) (15,11) (5,0) (1,9) (21,23) (8,15) (13,3) (10,20) (9,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph463", "image": "data/cycle/graph_visual/medium/graph463.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (15,3) (2,11) (1,17) (3,13) (3,12) (5,4) (8,2) (3,7) (11,16) (0,15) (6,11) (12,11) (4,9) (5,14) (10,12) (3,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph494", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (14,16) (3,10) (7,8) (18,0) (10,17) (16,15) (4,6) (1,16) (11,15) (11,0) (5,2) (12,1) (3,13) (7,15) (0,9) (9,4) (1,10) (2,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1219", "image": "data/cycle/graph_visual/medium/graph1219.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (12,8) (10,9) (2,0) (14,0) (7,0) (9,8) (4,15) (5,6) (12,1) (7,3) (13,4) (12,5) (11,0) (4,14) (7,12) (10,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1210", "image": "data/cycle/graph_visual/medium/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 15, and the edges are: (0,11) (9,13) (5,4) (4,9) (1,12) (0,1) (13,3) (3,11) (15,0) (3,0) (10,2) (10,6) (1,8) (7,4) (0,2) (8,10) (8,11) (14,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph352", "image": "data/cycle/graph_visual/medium/graph352.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (7,13) (9,1) (12,14) (0,14) (3,12) (11,10) (8,7) (15,7) (5,1) (11,15) (2,8) (0,6) (11,4) (3,5) (7,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph519", "image": "data/cycle/graph_visual/medium/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 18, and the edges are: (1,2) (11,10) (9,8) (7,9) (17,2) (2,11) (4,18) (3,15) (0,6) (18,6) (14,12) (18,13) (15,16) (4,17) (5,18) (11,8) (9,14) (8,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph688", "image": "data/cycle/graph_visual/medium/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 21, and the edges are: (16,4) (8,19) (11,16) (11,12) (4,19) (8,3) (10,13) (1,16) (5,3) (16,7) (13,20) (2,1) (14,6) (8,10) (6,12) (0,21) (15,9) (18,3) (3,21) (18,9) (8,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph1308", "image": "data/cycle/graph_visual/medium/graph1308.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (11,4) (7,16) (8,7) (14,2) (0,2) (0,1) (3,2) (0,3) (0,13) (12,5) (10,1) (4,0) (10,2) (0,6) (1,12) (0,5) (16,9) (1,6) (4,9) (15,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1347", "image": "data/cycle/graph_visual/medium/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 17, and the edges are: (11,8) (3,8) (0,11) (5,15) (6,1) (5,0) (2,11) (0,1) (12,7) (0,12) (2,0) (13,6) (12,4) (14,8) (16,9) (10,0) (9,2) (3,0) (17,0) (6,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph1652", "image": "data/cycle/graph_visual/medium/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 22, and the edges are: (9,19) (6,21) (17,5) (11,6) (22,1) (14,0) (12,3) (16,20) (0,4) (2,22) (2,10) (15,16) (3,0) (13,14) (2,0) (10,7) (9,12) (1,0) (0,8) (3,16) (3,13) (11,1) (0,5) (0,18) (20,17) (18,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-medium-graph383", "image": "data/cycle/graph_visual/medium/graph383.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (13,12) (8,0) (16,5) (7,1) (14,2) (15,12) (14,9) (0,15) (9,5) (6,0) (7,4) (11,0) (4,9) (5,10) (3,2) (15,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-medium-graph859", "image": "data/cycle/graph_visual/medium/graph859.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (12,3) (8,0) (17,23) (21,12) (16,22) (9,20) (13,3) (1,24) (18,24) (16,15) (7,23) (0,14) (2,22) (10,24) (5,17) (14,13) (6,10) (3,16) (0,4) (23,9) (2,11) (20,19) (0,18) (23,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph107", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (22,2) (1,26) (25,18) (25,0) (17,4) (20,7) (12,5) (0,4) (9,26) (19,1) (8,18) (14,4) (1,6) (16,13) (25,2) (7,12) (21,0) (2,3) (15,18) (20,26) (9,17) (10,23) (24,1) (16,17) (11,18) (10,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph129", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (2,17) (22,15) (7,19) (15,26) (26,10) (24,1) (0,20) (4,23) (2,3) (3,0) (6,8) (11,4) (6,23) (18,21) (7,25) (0,14) (14,8) (16,12) (13,9) (11,16) (22,2) (19,14) (24,0) (5,9) (12,13) (9,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph936", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (15,7) (22,13) (25,14) (12,15) (10,2) (9,23) (26,31) (34,29) (15,10) (22,16) (25,17) (5,29) (5,31) (14,20) (29,18) (33,26) (19,32) (7,21) (13,27) (22,20) (8,2) (28,19) (1,11) (9,3) (14,29) (33,0) (21,22) (17,23) (32,14) (3,1) (4,13) (16,24) (30,26) (0,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph797", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (23,26) (3,16) (14,21) (13,26) (29,5) (9,11) (22,8) (17,24) (21,30) (22,23) (32,18) (15,27) (29,25) (25,13) (0,9) (27,7) (7,5) (2,29) (12,22) (25,6) (10,32) (28,16) (17,29) (7,20) (4,11) (19,13) (9,12) (1,29) (13,3) (31,11) (19,14) (10,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph813", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (15,29) (12,1) (0,3) (19,22) (25,14) (22,11) (30,2) (15,4) (32,5) (24,17) (23,28) (17,25) (24,26) (31,11) (29,16) (15,8) (28,1) (23,19) (16,13) (10,6) (32,12) (1,7) (18,33) (3,33) (7,27) (20,21) (23,21) (30,0) (10,30) (16,2) (14,9) (25,0) (10,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1475", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (12,7) (22,18) (25,10) (16,1) (5,24) (15,22) (11,9) (3,22) (0,4) (13,2) (6,9) (12,26) (5,9) (13,8) (13,23) (0,2) (11,14) (28,16) (23,26) (17,19) (0,7) (16,25) (20,10) (25,4) (20,27) (21,17) (1,0) (24,0) (27,8) (27,29) (8,21) (3,0) (29,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph694", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (23,20) (21,14) (27,26) (13,4) (22,28) (3,26) (27,5) (3,28) (25,23) (21,8) (1,30) (8,16) (15,11) (30,16) (4,12) (31,15) (14,9) (19,16) (7,18) (11,24) (5,4) (0,30) (29,4) (6,31) (16,17) (10,12) (17,2) (25,15) (18,21) (22,0) (6,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1968", "image": "data/cycle/graph_visual/hard/graph1968.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (21,34) (28,25) (6,2) (14,16) (1,0) (10,14) (0,5) (22,18) (32,8) (0,4) (27,33) (5,20) (25,11) (19,17) (19,27) (31,12) (22,3) (7,5) (26,13) (24,12) (32,17) (33,26) (0,3) (2,0) (26,23) (31,5) (18,4) (26,30) (34,14) (12,34) (1,15) (1,2) (10,28) (14,32) (28,6) (27,29) (22,9) (22,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph147", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (20,24) (0,13) (8,6) (14,12) (7,13) (10,23) (8,14) (1,26) (25,13) (17,21) (7,9) (4,9) (22,1) (2,17) (14,17) (15,19) (16,18) (20,6) (14,11) (5,16) (15,20) (7,2) (14,16) (9,3) (22,19) (10,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1751", "image": "data/cycle/graph_visual/hard/graph1751.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (32,3) (10,28) (30,31) (26,18) (8,16) (30,10) (7,26) (1,17) (19,11) (0,3) (27,0) (2,24) (10,8) (0,1) (32,24) (9,23) (28,25) (15,4) (2,22) (17,31) (17,14) (26,31) (4,10) (28,20) (0,15) (2,0) (21,0) (3,5) (6,30) (11,22) (24,23) (26,12) (7,2) (14,29) (13,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1909", "image": "data/cycle/graph_visual/hard/graph1909.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (19,26) (16,28) (9,0) (22,34) (28,6) (12,25) (12,32) (0,1) (8,2) (16,29) (34,20) (2,0) (23,5) (30,5) (12,34) (6,18) (5,21) (0,10) (33,18) (0,3) (3,5) (23,26) (17,1) (31,27) (15,31) (6,2) (21,27) (13,20) (1,14) (12,2) (16,26) (31,4) (17,12) (23,11) (6,24) (9,30) (16,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph611", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (4,9) (2,21) (5,3) (5,23) (24,6) (26,23) (8,28) (9,18) (7,31) (11,26) (20,1) (25,30) (16,31) (12,1) (22,19) (22,4) (27,24) (2,28) (5,30) (29,31) (13,22) (16,6) (15,10) (15,31) (29,21) (15,17) (10,14) (0,9) (3,29) (11,19) (12,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph987", "image": "data/cycle/graph_visual/hard/graph987.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (26,27) (10,3) (28,8) (3,16) (25,13) (10,34) (4,29) (13,10) (5,22) (14,15) (28,30) (13,0) (7,23) (9,33) (24,11) (13,33) (8,0) (19,30) (1,12) (15,0) (16,2) (17,26) (6,23) (7,18) (4,8) (22,34) (20,15) (0,32) (10,24) (6,15) (24,21) (8,31) (1,29) (17,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph692", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (13,27) (6,8) (7,12) (13,5) (26,21) (31,19) (18,11) (6,25) (12,28) (2,9) (0,26) (18,19) (16,20) (24,23) (30,2) (19,8) (23,3) (28,24) (22,18) (4,29) (2,11) (30,13) (22,15) (3,6) (18,17) (31,0) (14,25) (1,12) (16,28) (10,12) (4,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph870", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (33,1) (6,11) (31,29) (5,15) (28,19) (26,31) (30,5) (24,3) (2,13) (20,13) (33,4) (16,10) (21,4) (22,29) (31,19) (21,20) (7,24) (5,16) (14,12) (23,32) (10,25) (13,8) (28,27) (10,20) (17,9) (12,10) (10,11) (1,7) (23,2) (9,18) (28,0) (4,19) (0,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph116", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (3,18) (6,0) (15,14) (7,26) (13,3) (16,6) (11,9) (1,15) (5,26) (18,22) (9,18) (24,17) (1,8) (1,9) (3,24) (0,10) (4,24) (26,23) (12,2) (20,13) (21,23) (21,18) (6,25) (19,8) (12,20) (16,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1912", "image": "data/cycle/graph_visual/hard/graph1912.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (8,7) (10,29) (27,0) (2,5) (4,26) (21,18) (16,6) (2,0) (13,19) (4,12) (3,29) (4,33) (13,22) (17,21) (23,4) (25,17) (16,26) (9,1) (26,30) (9,14) (32,9) (19,21) (25,5) (3,20) (21,8) (15,9) (11,22) (5,20) (0,1) (28,14) (34,32) (30,5) (29,31) (8,0) (24,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph192", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (1,8) (5,22) (23,6) (21,8) (9,23) (0,9) (17,6) (13,4) (23,20) (0,13) (18,4) (15,7) (5,4) (5,12) (17,2) (7,20) (7,19) (14,20) (16,21) (11,25) (4,26) (3,9) (21,10) (2,24) (26,21) (21,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph156", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (0,8) (18,4) (21,12) (22,0) (1,11) (11,12) (20,13) (9,13) (26,18) (23,20) (15,10) (16,5) (3,20) (25,12) (16,7) (14,7) (11,19) (23,0) (16,19) (5,24) (12,3) (19,6) (26,23) (17,10) (2,1) (15,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph915", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (11,33) (2,10) (28,12) (22,19) (29,15) (10,3) (23,13) (29,4) (26,16) (32,6) (5,9) (3,25) (17,9) (25,32) (7,30) (18,1) (3,21) (8,31) (30,28) (8,24) (32,20) (0,13) (14,23) (2,1) (10,27) (3,16) (34,5) (21,17) (23,29) (20,33) (12,14) (14,8) (8,22) (22,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1186", "image": "data/cycle/graph_visual/hard/graph1186.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (6,21) (24,19) (18,12) (0,1) (14,15) (23,12) (25,20) (26,0) (15,0) (3,8) (6,3) (8,2) (11,24) (7,24) (22,26) (1,4) (24,0) (13,19) (2,9) (25,24) (5,25) (14,16) (17,20) (4,18) (15,10) (12,13) (15,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph481", "image": "data/cycle/graph_visual/hard/graph481.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (14,0) (15,6) (21,16) (20,3) (24,18) (3,29) (9,22) (21,5) (28,14) (25,29) (2,17) (26,8) (14,27) (13,5) (2,22) (22,1) (23,9) (6,12) (0,24) (21,22) (4,19) (23,20) (5,11) (24,26) (5,6) (4,25) (7,12) (23,27) (10,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1168", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (12,1) (2,6) (4,24) (22,6) (13,9) (21,3) (16,19) (0,23) (8,6) (15,18) (23,1) (11,17) (26,6) (24,21) (4,14) (7,23) (0,1) (19,21) (25,7) (20,13) (5,16) (13,23) (10,19) (1,15) (17,24) (13,22) (5,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1726", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (31,22) (0,28) (16,17) (1,19) (32,3) (4,27) (6,15) (23,17) (29,1) (18,5) (1,0) (16,5) (25,1) (31,10) (29,7) (24,26) (19,3) (11,2) (0,2) (12,9) (22,14) (29,10) (12,27) (6,20) (12,8) (9,19) (31,20) (13,30) (24,29) (30,31) (28,8) (26,17) (2,32) (21,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1939", "image": "data/cycle/graph_visual/hard/graph1939.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,26) (5,33) (21,16) (1,0) (1,23) (24,11) (24,27) (13,12) (4,13) (3,0) (8,3) (8,4) (24,8) (4,0) (34,10) (15,11) (14,6) (22,21) (30,0) (32,28) (16,13) (34,33) (29,1) (11,28) (31,6) (19,7) (24,9) (19,23) (5,0) (12,6) (14,18) (2,0) (9,1) (4,20) (13,25) (3,26) (13,33) (30,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1520", "image": "data/cycle/graph_visual/hard/graph1520.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (14,24) (30,7) (20,11) (2,0) (5,19) (13,14) (0,18) (1,12) (21,10) (29,10) (3,0) (4,30) (27,0) (24,16) (4,22) (10,6) (20,10) (6,2) (3,27) (14,5) (0,12) (16,15) (21,13) (1,0) (22,3) (28,8) (4,25) (21,23) (19,28) (13,4) (5,9) (17,22) (26,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1450", "image": "data/cycle/graph_visual/hard/graph1450.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (15,25) (18,21) (26,17) (0,1) (8,22) (20,10) (27,24) (4,17) (24,7) (13,0) (23,11) (5,29) (9,1) (0,16) (4,19) (22,24) (14,16) (15,27) (10,26) (17,24) (11,19) (28,23) (16,8) (29,12) (6,14) (14,12) (2,0) (15,1) (3,9) (6,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph272", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (25,26) (13,8) (27,1) (24,16) (26,5) (25,22) (0,13) (20,21) (18,21) (7,17) (1,10) (4,16) (11,25) (18,3) (15,5) (20,10) (9,17) (18,2) (23,3) (16,15) (26,2) (12,18) (25,8) (24,19) (18,6) (21,17) (14,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph240", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (13,25) (25,20) (10,14) (10,1) (5,24) (27,25) (8,16) (4,11) (23,2) (21,2) (17,25) (1,7) (9,6) (4,12) (7,8) (4,5) (13,0) (0,26) (9,3) (27,22) (18,15) (27,21) (20,7) (25,19) (9,18) (12,1) (14,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1295", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (1,19) (22,25) (27,15) (14,0) (26,1) (1,6) (12,17) (7,0) (8,3) (0,1) (5,4) (25,20) (26,13) (1,17) (7,2) (2,27) (14,12) (13,23) (16,11) (23,8) (10,15) (9,16) (5,24) (14,11) (21,4) (11,5) (20,0) (18,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1155", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (21,14) (10,17) (3,6) (20,10) (0,26) (1,0) (10,24) (21,0) (4,8) (8,11) (1,19) (7,11) (25,0) (9,10) (11,10) (12,6) (1,22) (22,5) (25,16) (26,3) (0,2) (24,18) (15,12) (2,8) (5,13) (2,23) (16,4) (20,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1628", "image": "data/cycle/graph_visual/hard/graph1628.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (2,0) (30,13) (19,13) (23,12) (27,7) (0,16) (16,19) (20,7) (29,23) (16,24) (3,0) (28,10) (12,31) (30,17) (15,11) (5,15) (26,16) (31,8) (2,7) (15,12) (18,29) (21,4) (12,6) (18,22) (1,0) (31,21) (20,11) (0,21) (3,28) (31,9) (12,25) (10,15) (11,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph445", "image": "data/cycle/graph_visual/hard/graph445.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (14,4) (11,9) (8,4) (28,17) (19,15) (14,19) (18,11) (3,22) (10,21) (19,11) (16,13) (22,6) (19,27) (5,29) (17,27) (7,24) (3,14) (20,22) (26,18) (13,24) (16,0) (25,0) (9,1) (15,23) (2,1) (5,12) (21,25) (13,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1004", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (15,10) (2,9) (17,19) (14,3) (19,18) (15,2) (20,7) (22,16) (13,12) (12,23) (20,14) (9,21) (11,6) (24,11) (4,0) (4,17) (16,11) (0,13) (17,25) (10,19) (1,0) (2,5) (2,11) (7,25) (1,3) (8,19) (2,0) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1865", "image": "data/cycle/graph_visual/hard/graph1865.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (30,0) (5,7) (25,10) (28,7) (27,16) (17,20) (23,17) (0,27) (14,8) (0,12) (6,19) (33,12) (32,31) (20,10) (22,33) (7,19) (24,28) (16,17) (22,13) (3,7) (28,14) (9,26) (28,9) (18,11) (17,15) (0,1) (13,11) (15,26) (1,32) (32,29) (4,20) (32,2) (29,21) (2,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph30", "image": "data/cycle/graph_visual/hard/graph30.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (22,15) (15,0) (11,1) (22,1) (21,1) (23,25) (3,17) (21,10) (16,24) (24,21) (0,2) (14,7) (7,4) (20,23) (4,12) (4,19) (6,24) (1,4) (7,17) (12,8) (3,5) (18,4) (13,3) (9,4) (23,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph564", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (19,23) (18,8) (11,1) (24,9) (21,16) (15,2) (0,25) (19,9) (21,10) (23,29) (13,27) (25,30) (15,3) (7,0) (0,14) (12,14) (9,27) (9,0) (8,7) (28,26) (22,17) (4,21) (9,5) (13,15) (4,30) (26,10) (6,13) (20,22) (7,11) (7,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1701", "image": "data/cycle/graph_visual/hard/graph1701.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (14,24) (26,28) (32,19) (0,3) (29,15) (31,26) (0,6) (4,0) (29,26) (20,14) (12,7) (22,20) (23,16) (15,11) (13,25) (10,2) (3,9) (7,21) (3,1) (14,29) (18,22) (2,0) (16,22) (17,21) (1,0) (31,5) (25,17) (14,30) (22,13) (9,23) (5,0) (27,19) (8,15) (32,5) (4,13) (10,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph114", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (15,7) (24,6) (4,9) (23,22) (21,25) (22,16) (17,3) (11,1) (15,0) (19,4) (24,18) (3,5) (21,10) (12,4) (8,12) (7,4) (2,0) (21,1) (13,3) (20,4) (14,26) (23,17) (14,23) (4,1) (17,7) (1,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph615", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (24,18) (7,5) (19,28) (9,3) (10,23) (12,6) (4,26) (26,5) (0,23) (23,4) (27,23) (18,15) (17,27) (22,4) (2,8) (16,24) (29,0) (21,9) (14,1) (31,20) (18,23) (2,13) (0,30) (11,28) (1,20) (6,29) (5,3) (13,26) (28,2) (27,25) (14,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1585", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (7,1) (8,11) (0,14) (17,2) (25,20) (30,27) (21,27) (9,4) (2,16) (26,23) (14,2) (21,18) (6,9) (2,0) (10,29) (2,26) (26,9) (15,8) (24,2) (0,1) (29,5) (29,27) (19,1) (22,6) (14,3) (15,12) (19,23) (20,9) (12,23) (7,21) (30,28) (21,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph153", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (15,1) (13,9) (2,10) (4,9) (24,3) (22,18) (10,4) (8,21) (25,19) (1,23) (11,20) (16,17) (16,24) (13,8) (25,22) (18,24) (24,5) (4,6) (7,23) (20,8) (11,26) (25,23) (12,10) (11,3) (14,18) (17,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1140", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (11,22) (20,11) (1,25) (0,1) (3,10) (5,16) (23,13) (21,18) (15,1) (5,7) (6,0) (21,7) (10,14) (4,19) (11,8) (17,0) (16,9) (4,22) (3,23) (26,7) (6,2) (12,25) (3,0) (0,2) (8,24) (14,22) (7,11) (8,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1069", "image": "data/cycle/graph_visual/hard/graph1069.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (14,10) (21,15) (20,10) (20,0) (10,8) (23,11) (11,2) (2,12) (14,12) (16,0) (25,22) (6,25) (1,0) (17,25) (13,9) (0,2) (3,5) (5,24) (22,16) (15,11) (10,9) (19,0) (10,5) (22,18) (15,1) (17,4) (6,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph181", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (6,10) (18,5) (21,1) (25,17) (7,10) (16,13) (1,8) (14,23) (16,25) (17,3) (14,4) (5,22) (23,2) (2,3) (24,15) (11,22) (3,24) (8,14) (14,9) (0,4) (20,21) (11,13) (12,23) (19,12) (26,7) (6,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1110", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (13,1) (11,0) (0,1) (20,1) (9,23) (11,8) (14,15) (25,20) (21,19) (24,11) (15,6) (22,24) (26,18) (13,10) (4,18) (9,16) (2,17) (12,1) (6,12) (15,23) (26,0) (7,1) (17,21) (26,5) (2,25) (25,22) (3,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1637", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (3,10) (26,31) (13,0) (8,14) (0,1) (2,0) (10,2) (9,5) (29,11) (4,29) (20,22) (8,30) (3,21) (17,9) (24,10) (30,6) (23,27) (3,25) (8,22) (13,1) (20,25) (18,8) (3,16) (28,29) (15,22) (26,5) (28,12) (21,17) (12,14) (2,1) (16,19) (14,23) (7,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1180", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (2,22) (2,16) (21,9) (20,26) (12,5) (24,17) (6,13) (9,23) (2,0) (7,26) (21,15) (12,3) (22,1) (10,5) (22,19) (5,6) (5,21) (0,1) (0,24) (4,18) (11,6) (14,25) (4,25) (22,24) (3,0) (23,20) (0,14) (23,14) (18,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph991", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (20,19) (6,5) (4,5) (17,24) (14,8) (11,33) (29,9) (34,22) (28,23) (15,1) (6,7) (21,6) (29,20) (5,12) (0,31) (31,18) (19,8) (13,1) (7,27) (5,19) (19,24) (10,21) (2,23) (5,30) (10,25) (21,34) (11,26) (33,16) (32,5) (31,2) (12,2) (0,1) (16,19) (3,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph576", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (24,18) (9,4) (27,16) (15,20) (13,14) (22,30) (28,22) (10,29) (4,2) (25,19) (17,2) (11,24) (14,9) (7,17) (3,5) (17,25) (5,29) (3,14) (15,16) (20,19) (18,6) (27,1) (25,28) (6,5) (12,14) (25,26) (8,27) (21,16) (0,14) (23,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph758", "image": "data/cycle/graph_visual/hard/graph758.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (4,18) (26,1) (16,20) (13,16) (9,1) (19,5) (12,6) (4,13) (24,25) (4,8) (11,28) (15,11) (28,30) (19,21) (23,17) (10,14) (14,6) (31,24) (30,0) (11,32) (6,29) (8,3) (21,1) (3,23) (22,13) (13,12) (13,11) (26,7) (9,24) (2,0) (8,24) (27,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1878", "image": "data/cycle/graph_visual/hard/graph1878.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (15,8) (31,1) (22,18) (9,15) (14,13) (20,21) (7,20) (4,5) (11,24) (5,7) (12,10) (16,31) (14,12) (13,30) (27,12) (6,12) (1,17) (3,20) (16,30) (5,12) (26,11) (0,1) (0,25) (18,30) (9,32) (17,0) (2,16) (15,23) (12,33) (32,4) (11,21) (28,32) (29,24) (19,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph336", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (8,11) (24,14) (13,9) (21,7) (6,15) (19,28) (4,23) (26,9) (1,4) (14,18) (8,9) (5,2) (28,18) (17,2) (22,25) (22,3) (20,11) (15,27) (25,26) (21,28) (16,20) (15,8) (11,2) (6,0) (12,18) (17,23) (1,21) (10,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph251", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (11,10) (25,1) (9,3) (26,0) (8,2) (12,7) (21,16) (15,9) (10,6) (7,4) (17,4) (8,24) (19,22) (23,27) (6,26) (15,5) (8,0) (3,14) (16,0) (7,19) (18,17) (21,20) (15,26) (6,13) (5,25) (27,25) (20,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1722", "image": "data/cycle/graph_visual/hard/graph1722.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (11,6) (16,2) (0,4) (4,21) (0,2) (14,31) (26,28) (7,20) (8,24) (9,12) (0,25) (18,1) (3,18) (29,8) (1,27) (4,13) (15,14) (3,0) (17,9) (28,27) (8,11) (20,27) (10,14) (5,16) (30,27) (23,31) (16,8) (22,16) (9,5) (22,14) (1,0) (0,17) (11,19) (13,18) (27,23) (32,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph701", "image": "data/cycle/graph_visual/hard/graph701.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (20,16) (11,15) (11,13) (13,12) (21,1) (28,30) (29,6) (12,6) (13,16) (26,1) (21,19) (3,8) (27,15) (19,5) (4,13) (9,24) (24,31) (18,4) (32,11) (8,24) (3,23) (7,26) (24,25) (28,11) (0,2) (17,23) (30,0) (14,10) (13,22) (14,6) (4,8) (9,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph399", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (27,10) (6,9) (11,14) (13,7) (16,21) (3,26) (21,19) (4,3) (0,26) (11,13) (27,14) (0,12) (26,19) (1,17) (8,5) (22,8) (24,13) (25,11) (0,17) (9,20) (13,9) (15,18) (17,8) (5,2) (23,13) (28,25) (15,11) (0,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1281", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (25,12) (10,12) (9,2) (23,10) (1,0) (12,22) (17,24) (23,4) (17,15) (6,1) (27,24) (17,13) (9,5) (26,7) (12,16) (0,3) (23,11) (23,14) (6,9) (23,13) (27,19) (2,11) (4,3) (0,2) (20,21) (16,26) (2,8) (15,21) (5,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph331", "image": "data/cycle/graph_visual/hard/graph331.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (20,22) (9,24) (21,10) (21,16) (12,14) (18,8) (21,4) (23,4) (13,6) (20,7) (25,9) (15,3) (26,27) (26,10) (15,2) (7,11) (9,19) (13,27) (13,15) (9,0) (5,9) (14,0) (7,0) (23,19) (0,28) (7,8) (11,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph28", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (23,14) (7,3) (16,17) (12,14) (1,2) (11,5) (7,25) (24,15) (15,22) (18,15) (21,20) (0,14) (20,0) (6,10) (19,12) (6,16) (7,4) (1,13) (2,4) (6,18) (12,6) (8,12) (22,11) (25,12) (9,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph322", "image": "data/cycle/graph_visual/hard/graph322.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (4,2) (14,12) (24,16) (27,8) (24,10) (27,21) (27,1) (3,5) (5,26) (2,17) (16,15) (9,14) (3,14) (6,18) (18,22) (6,5) (11,14) (0,14) (17,25) (17,7) (4,9) (28,25) (20,19) (25,19) (27,28) (15,20) (23,25) (13,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph227", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (20,22) (6,17) (26,27) (14,3) (2,11) (10,21) (2,18) (2,26) (20,9) (16,21) (21,27) (2,15) (15,8) (4,9) (19,23) (12,13) (26,9) (7,21) (8,5) (14,0) (14,2) (12,23) (9,6) (7,1) (24,23) (27,25) (1,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph729", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (24,20) (16,17) (19,7) (18,26) (14,15) (22,13) (2,24) (8,1) (31,23) (17,23) (28,14) (9,6) (30,28) (19,21) (26,17) (5,21) (32,0) (28,2) (10,31) (13,12) (4,28) (31,3) (21,18) (30,8) (6,16) (3,12) (29,9) (27,5) (24,0) (17,0) (28,25) (24,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1916", "image": "data/cycle/graph_visual/hard/graph1916.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (4,8) (26,13) (23,24) (28,16) (2,31) (5,6) (31,4) (2,5) (21,9) (19,6) (20,17) (1,16) (30,6) (25,15) (31,7) (18,3) (22,18) (11,28) (26,15) (29,10) (1,33) (8,18) (13,9) (20,29) (1,0) (32,27) (4,25) (0,7) (8,34) (22,32) (24,17) (28,24) (8,12) (20,14) (7,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph761", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (1,29) (20,6) (25,6) (7,5) (8,28) (15,31) (7,31) (16,4) (24,10) (24,13) (23,17) (0,30) (20,1) (12,6) (28,31) (0,24) (1,27) (8,2) (14,28) (1,14) (21,0) (27,13) (14,17) (18,24) (22,28) (1,26) (31,32) (3,4) (16,1) (9,30) (19,27) (11,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1538", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (3,24) (18,12) (12,19) (0,17) (23,15) (26,8) (11,10) (1,0) (30,22) (9,18) (19,1) (30,29) (12,16) (8,30) (5,2) (0,21) (0,3) (23,17) (20,13) (13,2) (8,10) (16,14) (25,28) (4,11) (27,30) (17,6) (25,1) (29,0) (14,7) (13,21) (15,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1465", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (17,7) (16,4) (1,29) (23,25) (14,25) (3,24) (18,21) (26,5) (1,28) (17,9) (8,13) (21,20) (1,0) (24,22) (17,28) (18,12) (2,26) (21,19) (26,27) (10,1) (2,18) (20,10) (15,16) (25,8) (16,25) (18,6) (2,0) (5,15) (25,11) (3,18) (13,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph180", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (0,16) (13,18) (15,25) (19,5) (8,24) (26,13) (12,9) (20,16) (17,2) (2,9) (8,17) (17,11) (2,18) (23,21) (14,0) (11,23) (8,7) (7,5) (22,20) (10,25) (1,0) (3,10) (1,4) (6,25) (15,26) (20,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1348", "image": "data/cycle/graph_visual/hard/graph1348.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (6,18) (1,10) (24,6) (26,21) (28,27) (7,20) (27,25) (9,25) (12,9) (15,3) (13,23) (7,6) (0,1) (8,17) (2,4) (22,19) (4,25) (4,5) (16,17) (21,3) (0,17) (17,11) (24,22) (20,15) (16,14) (16,24) (10,22) (17,27) (13,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1008", "image": "data/cycle/graph_visual/hard/graph1008.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,9) (9,18) (0,3) (1,19) (4,8) (0,10) (14,10) (2,0) (0,1) (20,1) (2,19) (5,8) (25,21) (20,23) (8,25) (22,3) (9,23) (11,8) (13,9) (13,6) (2,12) (0,15) (24,25) (2,4) (16,2) (15,17) (15,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph655", "image": "data/cycle/graph_visual/hard/graph655.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (22,28) (26,19) (24,22) (13,17) (20,5) (14,12) (13,31) (25,5) (5,0) (19,24) (29,7) (21,11) (28,5) (11,27) (16,13) (30,21) (24,11) (28,6) (23,13) (3,25) (8,29) (15,31) (15,10) (4,29) (18,24) (12,23) (24,23) (27,29) (16,9) (11,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1312", "image": "data/cycle/graph_visual/hard/graph1312.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (17,25) (4,17) (23,18) (12,28) (16,7) (2,0) (28,22) (2,17) (10,20) (25,15) (1,15) (23,26) (12,21) (7,14) (6,24) (23,6) (28,17) (8,15) (19,2) (4,0) (11,15) (19,14) (1,6) (9,5) (9,28) (1,0) (10,18) (27,14) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1621", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (0,30) (22,23) (9,0) (1,25) (25,4) (7,26) (13,17) (28,9) (20,6) (26,24) (11,13) (31,1) (16,5) (5,20) (25,19) (3,0) (10,14) (24,15) (10,15) (22,11) (0,1) (21,23) (18,23) (3,29) (24,3) (17,16) (23,12) (23,14) (10,8) (0,2) (8,28) (6,1) (2,17) (27,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph183", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (10,5) (8,20) (6,13) (7,5) (12,16) (8,23) (26,18) (12,0) (17,22) (7,11) (19,2) (7,4) (2,14) (23,13) (24,12) (1,12) (22,21) (4,24) (18,19) (3,6) (25,15) (17,2) (9,19) (15,6) (19,23) (21,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1743", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (27,29) (0,4) (18,2) (0,2) (7,27) (12,29) (8,6) (26,3) (32,23) (31,1) (30,9) (4,23) (19,21) (23,13) (21,17) (23,24) (14,5) (3,0) (15,0) (31,5) (32,16) (20,22) (6,16) (30,6) (10,22) (10,2) (1,0) (19,30) (27,15) (17,20) (1,9) (9,28) (14,25) (25,26) (4,11) (24,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1528", "image": "data/cycle/graph_visual/hard/graph1528.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (2,0) (3,24) (24,27) (26,28) (13,10) (30,18) (21,22) (14,19) (2,1) (10,21) (0,19) (2,10) (7,0) (29,27) (6,28) (6,9) (15,22) (4,23) (20,2) (18,2) (7,4) (4,8) (8,16) (11,17) (19,12) (18,4) (0,1) (5,14) (22,9) (5,27) (27,11) (13,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph858", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (19,27) (16,31) (15,29) (31,29) (9,6) (12,29) (33,3) (32,17) (25,3) (27,7) (5,9) (7,24) (26,6) (17,11) (30,8) (14,6) (9,28) (10,6) (13,23) (32,10) (27,21) (1,18) (4,3) (25,22) (18,2) (4,24) (20,23) (24,8) (2,0) (32,31) (23,11) (24,11) (32,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1420", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (7,20) (6,11) (26,12) (2,11) (3,0) (29,16) (29,17) (24,11) (27,14) (5,2) (1,3) (16,23) (11,25) (21,19) (10,15) (0,5) (1,0) (18,27) (2,9) (28,19) (19,8) (4,0) (22,9) (0,13) (25,7) (12,13) (29,10) (0,2) (15,2) (20,14) (4,17) (27,3) (19,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1142", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (10,5) (6,11) (16,8) (10,7) (0,22) (0,1) (5,14) (3,11) (3,4) (16,21) (12,3) (5,9) (19,0) (18,25) (16,2) (19,25) (3,14) (14,24) (8,10) (16,22) (1,19) (23,8) (17,6) (15,9) (16,26) (20,14) (25,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph597", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (21,6) (16,24) (4,2) (5,2) (0,14) (17,20) (19,9) (13,0) (14,23) (15,19) (0,2) (8,1) (29,5) (7,0) (18,26) (26,29) (26,28) (19,16) (19,26) (6,8) (17,3) (25,29) (20,4) (25,10) (1,12) (22,12) (12,20) (7,27) (9,11) (30,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1498", "image": "data/cycle/graph_visual/hard/graph1498.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,9) (15,23) (24,12) (7,27) (1,0) (14,9) (21,2) (12,23) (24,29) (27,28) (7,8) (21,27) (23,18) (1,19) (2,0) (4,0) (21,14) (20,6) (19,2) (29,28) (7,11) (10,16) (13,8) (16,8) (8,3) (0,3) (3,26) (0,5) (4,22) (14,20) (24,5) (25,12) (9,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1837", "image": "data/cycle/graph_visual/hard/graph1837.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (24,8) (4,13) (18,23) (32,33) (7,19) (0,3) (28,31) (11,15) (9,24) (0,30) (8,3) (16,13) (23,13) (13,12) (24,11) (9,1) (5,33) (3,25) (33,13) (15,29) (26,24) (6,30) (21,16) (26,10) (21,20) (27,1) (17,14) (0,2) (4,19) (4,8) (0,1) (12,6) (22,1) (6,14) (11,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1848", "image": "data/cycle/graph_visual/hard/graph1848.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (24,14) (25,3) (18,5) (15,21) (30,27) (19,33) (13,11) (25,4) (10,33) (4,24) (7,17) (0,20) (27,6) (2,0) (31,19) (1,23) (16,12) (17,15) (1,15) (8,19) (10,26) (16,8) (13,3) (6,17) (32,8) (0,1) (1,25) (2,18) (22,4) (22,29) (9,1) (7,31) (0,33) (28,25) (5,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph110", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (13,22) (19,0) (22,15) (2,7) (1,22) (11,25) (24,2) (9,0) (5,14) (19,5) (17,21) (18,20) (14,12) (5,17) (7,8) (23,13) (7,4) (20,11) (10,19) (23,3) (21,23) (26,1) (6,4) (10,25) (1,8) (16,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1488", "image": "data/cycle/graph_visual/hard/graph1488.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (6,23) (0,2) (22,18) (13,22) (20,0) (17,11) (10,7) (0,22) (2,25) (16,19) (11,9) (14,7) (1,2) (27,10) (25,7) (21,19) (14,29) (0,3) (0,1) (23,21) (5,11) (9,23) (4,19) (4,0) (19,3) (22,26) (15,17) (12,4) (28,12) (22,24) (8,5) (4,20) (22,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph53", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (2,20) (12,5) (11,7) (23,14) (23,1) (10,17) (16,15) (6,19) (17,19) (16,14) (24,12) (25,23) (0,13) (21,1) (14,3) (10,0) (10,2) (21,11) (4,8) (22,5) (5,4) (14,22) (19,22) (19,18) (8,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1009", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (6,19) (0,2) (0,4) (19,8) (2,11) (16,23) (10,23) (15,21) (25,11) (9,17) (8,9) (5,7) (3,2) (6,22) (20,13) (5,13) (14,25) (12,25) (0,1) (2,4) (20,12) (24,23) (11,16) (19,1) (3,0) (21,18) (21,5) (1,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph51", "image": "data/cycle/graph_visual/hard/graph51.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,21) (17,7) (16,23) (10,5) (25,18) (0,3) (12,18) (24,9) (5,24) (9,22) (22,6) (0,15) (13,1) (22,20) (7,13) (4,17) (7,3) (19,18) (14,9) (20,12) (12,11) (5,3) (2,16) (22,16) (3,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph389", "image": "data/cycle/graph_visual/hard/graph389.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,2) (1,7) (21,17) (13,1) (26,11) (22,24) (11,3) (1,12) (20,25) (15,23) (24,28) (25,22) (5,26) (11,0) (9,23) (11,8) (20,1) (21,19) (24,0) (15,6) (14,15) (18,26) (25,2) (6,12) (18,4) (24,27) (13,10) (16,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1197", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (25,14) (1,3) (13,18) (17,12) (15,13) (13,21) (18,14) (24,17) (23,16) (20,26) (2,19) (5,2) (25,3) (25,9) (16,10) (0,1) (11,7) (4,1) (14,26) (10,17) (25,11) (25,17) (22,26) (10,8) (0,2) (6,5) (0,21) (14,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph832", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (16,30) (1,29) (24,17) (7,27) (27,15) (29,17) (29,2) (13,25) (4,11) (23,26) (26,13) (29,5) (3,16) (21,14) (11,32) (18,32) (7,33) (9,12) (20,7) (23,22) (24,10) (11,9) (0,9) (14,19) (8,22) (25,6) (19,13) (7,10) (22,12) (29,25) (21,31) (5,28) (13,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1570", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (7,24) (13,1) (18,26) (16,25) (22,5) (6,9) (25,1) (28,3) (3,15) (26,17) (15,2) (16,11) (4,0) (15,10) (15,13) (26,14) (27,18) (0,1) (5,8) (17,9) (2,30) (29,24) (29,6) (4,26) (12,9) (23,21) (4,3) (8,21) (19,5) (25,20) (5,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1029", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (21,7) (3,14) (21,4) (20,2) (2,17) (6,22) (20,9) (2,14) (23,19) (25,10) (9,6) (18,21) (11,8) (21,13) (1,0) (0,2) (1,7) (12,23) (15,8) (10,4) (15,12) (23,9) (0,14) (5,9) (16,2) (2,24) (19,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1958", "image": "data/cycle/graph_visual/hard/graph1958.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (12,26) (5,8) (31,27) (18,33) (30,5) (14,7) (5,21) (2,0) (12,4) (20,25) (1,25) (33,32) (24,3) (0,1) (31,23) (29,9) (5,33) (28,12) (5,22) (23,24) (29,11) (3,0) (2,17) (16,24) (6,11) (21,11) (2,25) (0,34) (30,20) (16,15) (0,17) (34,19) (9,13) (15,10) (24,13) (8,14) (13,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph341", "image": "data/cycle/graph_visual/hard/graph341.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (14,24) (11,5) (20,22) (1,2) (7,3) (4,9) (4,17) (16,6) (13,1) (7,25) (19,16) (26,12) (20,0) (10,6) (26,27) (21,12) (18,6) (23,15) (15,25) (0,14) (18,15) (22,11) (7,4) (28,2) (12,14) (12,2) (8,12) (28,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph840", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (31,10) (2,24) (3,12) (19,7) (32,23) (16,17) (21,33) (18,26) (21,5) (24,11) (30,9) (28,25) (3,31) (24,0) (5,27) (13,12) (21,19) (13,22) (28,2) (0,33) (6,9) (16,6) (29,18) (20,24) (26,17) (0,17) (8,30) (8,1) (4,28) (31,28) (23,17) (14,15) (28,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1022", "image": "data/cycle/graph_visual/hard/graph1022.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (2,4) (0,2) (18,6) (13,0) (14,0) (15,19) (5,19) (14,22) (10,25) (16,25) (24,7) (3,17) (0,7) (8,1) (4,20) (2,5) (12,21) (16,19) (6,8) (17,20) (19,9) (0,1) (23,16) (11,9) (1,12) (20,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph673", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (4,2) (11,17) (9,15) (10,26) (8,23) (23,1) (30,20) (31,19) (3,19) (19,30) (22,10) (16,6) (26,1) (29,28) (24,7) (12,28) (24,8) (1,0) (29,25) (14,18) (16,15) (20,13) (0,13) (27,7) (31,6) (23,4) (13,29) (27,5) (18,8) (4,21) (29,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph303", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (21,0) (22,2) (12,13) (0,3) (4,11) (11,16) (19,7) (5,9) (17,26) (15,22) (1,24) (0,27) (16,12) (19,14) (6,8) (24,18) (15,28) (14,8) (10,28) (9,18) (9,13) (28,14) (23,4) (0,25) (26,7) (23,6) (20,2) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph919", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (3,4) (3,25) (27,7) (20,23) (29,31) (24,4) (5,9) (27,19) (22,25) (28,9) (10,32) (7,24) (6,9) (32,1) (23,13) (32,17) (29,15) (29,12) (11,23) (8,24) (0,2) (3,33) (8,30) (26,6) (6,10) (11,24) (34,3) (17,11) (27,21) (2,18) (32,31) (6,14) (1,18) (16,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1334", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (20,7) (19,9) (16,21) (6,13) (0,2) (0,14) (4,23) (12,14) (0,1) (18,8) (28,0) (15,3) (9,5) (22,20) (13,27) (9,24) (19,23) (21,10) (11,7) (7,0) (2,15) (10,26) (21,4) (27,26) (25,9) (7,8) (15,13) (1,11) (22,17) (0,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph732", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (3,25) (28,7) (6,31) (20,11) (32,10) (13,8) (8,1) (22,17) (1,23) (4,2) (20,21) (15,13) (9,29) (3,20) (24,12) (3,8) (30,32) (16,7) (3,26) (14,21) (17,28) (9,19) (2,15) (6,26) (16,20) (0,29) (19,10) (12,29) (18,5) (22,18) (14,9) (27,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1756", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (7,19) (9,6) (2,14) (18,24) (19,32) (27,12) (12,32) (2,23) (29,14) (24,14) (24,17) (5,14) (27,20) (22,20) (30,3) (21,25) (16,2) (0,29) (11,5) (9,11) (0,3) (22,13) (32,26) (25,16) (2,0) (24,3) (0,28) (31,27) (5,1) (5,8) (4,12) (15,30) (19,10) (5,32) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1331", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (4,0) (28,25) (16,21) (2,5) (13,7) (19,21) (11,25) (3,4) (17,0) (5,8) (2,0) (3,26) (14,27) (0,26) (14,11) (20,9) (0,12) (23,0) (13,24) (17,8) (27,10) (15,11) (9,6) (3,0) (1,17) (0,1) (8,22) (13,23) (13,9) (13,11) (19,26) (18,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph884", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (1,25) (0,16) (16,17) (29,8) (12,3) (22,8) (9,20) (32,24) (1,22) (26,33) (32,18) (29,23) (27,20) (31,10) (22,2) (20,4) (6,28) (28,27) (9,12) (0,11) (10,2) (9,13) (12,14) (12,5) (7,32) (1,15) (33,15) (12,24) (30,23) (3,19) (1,6) (32,21) (5,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph811", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (32,14) (4,12) (23,26) (29,17) (28,13) (0,9) (0,24) (23,18) (21,10) (30,19) (15,24) (31,1) (5,25) (9,11) (17,6) (14,22) (16,0) (28,9) (10,23) (20,17) (3,32) (27,33) (4,32) (12,29) (30,2) (27,5) (7,33) (5,14) (25,21) (30,21) (13,3) (3,1) (8,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1409", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (25,6) (21,0) (5,10) (2,0) (12,25) (22,2) (5,26) (17,9) (29,8) (16,22) (11,2) (19,22) (11,24) (0,28) (12,14) (29,20) (18,25) (15,1) (11,15) (14,10) (28,16) (0,27) (10,13) (17,4) (20,10) (6,7) (20,2) (23,15) (3,5) (9,10) (1,0) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1377", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (25,24) (5,13) (3,28) (20,3) (16,21) (14,26) (9,22) (12,6) (22,2) (2,17) (0,1) (27,14) (0,14) (0,24) (0,2) (5,6) (6,15) (4,25) (9,23) (19,4) (5,21) (21,22) (10,18) (22,1) (26,8) (23,20) (24,18) (27,23) (11,5) (7,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph193", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (8,21) (4,18) (10,9) (7,3) (15,6) (16,11) (21,0) (10,24) (18,17) (9,16) (19,4) (26,8) (13,10) (2,1) (12,6) (3,25) (16,14) (23,8) (20,3) (19,8) (5,16) (13,22) (11,12) (25,1) (9,26) (3,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1902", "image": "data/cycle/graph_visual/hard/graph1902.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (15,28) (9,23) (23,17) (10,3) (4,34) (13,2) (8,29) (31,8) (5,27) (7,23) (6,4) (30,22) (20,15) (0,3) (27,12) (1,4) (0,12) (20,7) (8,6) (16,26) (28,21) (25,16) (32,34) (1,3) (0,4) (12,11) (1,0) (30,4) (2,1) (33,34) (14,17) (18,1) (6,11) (24,19) (0,2) (34,26) (15,34) (11,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1948", "image": "data/cycle/graph_visual/hard/graph1948.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,28) (2,0) (19,33) (29,14) (18,23) (24,0) (15,27) (30,27) (4,0) (28,6) (23,2) (33,23) (23,13) (8,12) (31,5) (21,8) (13,3) (0,14) (5,6) (5,7) (27,22) (24,16) (25,1) (20,22) (3,0) (1,32) (29,26) (0,1) (13,11) (4,18) (11,32) (2,31) (12,17) (34,18) (1,26) (1,9) (22,3) (19,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1114", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (16,15) (0,17) (10,0) (13,22) (0,1) (11,26) (26,19) (2,5) (14,11) (14,25) (4,3) (13,7) (19,20) (18,9) (0,2) (15,11) (1,17) (6,9) (8,21) (8,5) (23,0) (8,17) (9,13) (3,0) (11,13) (3,26) (12,21) (13,23) (24,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1454", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (29,23) (25,19) (18,25) (21,8) (26,17) (22,21) (13,1) (26,12) (29,15) (24,5) (3,27) (8,5) (25,14) (26,18) (0,1) (9,17) (15,7) (11,9) (26,4) (20,5) (24,1) (0,4) (0,2) (15,3) (3,4) (13,15) (2,24) (6,9) (5,16) (6,28) (16,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1313", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (24,17) (21,24) (4,0) (16,5) (24,4) (1,23) (6,2) (9,13) (13,23) (17,11) (7,23) (0,2) (6,8) (16,19) (25,28) (27,6) (22,27) (22,13) (3,0) (14,4) (10,19) (15,18) (19,21) (6,25) (21,3) (13,20) (1,0) (1,12) (1,15) (23,0) (7,26) (5,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph483", "image": "data/cycle/graph_visual/hard/graph483.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (26,14) (29,6) (17,20) (25,1) (26,6) (17,4) (28,15) (3,18) (3,9) (21,16) (0,16) (25,5) (15,5) (15,9) (20,21) (6,10) (10,11) (0,26) (8,2) (0,8) (25,26) (13,6) (7,19) (17,22) (19,23) (7,4) (7,12) (27,24) (8,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph77", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (24,9) (9,21) (2,11) (0,11) (3,25) (4,8) (16,0) (10,12) (7,6) (0,3) (20,17) (11,20) (2,21) (7,12) (18,25) (1,6) (0,13) (8,21) (8,19) (5,22) (6,14) (5,0) (22,23) (18,15) (12,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1815", "image": "data/cycle/graph_visual/hard/graph1815.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (5,32) (5,8) (6,11) (30,20) (21,5) (25,1) (25,20) (14,7) (26,13) (31,33) (24,16) (11,21) (9,13) (12,27) (29,11) (17,0) (22,31) (12,26) (23,24) (23,28) (0,1) (0,33) (9,29) (24,13) (30,5) (2,25) (16,15) (18,33) (14,8) (12,4) (15,10) (24,3) (2,17) (5,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1353", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (13,1) (16,4) (22,9) (4,9) (16,6) (14,16) (18,11) (11,15) (25,12) (28,7) (3,19) (25,19) (5,24) (13,10) (2,12) (17,15) (4,24) (2,0) (23,15) (27,0) (26,21) (1,8) (27,9) (28,18) (1,0) (8,25) (3,24) (6,26) (20,12) (8,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1961", "image": "data/cycle/graph_visual/hard/graph1961.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (21,7) (16,24) (29,18) (10,2) (12,15) (5,31) (4,13) (0,33) (28,19) (27,13) (16,22) (25,17) (26,30) (0,1) (11,1) (23,17) (25,14) (13,22) (26,31) (0,6) (20,14) (29,5) (3,9) (32,14) (7,15) (29,14) (26,33) (21,22) (29,34) (15,10) (8,2) (32,19) (9,23) (22,20) (3,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph636", "image": "data/cycle/graph_visual/hard/graph636.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (25,8) (28,20) (27,1) (11,5) (4,19) (28,21) (23,21) (31,2) (6,13) (16,22) (8,9) (24,10) (1,29) (21,18) (11,3) (18,30) (22,29) (10,21) (12,18) (25,18) (7,20) (11,21) (4,25) (14,1) (15,31) (31,20) (26,0) (20,13) (17,22) (0,5) (9,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1988", "image": "data/cycle/graph_visual/hard/graph1988.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (28,16) (33,8) (32,3) (1,14) (26,25) (15,7) (30,14) (20,7) (30,5) (28,31) (24,19) (13,18) (23,4) (17,2) (10,32) (0,1) (34,20) (26,19) (13,4) (22,4) (29,3) (23,7) (11,20) (27,17) (31,15) (33,12) (18,33) (30,27) (20,3) (19,33) (11,9) (21,18) (34,6) (0,10) (17,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1093", "image": "data/cycle/graph_visual/hard/graph1093.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (10,23) (9,8) (25,12) (22,6) (4,2) (0,2) (11,2) (5,13) (21,15) (11,16) (0,3) (25,14) (19,6) (19,8) (25,11) (23,16) (13,20) (5,21) (23,24) (1,0) (1,19) (18,21) (18,1) (0,5) (17,9) (7,5) (0,4) (2,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1566", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (19,12) (13,5) (22,18) (3,6) (1,0) (7,23) (19,26) (2,26) (21,4) (22,27) (7,17) (2,30) (11,24) (11,10) (25,0) (20,15) (11,19) (13,15) (2,4) (8,14) (9,5) (11,22) (0,3) (29,22) (0,2) (16,7) (3,23) (26,15) (0,6) (23,15) (1,4) (28,9) (14,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph986", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (19,11) (34,22) (16,22) (27,1) (13,18) (22,7) (33,23) (5,9) (8,25) (9,12) (11,8) (24,13) (23,27) (16,8) (34,4) (17,9) (11,6) (2,16) (3,18) (16,5) (1,18) (14,15) (10,14) (27,20) (30,8) (20,7) (0,26) (14,31) (31,27) (4,21) (28,27) (32,14) (28,29) (0,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1963", "image": "data/cycle/graph_visual/hard/graph1963.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (14,8) (28,32) (0,6) (2,3) (33,16) (34,22) (33,31) (18,34) (20,9) (26,25) (2,31) (0,1) (12,11) (13,29) (0,5) (24,29) (9,2) (23,19) (2,27) (14,21) (30,9) (31,4) (21,25) (30,8) (1,18) (0,15) (10,20) (34,12) (29,2) (32,18) (17,31) (7,33) (33,6) (12,15) (23,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1368", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (4,14) (16,7) (20,24) (27,9) (2,0) (9,18) (19,9) (21,0) (23,14) (2,24) (1,0) (9,7) (7,10) (3,11) (10,2) (1,11) (9,6) (6,8) (12,5) (7,15) (0,4) (26,13) (14,15) (12,13) (5,0) (1,17) (26,22) (25,17) (3,0) (25,10) (21,28) (27,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1562", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (5,17) (29,0) (2,0) (4,9) (15,13) (17,26) (7,1) (20,14) (17,8) (15,12) (11,19) (30,27) (0,1) (27,20) (16,18) (24,8) (18,2) (19,0) (22,6) (15,22) (6,7) (12,20) (17,28) (11,4) (10,29) (15,17) (3,18) (26,29) (25,7) (26,21) (2,19) (23,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph148", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (14,3) (10,6) (21,9) (26,2) (20,24) (26,22) (1,16) (12,16) (14,21) (17,8) (15,26) (15,12) (10,0) (26,21) (0,19) (0,17) (9,10) (23,11) (19,24) (4,14) (18,5) (7,9) (25,23) (11,7) (5,4) (17,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph577", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (15,29) (22,24) (11,0) (2,25) (20,25) (11,28) (3,11) (12,1) (23,9) (10,13) (1,20) (22,27) (18,26) (26,6) (17,2) (8,11) (0,24) (23,15) (16,9) (24,29) (5,26) (25,30) (18,4) (17,21) (21,19) (12,6) (13,1) (14,15) (24,25) (1,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1024", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (0,13) (10,15) (14,6) (18,2) (6,16) (15,2) (13,8) (14,3) (14,5) (0,1) (11,25) (16,21) (8,1) (5,19) (0,24) (20,9) (4,3) (9,18) (23,24) (11,13) (16,7) (15,12) (12,16) (0,3) (18,17) (22,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1704", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (27,16) (0,32) (31,19) (9,14) (11,1) (13,16) (10,25) (18,4) (20,0) (25,32) (0,12) (27,22) (13,2) (12,8) (21,23) (1,7) (1,18) (15,11) (29,27) (3,16) (30,6) (14,22) (17,19) (0,23) (1,0) (4,17) (24,5) (29,4) (27,26) (24,6) (6,25) (28,22) (16,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1324", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (8,20) (8,2) (0,25) (3,10) (19,7) (6,2) (1,23) (16,11) (18,6) (24,4) (22,16) (0,2) (0,1) (9,25) (5,16) (11,26) (13,4) (0,26) (19,6) (8,12) (24,17) (26,14) (10,0) (28,4) (21,16) (6,16) (1,19) (27,22) (15,26) (14,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1891", "image": "data/cycle/graph_visual/hard/graph1891.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (26,18) (0,2) (0,20) (7,29) (3,17) (13,21) (11,3) (15,5) (24,26) (27,23) (25,32) (3,25) (3,31) (27,3) (23,6) (4,12) (32,20) (4,28) (9,26) (14,2) (25,10) (15,4) (19,33) (27,5) (5,22) (14,30) (2,13) (4,0) (1,9) (7,9) (3,14) (6,16) (2,8) (0,1) (19,7) (0,3) (8,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1856", "image": "data/cycle/graph_visual/hard/graph1856.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (15,17) (24,14) (10,26) (1,15) (19,8) (0,33) (12,16) (5,29) (1,9) (16,8) (1,23) (7,31) (33,10) (17,6) (28,25) (15,21) (32,8) (24,4) (4,25) (3,13) (22,4) (18,5) (1,25) (30,27) (3,25) (0,20) (19,33) (22,29) (19,31) (11,13) (1,0) (7,17) (6,27) (18,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1936", "image": "data/cycle/graph_visual/hard/graph1936.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (9,21) (1,0) (29,20) (31,22) (5,18) (34,7) (19,11) (0,28) (5,32) (24,14) (6,22) (26,16) (30,23) (19,24) (21,8) (17,22) (15,22) (1,9) (4,18) (1,20) (4,28) (14,13) (0,27) (29,25) (17,16) (8,12) (3,11) (15,33) (14,23) (23,10) (2,4) (23,31) (26,1) (14,32) (31,34)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1576", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (27,22) (18,26) (25,30) (6,26) (13,1) (14,15) (7,1) (25,2) (2,17) (12,6) (25,24) (0,1) (16,9) (29,24) (11,3) (21,17) (0,24) (29,15) (11,0) (5,26) (15,23) (11,28) (10,13) (24,22) (4,18) (8,11) (19,21) (12,1) (1,20) (20,25) (23,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph676", "image": "data/cycle/graph_visual/hard/graph676.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (19,20) (4,23) (9,11) (26,1) (30,26) (12,7) (27,6) (24,4) (25,31) (6,17) (16,20) (22,12) (29,7) (16,14) (13,6) (5,25) (22,8) (0,2) (25,27) (2,7) (18,17) (6,4) (20,21) (15,26) (18,10) (9,16) (19,1) (6,1) (12,28) (12,3) (29,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph898", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (20,13) (6,27) (15,14) (16,5) (25,4) (14,21) (9,18) (2,17) (32,0) (11,5) (6,12) (28,33) (22,23) (29,27) (14,20) (10,21) (19,6) (0,14) (9,22) (20,22) (3,23) (24,12) (1,31) (26,21) (17,27) (4,21) (21,17) (31,27) (5,30) (15,7) (5,4) (12,28) (30,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1786", "image": "data/cycle/graph_visual/hard/graph1786.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (1,4) (12,26) (23,27) (0,1) (11,25) (5,15) (16,11) (21,16) (20,21) (20,18) (1,27) (19,25) (19,28) (0,8) (2,15) (3,24) (12,11) (30,7) (11,22) (3,20) (19,32) (10,7) (32,9) (6,28) (14,5) (14,17) (13,22) (3,7) (1,16) (29,26) (17,3) (8,11) (9,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1052", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (18,20) (10,1) (22,15) (19,5) (4,6) (13,22) (12,14) (9,0) (20,11) (24,2) (25,11) (14,5) (8,1) (16,3) (2,7) (19,10) (1,0) (4,7) (3,23) (5,17) (8,7) (21,17) (21,23) (22,25) (0,19) (13,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1169", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (9,6) (0,1) (0,5) (24,5) (15,22) (1,16) (13,2) (17,21) (22,18) (11,14) (22,3) (3,0) (2,0) (10,25) (4,0) (19,17) (7,0) (12,26) (20,10) (8,13) (7,12) (16,8) (4,25) (5,9) (21,8) (16,25) (24,23) (11,9) (26,20) (23,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph988", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (25,17) (29,3) (14,9) (30,5) (0,27) (10,29) (32,34) (22,13) (17,21) (4,26) (5,2) (16,6) (5,25) (8,0) (33,4) (19,21) (4,23) (13,19) (16,26) (8,21) (5,20) (15,9) (22,11) (9,32) (26,30) (1,0) (8,7) (21,18) (12,4) (14,28) (24,10) (31,29) (9,1) (3,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1749", "image": "data/cycle/graph_visual/hard/graph1749.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (28,12) (2,5) (3,4) (16,32) (30,23) (2,12) (31,15) (13,28) (18,32) (29,8) (14,18) (20,28) (10,0) (30,10) (32,22) (21,11) (4,0) (29,1) (1,15) (7,28) (20,29) (12,14) (9,5) (24,11) (12,17) (26,19) (3,2) (6,11) (28,6) (1,0) (27,25) (28,25) (9,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1477", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (0,13) (22,13) (15,22) (29,3) (19,6) (0,2) (10,17) (1,0) (12,27) (17,7) (16,5) (9,4) (0,6) (14,20) (5,26) (23,8) (14,24) (26,4) (19,11) (13,7) (6,28) (6,24) (3,2) (20,21) (3,1) (23,6) (7,2) (4,19) (4,25) (4,18) (12,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph269", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (6,2) (3,11) (13,22) (27,2) (3,26) (10,11) (7,10) (27,1) (8,11) (2,17) (15,14) (0,15) (18,2) (4,11) (21,17) (6,7) (9,20) (20,10) (24,15) (23,21) (7,12) (24,4) (5,8) (26,25) (19,17) (10,16) (7,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1274", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (22,25) (9,27) (26,6) (14,25) (24,19) (8,23) (13,9) (23,7) (8,14) (0,2) (11,12) (6,15) (19,13) (0,1) (5,6) (1,17) (16,6) (4,6) (20,14) (0,3) (12,21) (25,18) (6,1) (18,3) (15,27) (15,0) (9,11) (10,20) (18,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph151", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (15,25) (12,24) (8,20) (7,5) (23,19) (7,4) (19,9) (2,17) (17,22) (10,5) (6,15) (16,21) (21,22) (6,3) (26,18) (1,12) (14,2) (12,16) (11,7) (19,2) (23,13) (0,12) (4,24) (23,8) (13,6) (18,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph589", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (26,5) (15,30) (13,11) (2,0) (14,10) (15,3) (9,1) (3,2) (29,21) (12,8) (1,20) (16,30) (8,29) (15,13) (19,22) (6,20) (28,23) (25,21) (6,24) (5,1) (3,21) (3,5) (14,5) (14,28) (9,27) (17,19) (18,13) (7,13) (24,4) (19,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1622", "image": "data/cycle/graph_visual/hard/graph1622.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (29,21) (9,0) (24,6) (20,1) (19,22) (19,11) (10,15) (31,29) (15,17) (2,21) (5,30) (1,12) (28,2) (4,0) (29,3) (9,18) (15,31) (9,4) (14,10) (26,23) (0,2) (5,23) (25,30) (3,5) (6,16) (28,8) (0,1) (12,7) (7,31) (16,31) (3,0) (13,22) (24,27) (11,26) (22,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph706", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (15,32) (4,1) (32,23) (4,27) (8,4) (31,20) (6,19) (32,24) (9,30) (10,16) (21,31) (22,14) (20,0) (27,12) (27,28) (21,6) (7,32) (10,30) (10,8) (29,31) (26,13) (17,9) (11,12) (21,18) (8,2) (13,1) (19,5) (3,8) (14,13) (15,6) (25,9) (18,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph740", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (12,30) (13,30) (16,13) (30,27) (10,18) (31,21) (8,26) (9,1) (11,18) (26,6) (17,32) (22,27) (26,27) (28,26) (15,19) (7,23) (20,0) (10,3) (32,11) (5,9) (4,9) (15,0) (1,23) (29,14) (2,21) (5,32) (28,2) (0,23) (14,25) (7,31) (4,24) (2,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph802", "image": "data/cycle/graph_visual/hard/graph802.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,5) (4,8) (24,17) (19,30) (11,28) (16,32) (8,1) (11,25) (25,16) (3,32) (21,11) (11,9) (21,31) (6,23) (2,33) (18,2) (6,7) (12,6) (23,30) (0,8) (22,23) (17,26) (10,7) (32,10) (23,24) (1,14) (15,12) (5,0) (33,19) (9,27) (29,25) (13,31) (12,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph708", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (29,8) (23,21) (30,5) (22,24) (3,27) (26,2) (12,17) (16,18) (32,28) (23,19) (4,15) (2,1) (20,4) (11,19) (29,16) (10,2) (0,13) (2,25) (11,31) (31,9) (6,0) (23,8) (10,13) (24,26) (28,15) (30,22) (18,26) (20,17) (27,8) (15,29) (31,14) (29,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph778", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (19,32) (17,5) (23,30) (29,21) (20,23) (5,0) (23,6) (11,9) (32,3) (19,30) (24,23) (8,1) (8,4) (2,18) (12,15) (28,25) (27,11) (17,24) (10,7) (25,16) (14,1) (11,25) (11,21) (12,6) (22,17) (9,26) (7,6) (31,13) (0,8) (2,12) (16,32) (10,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1301", "image": "data/cycle/graph_visual/hard/graph1301.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (26,12) (1,2) (18,6) (14,24) (5,11) (11,22) (2,0) (12,21) (8,12) (1,13) (10,6) (26,27) (15,18) (0,14) (4,17) (16,19) (1,0) (12,14) (3,0) (15,23) (16,6) (25,15) (4,7) (2,28) (4,9) (20,22) (7,25) (3,7) (20,0) (2,12) (28,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph545", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (8,12) (7,21) (26,21) (22,16) (9,17) (19,9) (18,13) (27,24) (20,23) (17,8) (0,18) (22,24) (10,29) (5,6) (14,0) (15,28) (12,1) (12,11) (29,4) (2,10) (5,28) (12,27) (7,3) (28,4) (4,23) (23,30) (18,25) (14,30) (7,24) (26,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1997", "image": "data/cycle/graph_visual/hard/graph1997.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (32,8) (29,28) (25,17) (11,29) (6,20) (4,34) (29,10) (27,24) (31,10) (22,31) (7,27) (5,20) (24,34) (26,1) (16,5) (22,15) (17,16) (18,6) (14,30) (12,30) (31,21) (2,13) (32,2) (19,3) (28,0) (8,12) (0,1) (23,22) (17,26) (1,19) (19,9) (4,3) (9,12) (33,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1770", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (17,30) (32,12) (2,31) (18,25) (24,0) (22,23) (12,13) (21,19) (1,22) (8,13) (24,19) (1,0) (3,30) (4,0) (32,17) (26,0) (20,2) (23,0) (12,29) (3,0) (25,10) (14,18) (32,11) (16,12) (31,8) (2,5) (22,6) (11,25) (10,28) (7,26) (27,12) (4,31) (3,9) (15,4) (0,2) (21,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1762", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (30,28) (29,11) (25,28) (5,32) (29,23) (20,16) (2,24) (23,14) (16,7) (21,12) (26,10) (9,28) (27,17) (18,3) (8,22) (30,32) (27,7) (28,13) (23,22) (31,14) (10,8) (14,25) (26,0) (4,19) (0,1) (8,7) (2,16) (6,14) (18,14) (15,21) (30,12) (1,18) (29,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1547", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (28,20) (4,7) (15,14) (0,13) (1,0) (7,8) (10,1) (29,5) (18,3) (20,22) (14,5) (16,22) (11,25) (30,8) (2,0) (17,28) (3,23) (0,19) (29,23) (29,30) (2,7) (24,11) (17,21) (2,26) (27,1) (10,19) (23,21) (4,12) (9,29) (19,5) (30,6) (28,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1438", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (18,22) (22,3) (19,17) (5,9) (26,23) (1,0) (7,0) (2,13) (11,14) (6,9) (16,28) (24,0) (2,0) (5,24) (20,10) (22,15) (8,27) (20,27) (21,8) (4,25) (7,12) (8,13) (29,27) (12,26) (3,29) (25,16) (21,17) (10,25) (1,16) (9,11) (13,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1767", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (5,2) (23,29) (15,8) (25,13) (10,12) (17,26) (32,6) (23,3) (29,21) (24,30) (1,14) (28,31) (24,7) (16,7) (16,6) (32,15) (11,2) (31,14) (14,0) (25,12) (17,1) (31,5) (20,1) (31,22) (8,18) (19,13) (8,9) (5,25) (1,0) (0,2) (30,26) (27,24) (12,29) (4,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1877", "image": "data/cycle/graph_visual/hard/graph1877.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (29,15) (16,2) (8,15) (26,24) (2,0) (28,23) (30,0) (0,25) (5,32) (2,30) (16,13) (24,17) (0,4) (12,1) (10,30) (17,25) (1,0) (16,29) (33,3) (11,31) (28,10) (20,21) (15,4) (33,18) (22,19) (12,32) (25,14) (27,7) (11,22) (6,10) (1,7) (0,3) (1,28) (19,23) (14,9) (21,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1208", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (14,26) (9,7) (15,21) (24,21) (4,0) (3,0) (22,27) (2,14) (6,20) (6,19) (8,11) (25,14) (23,8) (18,3) (1,4) (1,0) (20,13) (20,1) (2,0) (16,0) (1,10) (0,26) (9,21) (17,6) (18,4) (5,16) (23,16) (4,23) (22,19) (7,12) (24,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph342", "image": "data/cycle/graph_visual/hard/graph342.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (6,15) (21,12) (18,2) (5,6) (17,1) (22,25) (19,13) (18,26) (14,25) (8,24) (10,20) (14,20) (23,28) (3,18) (15,28) (23,7) (9,13) (6,4) (11,9) (1,6) (16,6) (8,14) (11,12) (27,9) (3,0) (6,27) (0,15) (25,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph318", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (1,4) (21,9) (20,1) (13,7) (14,25) (27,23) (0,26) (8,11) (2,14) (11,22) (18,6) (6,28) (12,1) (20,6) (19,4) (21,17) (10,16) (28,8) (0,16) (4,23) (28,5) (15,20) (24,23) (14,26) (21,24) (18,3) (28,16) (7,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph430", "image": "data/cycle/graph_visual/hard/graph430.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,7) (20,15) (2,10) (0,12) (27,4) (25,13) (21,16) (20,8) (29,28) (6,1) (0,27) (3,11) (22,13) (9,24) (18,6) (22,7) (17,23) (18,24) (16,9) (29,1) (6,26) (19,2) (17,5) (24,0) (17,29) (20,10) (8,18) (11,19) (15,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph704", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (15,31) (2,7) (3,30) (6,20) (31,0) (31,2) (18,12) (25,23) (27,12) (22,21) (8,0) (5,30) (11,4) (8,26) (23,0) (5,21) (14,15) (21,7) (29,18) (32,20) (16,1) (9,13) (13,4) (7,10) (28,10) (32,1) (1,28) (17,2) (3,24) (19,9) (6,19) (12,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph510", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (17,0) (29,30) (10,11) (17,23) (14,16) (18,12) (0,3) (28,25) (19,12) (16,12) (23,15) (21,0) (3,24) (11,4) (8,30) (27,30) (18,9) (7,14) (6,17) (10,8) (8,26) (13,2) (0,29) (13,20) (13,21) (1,25) (15,25) (19,1) (2,5) (30,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph725", "image": "data/cycle/graph_visual/hard/graph725.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (20,30) (25,29) (23,4) (3,19) (4,2) (16,6) (23,8) (27,5) (19,30) (8,24) (28,7) (26,10) (0,1) (0,13) (8,18) (31,6) (15,9) (11,29) (12,28) (27,1) (10,22) (19,32) (17,11) (4,21) (31,29) (29,13) (20,13) (23,1) (18,14) (15,16) (32,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph932", "image": "data/cycle/graph_visual/hard/graph932.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (26,9) (14,3) (13,21) (2,8) (3,31) (3,11) (22,5) (6,17) (9,1) (3,25) (29,7) (23,27) (15,5) (6,23) (3,27) (25,32) (10,25) (30,14) (0,20) (15,4) (14,2) (32,20) (4,28) (5,27) (12,4) (7,33) (13,2) (18,26) (34,9) (7,34) (19,3) (34,16) (26,24) (8,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1267", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (1,4) (13,1) (5,24) (0,6) (21,26) (2,10) (9,13) (0,1) (11,23) (25,20) (26,14) (13,27) (11,1) (23,7) (19,15) (3,18) (0,2) (15,10) (6,14) (3,0) (12,15) (25,16) (7,2) (22,8) (18,0) (17,18) (16,15) (5,1) (27,26) (20,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph554", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (22,14) (24,5) (17,8) (7,27) (23,16) (29,24) (24,12) (14,21) (20,6) (19,23) (30,11) (9,14) (3,8) (21,27) (12,26) (3,29) (28,27) (10,16) (20,2) (23,9) (12,25) (7,13) (3,0) (21,2) (9,18) (7,8) (22,4) (28,30) (15,8) (1,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1384", "image": "data/cycle/graph_visual/hard/graph1384.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,15) (5,1) (0,2) (21,23) (5,0) (8,19) (14,26) (24,4) (14,5) (5,3) (4,0) (20,1) (13,7) (15,13) (8,28) (13,11) (25,9) (9,1) (20,6) (18,19) (21,3) (19,16) (24,5) (0,3) (28,15) (14,10) (27,21) (2,3) (12,8) (1,0) (6,22) (17,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph67", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (6,2) (13,6) (1,15) (13,20) (0,23) (17,10) (17,15) (13,23) (22,25) (24,7) (23,1) (22,13) (11,1) (21,3) (16,5) (16,19) (14,24) (19,9) (21,18) (21,19) (20,5) (6,8) (12,4) (23,7) (4,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph928", "image": "data/cycle/graph_visual/hard/graph928.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (26,10) (17,20) (28,19) (17,33) (32,27) (1,16) (21,30) (18,2) (32,4) (14,1) (15,18) (0,23) (13,14) (32,7) (25,20) (7,10) (18,21) (4,6) (3,26) (22,29) (6,0) (24,25) (7,14) (22,4) (20,6) (5,33) (24,19) (9,7) (10,31) (24,11) (2,34) (11,12) (6,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1405", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (2,17) (24,25) (2,4) (3,5) (23,18) (13,14) (20,15) (6,18) (1,0) (14,3) (12,14) (0,14) (25,28) (16,26) (29,10) (1,27) (22,27) (24,11) (15,16) (28,29) (3,0) (25,19) (0,2) (25,17) (9,14) (21,16) (19,20) (9,4) (8,27) (7,17) (5,6) (5,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1448", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (21,26) (3,16) (13,6) (1,0) (20,14) (27,11) (18,5) (1,19) (23,13) (10,11) (22,8) (9,23) (23,19) (15,24) (9,15) (12,18) (22,10) (28,8) (24,18) (5,21) (2,11) (3,2) (29,12) (11,14) (1,25) (19,10) (22,17) (0,20) (24,7) (13,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph346", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (22,5) (22,19) (5,4) (28,13) (16,14) (2,10) (11,7) (3,14) (27,12) (12,5) (17,10) (21,15) (18,0) (27,11) (14,23) (6,19) (22,14) (23,13) (20,16) (17,19) (8,4) (9,8) (0,10) (1,23) (19,24) (28,21) (25,2) (26,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1755", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (23,2) (5,16) (28,0) (13,2) (6,11) (22,29) (4,21) (10,16) (19,30) (0,3) (12,10) (13,20) (15,5) (9,18) (18,0) (11,10) (20,21) (2,0) (20,10) (4,19) (7,24) (28,26) (13,8) (32,4) (1,10) (9,17) (31,23) (31,25) (19,27) (3,24) (0,1) (5,29) (14,12) (1,7) (31,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph854", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (17,26) (1,19) (25,17) (27,24) (5,20) (30,8) (2,32) (29,10) (19,3) (33,4) (22,23) (14,30) (22,15) (32,31) (8,12) (28,12) (1,26) (31,10) (16,5) (22,31) (9,12) (29,24) (7,27) (29,1) (17,16) (4,3) (0,28) (20,6) (13,2) (11,29) (9,19) (31,21) (18,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1765", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (32,9) (3,20) (0,25) (20,21) (15,8) (16,30) (7,19) (0,1) (16,2) (21,11) (32,28) (15,23) (0,17) (10,12) (12,6) (5,4) (15,9) (30,13) (20,7) (7,5) (4,12) (27,12) (14,13) (29,24) (31,16) (26,11) (31,1) (32,5) (1,17) (14,12) (24,11) (18,22) (30,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph538", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (18,8) (25,10) (19,24) (29,3) (28,11) (13,17) (30,16) (14,3) (0,11) (6,28) (17,22) (2,26) (15,26) (26,7) (12,8) (8,0) (24,12) (28,3) (29,22) (16,15) (28,10) (22,27) (17,20) (2,24) (5,6) (23,4) (10,21) (9,26) (4,1) (20,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1509", "image": "data/cycle/graph_visual/hard/graph1509.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (17,29) (16,9) (7,3) (0,14) (29,30) (8,18) (24,18) (25,17) (6,18) (27,6) (22,13) (24,9) (24,0) (30,4) (21,15) (26,13) (22,7) (16,23) (11,3) (1,29) (19,2) (20,10) (19,11) (17,12) (0,28) (1,6) (0,1) (15,20) (27,5) (2,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph474", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (18,6) (16,9) (29,1) (8,20) (19,2) (0,24) (6,1) (2,10) (28,29) (13,25) (24,18) (24,9) (13,22) (17,29) (19,11) (21,16) (17,5) (3,7) (23,17) (18,8) (20,15) (0,27) (15,14) (4,27) (6,26) (3,11) (7,22) (20,10) (0,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph352", "image": "data/cycle/graph_visual/hard/graph352.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (11,10) (8,24) (3,9) (28,26) (3,14) (0,26) (19,7) (22,19) (17,20) (0,16) (6,26) (0,8) (16,21) (20,21) (18,17) (4,17) (12,7) (5,15) (15,27) (25,1) (26,25) (9,15) (8,2) (25,5) (23,27) (6,13) (10,6) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph672", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (11,15) (9,6) (16,30) (28,22) (15,31) (16,19) (3,26) (14,21) (28,3) (31,6) (4,12) (18,7) (5,4) (8,16) (27,5) (17,2) (25,15) (25,23) (26,27) (9,14) (8,21) (10,12) (4,13) (23,20) (29,4) (0,30) (16,17) (22,0) (30,1) (21,18) (24,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph264", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (1,2) (6,26) (14,0) (27,2) (3,7) (17,4) (8,12) (12,2) (15,23) (14,12) (6,18) (11,22) (15,18) (6,10) (19,16) (25,7) (13,1) (4,7) (20,22) (26,12) (16,6) (9,4) (11,5) (24,14) (0,20) (21,12) (25,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1106", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (25,10) (23,19) (26,24) (11,7) (18,20) (9,5) (0,7) (23,4) (13,21) (1,11) (15,2) (8,7) (0,14) (15,3) (10,21) (13,15) (9,22) (1,0) (20,7) (9,26) (13,6) (8,17) (16,22) (2,0) (14,12) (4,21) (9,19) (9,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph798", "image": "data/cycle/graph_visual/hard/graph798.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (14,2) (8,32) (4,23) (10,1) (5,16) (32,22) (26,19) (7,3) (17,8) (21,22) (5,24) (6,13) (10,3) (12,13) (9,20) (28,29) (30,15) (10,18) (32,7) (30,27) (25,17) (0,26) (20,28) (2,1) (31,20) (20,1) (22,15) (21,16) (20,23) (11,25) (30,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1866", "image": "data/cycle/graph_visual/hard/graph1866.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (20,1) (33,1) (2,8) (17,23) (4,3) (0,24) (6,20) (28,22) (27,13) (31,15) (8,28) (1,29) (28,31) (26,1) (32,14) (11,13) (5,7) (0,30) (33,31) (0,1) (30,9) (21,0) (1,16) (4,16) (6,12) (13,24) (24,18) (1,27) (14,28) (7,31) (27,19) (17,14) (24,10) (6,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1021", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (25,9) (1,23) (19,3) (10,15) (2,3) (5,0) (11,24) (2,24) (25,6) (13,23) (21,18) (17,20) (22,5) (4,10) (13,14) (20,10) (18,14) (7,21) (13,0) (18,15) (1,0) (12,4) (16,8) (6,13) (8,21) (3,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1922", "image": "data/cycle/graph_visual/hard/graph1922.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (16,11) (1,16) (29,19) (7,31) (27,3) (27,24) (25,11) (21,16) (28,6) (3,18) (33,3) (19,25) (1,28) (1,0) (22,13) (4,1) (32,9) (21,20) (8,0) (2,0) (17,34) (15,2) (14,5) (30,26) (3,20) (11,23) (26,12) (7,10) (14,17) (5,15) (33,7) (32,19) (8,11) (11,12) (17,9) (20,22) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph25", "image": "data/cycle/graph_visual/hard/graph25.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (8,23) (21,12) (20,10) (13,19) (12,11) (7,23) (20,14) (3,0) (9,18) (5,6) (16,6) (14,8) (11,9) (13,9) (24,19) (2,18) (22,25) (3,18) (6,1) (6,4) (6,15) (17,1) (25,6) (14,25) (0,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph610", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (25,24) (8,27) (16,17) (19,9) (27,4) (2,30) (15,5) (6,20) (29,1) (22,20) (23,1) (29,10) (3,31) (8,12) (13,22) (21,31) (11,2) (17,26) (7,29) (14,6) (3,19) (10,30) (16,5) (12,26) (31,18) (0,28) (19,1) (24,29) (9,12) (17,22) (28,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph230", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (21,1) (11,2) (19,9) (21,18) (7,27) (27,9) (16,7) (13,5) (20,1) (3,6) (11,17) (14,23) (14,4) (17,16) (16,12) (24,23) (13,25) (10,3) (4,8) (10,24) (0,2) (25,8) (1,23) (1,15) (19,26) (17,20) (24,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph57", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (0,15) (7,19) (17,18) (0,8) (25,5) (9,3) (24,6) (15,5) (21,16) (11,10) (4,7) (2,8) (19,22) (25,6) (16,0) (8,23) (14,3) (10,6) (6,13) (15,9) (1,25) (20,21) (17,20) (17,4) (7,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph35", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (12,1) (8,5) (25,21) (24,7) (2,6) (16,12) (21,18) (4,19) (16,22) (22,3) (13,14) (24,15) (19,5) (4,22) (0,11) (0,17) (0,10) (10,13) (23,4) (20,14) (14,5) (7,3) (10,21) (9,20) (6,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1959", "image": "data/cycle/graph_visual/hard/graph1959.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (4,0) (3,2) (15,13) (8,17) (24,9) (10,25) (7,5) (8,22) (21,25) (26,13) (19,34) (14,8) (33,21) (1,7) (7,18) (25,1) (0,1) (21,31) (9,2) (6,7) (30,5) (26,29) (34,13) (14,34) (32,12) (16,2) (13,12) (9,11) (0,30) (20,14) (28,33) (8,3) (23,15) (28,27) (23,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph785", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (16,26) (0,16) (16,24) (29,23) (15,10) (32,21) (12,15) (11,15) (31,8) (3,28) (10,28) (14,11) (20,7) (12,6) (18,22) (13,31) (31,12) (12,25) (13,19) (16,19) (23,32) (15,5) (30,17) (20,11) (12,30) (7,2) (9,31) (0,21) (1,11) (21,4) (27,7) (18,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1657", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (16,31) (31,10) (24,7) (11,17) (9,27) (24,11) (1,18) (27,20) (1,0) (3,0) (15,29) (6,25) (23,19) (5,9) (14,6) (3,30) (3,4) (6,10) (3,23) (31,3) (4,24) (27,1) (2,18) (28,8) (29,12) (29,17) (13,23) (2,0) (9,6) (7,26) (24,8) (22,11) (25,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1109", "image": "data/cycle/graph_visual/hard/graph1109.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (10,25) (7,20) (9,22) (5,9) (13,15) (18,20) (4,23) (24,26) (7,11) (15,2) (17,8) (4,21) (0,7) (0,14) (13,21) (9,19) (12,14) (19,23) (9,26) (7,8) (21,10) (1,0) (3,15) (1,11) (13,6) (9,0) (22,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph952", "image": "data/cycle/graph_visual/hard/graph952.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (18,30) (8,20) (3,16) (24,12) (26,1) (8,17) (10,1) (28,19) (20,21) (25,5) (14,26) (13,32) (26,22) (0,9) (12,2) (21,28) (34,12) (13,23) (5,27) (16,4) (5,12) (6,4) (6,7) (20,9) (15,13) (30,31) (26,20) (10,11) (33,29) (6,5) (27,21) (33,6) (2,15) (25,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1560", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (25,15) (11,28) (6,1) (12,24) (9,8) (17,25) (18,23) (14,4) (14,7) (27,28) (16,15) (0,2) (6,28) (23,6) (0,29) (15,9) (0,1) (17,5) (14,17) (20,12) (15,1) (7,21) (14,19) (13,30) (2,19) (22,10) (4,3) (29,26) (12,28) (2,30) (10,18) (23,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph44", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (2,24) (4,0) (15,3) (25,12) (6,24) (5,14) (13,15) (11,9) (3,4) (8,5) (13,1) (25,16) (10,16) (15,25) (21,8) (17,4) (18,3) (7,15) (5,24) (9,6) (5,19) (17,9) (20,21) (22,1) (23,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph329", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (5,6) (26,0) (19,23) (20,24) (7,24) (0,18) (10,12) (12,8) (18,22) (4,14) (14,0) (11,18) (28,5) (1,12) (15,22) (4,27) (27,12) (9,16) (13,28) (9,17) (23,4) (21,26) (28,23) (3,7) (21,7) (17,8) (25,24) (2,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1141", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (9,17) (6,18) (8,4) (25,15) (6,24) (15,0) (9,5) (1,12) (20,25) (7,2) (1,13) (6,19) (14,1) (9,11) (3,14) (2,26) (15,6) (1,0) (2,22) (17,25) (4,13) (1,23) (4,11) (21,5) (12,10) (20,26) (20,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph765", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (26,5) (29,20) (0,11) (7,3) (26,14) (4,24) (5,22) (32,8) (9,23) (29,1) (5,32) (8,16) (31,4) (27,10) (15,3) (29,28) (2,21) (11,17) (27,28) (25,10) (32,19) (24,2) (13,14) (8,7) (15,10) (6,24) (10,30) (17,12) (18,13) (23,21) (18,6) (21,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph179", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (15,18) (9,6) (7,20) (14,15) (2,21) (25,20) (13,25) (8,7) (10,1) (22,2) (25,23) (10,14) (9,18) (23,26) (12,4) (4,5) (13,0) (12,1) (5,21) (17,25) (3,9) (19,25) (11,4) (8,16) (24,0) (1,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1459", "image": "data/cycle/graph_visual/hard/graph1459.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (6,14) (26,17) (27,24) (0,1) (4,19) (12,14) (19,11) (8,22) (0,16) (15,1) (23,2) (29,5) (28,23) (0,2) (11,23) (0,13) (16,8) (24,17) (24,7) (9,3) (3,0) (1,9) (27,15) (15,25) (18,21) (12,29) (4,17) (20,10) (6,21) (26,10) (24,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph520", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (14,21) (6,20) (10,16) (27,21) (14,9) (22,14) (1,19) (16,23) (8,7) (22,4) (3,29) (9,23) (12,25) (8,17) (15,8) (30,11) (12,24) (13,7) (24,29) (5,24) (19,23) (27,7) (30,28) (26,12) (3,0) (8,3) (2,20) (9,18) (21,2) (28,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1873", "image": "data/cycle/graph_visual/hard/graph1873.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,1) (25,14) (0,3) (25,17) (2,10) (0,4) (21,22) (26,30) (23,9) (22,16) (18,29) (24,16) (0,33) (14,20) (1,11) (5,31) (32,14) (4,13) (29,26) (13,27) (23,17) (15,12) (19,32) (31,26) (14,29) (28,19) (10,15) (3,9) (1,3) (8,2) (13,22) (21,7) (0,6) (33,5) (20,22) (15,7) (0,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph653", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (9,15) (23,8) (7,29) (11,5) (21,3) (8,19) (14,11) (10,19) (22,7) (0,6) (7,10) (1,25) (14,12) (2,12) (0,21) (21,29) (11,24) (26,30) (20,26) (28,12) (11,31) (3,9) (4,21) (28,25) (27,20) (29,16) (18,14) (8,17) (28,15) (27,8) (13,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1092", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (7,17) (16,11) (21,3) (8,15) (8,2) (0,2) (7,24) (14,20) (14,25) (23,22) (19,22) (12,13) (6,21) (4,14) (4,10) (16,5) (11,9) (12,0) (21,19) (15,11) (25,18) (0,17) (0,21) (1,15) (0,1) (4,19) (20,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1705", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (1,0) (12,11) (7,10) (21,3) (24,8) (22,31) (9,22) (7,9) (0,27) (6,21) (21,16) (0,12) (29,4) (15,27) (32,7) (14,7) (25,23) (27,28) (6,29) (30,18) (9,1) (13,32) (17,15) (12,30) (28,24) (26,2) (19,16) (8,1) (5,11) (20,28) (30,2) (3,5) (23,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1881", "image": "data/cycle/graph_visual/hard/graph1881.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (24,7) (30,4) (3,0) (11,9) (6,5) (0,31) (7,4) (26,14) (18,29) (10,19) (2,7) (12,5) (0,1) (21,13) (10,6) (23,25) (13,25) (21,18) (15,22) (4,31) (30,13) (3,10) (0,4) (27,10) (9,16) (3,4) (22,23) (7,17) (20,2) (0,2) (32,5) (18,28) (7,8) (33,5) (14,30) (11,25) (1,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1444", "image": "data/cycle/graph_visual/hard/graph1444.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (21,23) (14,24) (4,13) (5,19) (2,0) (1,0) (12,0) (22,3) (28,8) (4,22) (5,9) (4,29) (18,0) (5,14) (2,6) (24,16) (16,15) (10,6) (27,0) (13,14) (21,13) (20,11) (10,21) (28,10) (19,27) (3,7) (7,26) (22,17) (20,10) (1,12) (4,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph411", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (26,12) (23,16) (15,10) (11,6) (19,28) (0,13) (1,0) (29,17) (8,19) (27,3) (29,10) (2,15) (11,24) (17,19) (7,20) (7,25) (3,1) (25,11) (20,14) (4,17) (5,2) (18,27) (2,9) (9,22) (27,14) (11,2) (21,19) (16,29) (13,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph626", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (7,19) (5,11) (27,12) (9,11) (20,22) (20,27) (9,6) (5,1) (19,24) (2,14) (23,2) (24,18) (29,0) (31,13) (14,24) (5,8) (24,3) (22,15) (0,26) (14,12) (14,28) (29,3) (17,30) (2,16) (5,27) (21,25) (4,12) (5,30) (25,16) (10,19) (14,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph997", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (21,22) (13,16) (19,23) (29,1) (13,33) (1,9) (24,8) (24,27) (6,12) (33,34) (23,1) (4,13) (11,24) (6,31) (19,7) (0,30) (8,3) (14,6) (11,28) (15,30) (18,14) (24,9) (4,20) (17,26) (13,12) (5,33) (26,3) (11,15) (0,2) (28,32) (8,4) (13,25) (34,10) (16,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph934", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (24,22) (24,11) (13,12) (29,30) (11,18) (24,8) (10,2) (26,3) (14,28) (11,20) (3,5) (26,19) (27,14) (22,32) (10,28) (20,29) (30,33) (4,29) (31,0) (2,15) (13,17) (6,5) (30,12) (21,19) (2,1) (16,3) (34,20) (23,5) (8,7) (9,25) (29,1) (19,12) (22,9) (1,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph162", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (9,22) (18,20) (11,1) (8,17) (11,7) (9,0) (25,10) (14,0) (26,24) (7,20) (7,0) (9,5) (13,21) (9,19) (21,4) (19,23) (3,15) (10,21) (13,6) (16,22) (4,23) (15,13) (15,2) (26,9) (14,12) (8,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph890", "image": "data/cycle/graph_visual/hard/graph890.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (0,30) (9,20) (5,24) (30,27) (33,7) (18,10) (16,21) (6,13) (25,11) (30,15) (20,28) (26,19) (22,21) (4,23) (7,3) (1,2) (17,25) (21,6) (13,12) (26,0) (23,20) (8,17) (2,14) (3,10) (32,8) (33,22) (32,31) (15,22) (28,29) (20,1) (5,16) (1,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1992", "image": "data/cycle/graph_visual/hard/graph1992.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (30,24) (5,3) (29,21) (31,18) (27,19) (9,20) (5,23) (11,26) (17,15) (7,6) (21,2) (28,8) (29,6) (16,31) (12,7) (19,11) (24,6) (1,0) (2,31) (22,4) (9,0) (10,14) (26,30) (15,10) (2,0) (1,12) (1,22) (0,3) (4,9) (25,31) (3,29) (23,28) (16,32) (13,22) (15,7) (34,15) (33,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph637", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (26,24) (27,16) (6,3) (13,29) (19,23) (0,5) (15,12) (7,28) (31,0) (10,0) (3,1) (15,25) (25,10) (26,4) (9,11) (4,17) (30,20) (17,14) (13,18) (23,31) (25,22) (20,10) (11,18) (24,22) (11,31) (2,21) (1,18) (5,8) (21,17) (31,7) (27,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1887", "image": "data/cycle/graph_visual/hard/graph1887.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (23,1) (3,25) (17,6) (8,19) (8,16) (25,4) (25,28) (22,29) (7,17) (15,17) (10,26) (9,1) (18,2) (14,24) (10,33) (1,25) (27,6) (15,21) (33,0) (5,18) (20,0) (7,31) (3,13) (15,1) (16,12) (4,22) (0,1) (19,33) (4,24) (8,32) (5,29) (30,27) (13,11) (19,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph401", "image": "data/cycle/graph_visual/hard/graph401.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (27,18) (2,9) (14,20) (21,19) (25,11) (7,20) (17,4) (0,1) (14,27) (19,28) (23,16) (24,11) (11,2) (2,5) (7,25) (10,29) (12,13) (17,19) (6,11) (16,29) (3,1) (29,17) (13,0) (27,3) (2,15) (22,9) (19,8) (15,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph113", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (3,14) (10,14) (5,3) (5,24) (0,14) (2,4) (8,14) (18,25) (25,22) (13,6) (11,16) (24,7) (16,15) (21,16) (20,26) (15,20) (19,23) (4,9) (20,22) (17,1) (18,12) (9,14) (17,2) (25,17) (25,19) (6,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph463", "image": "data/cycle/graph_visual/hard/graph463.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (8,9) (6,15) (8,15) (15,28) (25,24) (7,21) (19,28) (28,18) (14,25) (1,21) (1,4) (26,27) (22,11) (23,17) (14,18) (12,18) (16,20) (9,26) (23,4) (13,9) (29,20) (2,11) (20,21) (5,2) (22,3) (18,10) (6,0) (2,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph478", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (12,7) (25,24) (28,14) (13,15) (10,3) (10,16) (5,19) (20,17) (3,1) (21,24) (6,8) (9,15) (25,5) (8,28) (27,29) (8,23) (14,9) (5,27) (4,14) (2,21) (21,16) (26,6) (15,20) (28,22) (22,3) (7,6) (18,15) (10,11) (0,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1618", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (23,25) (22,19) (2,23) (15,1) (27,5) (19,20) (1,0) (9,29) (5,6) (21,10) (14,3) (31,0) (31,18) (7,11) (7,6) (24,17) (12,5) (5,19) (8,19) (2,12) (0,4) (3,0) (6,31) (0,2) (4,5) (26,20) (8,14) (10,24) (19,16) (13,1) (11,21) (29,5) (28,2) (30,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph102", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (26,10) (1,23) (25,24) (0,17) (1,14) (8,22) (21,10) (10,3) (9,7) (19,11) (13,23) (15,7) (2,5) (15,11) (4,6) (16,22) (1,16) (0,12) (6,2) (9,4) (16,20) (25,26) (15,22) (17,24) (19,0) (18,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph24", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (19,2) (22,21) (5,7) (23,19) (17,2) (12,1) (6,13) (17,22) (12,16) (24,15) (5,10) (12,20) (12,0) (15,6) (4,24) (4,7) (21,16) (3,6) (7,11) (8,18) (23,13) (9,19) (25,19) (8,23) (14,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1183", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (12,22) (19,2) (22,1) (13,24) (7,16) (6,0) (24,21) (6,7) (10,3) (4,26) (24,10) (14,9) (26,14) (19,18) (11,15) (21,18) (5,3) (14,18) (19,25) (0,2) (6,8) (1,0) (7,24) (3,0) (17,7) (11,18) (17,12) (21,20) (23,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1915", "image": "data/cycle/graph_visual/hard/graph1915.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (1,12) (29,6) (22,4) (17,15) (22,13) (11,19) (20,9) (9,0) (33,5) (10,14) (12,7) (2,21) (31,2) (1,22) (28,23) (26,30) (3,0) (16,32) (9,4) (3,29) (25,31) (29,21) (0,1) (11,26) (3,5) (16,31) (4,0) (0,2) (6,24) (31,18) (24,30) (6,7) (28,8) (7,15) (27,19) (15,34) (15,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1325", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (24,16) (20,12) (22,12) (5,26) (0,14) (8,1) (4,20) (26,19) (19,9) (20,17) (1,12) (5,2) (8,6) (25,7) (0,7) (25,10) (1,0) (3,17) (11,9) (28,16) (27,26) (15,19) (14,23) (2,4) (18,26) (13,0) (19,16) (0,2) (6,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph913", "image": "data/cycle/graph_visual/hard/graph913.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (8,4) (22,5) (10,3) (16,3) (1,12) (15,14) (30,19) (27,26) (10,13) (18,7) (23,6) (29,1) (4,29) (34,10) (25,13) (30,28) (0,13) (9,33) (15,6) (32,0) (21,24) (15,20) (34,22) (24,10) (13,33) (23,7) (0,15) (11,17) (26,17) (11,24) (8,31) (8,28) (2,16) (8,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1161", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (8,22) (4,13) (0,20) (7,24) (9,15) (22,10) (11,14) (2,3) (23,9) (2,11) (0,1) (19,1) (11,10) (17,14) (19,23) (22,16) (18,11) (20,1) (24,21) (15,26) (18,5) (21,5) (10,19) (12,23) (3,13) (8,25) (6,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1344", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (0,1) (19,6) (26,4) (27,7) (8,24) (7,12) (14,9) (10,15) (21,22) (13,21) (9,1) (25,13) (23,21) (21,18) (16,10) (28,8) (3,0) (4,14) (12,20) (4,0) (2,16) (25,12) (6,22) (20,2) (5,22) (26,19) (2,0) (3,17) (4,3) (10,24) (14,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1131", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (3,0) (13,8) (2,15) (17,11) (2,18) (24,0) (9,18) (1,0) (14,3) (16,6) (24,25) (15,10) (14,5) (12,15) (8,1) (26,17) (13,11) (14,6) (5,20) (16,12) (7,16) (3,4) (13,0) (23,8) (22,16) (18,19) (9,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph377", "image": "data/cycle/graph_visual/hard/graph377.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,25) (2,20) (6,7) (0,26) (2,11) (10,5) (23,11) (18,22) (27,16) (22,16) (12,24) (25,5) (20,28) (5,3) (9,13) (9,10) (14,10) (14,12) (1,15) (22,2) (25,6) (4,17) (21,15) (10,8) (28,0) (19,0) (11,15) (10,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1543", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (30,19) (17,25) (25,20) (2,26) (11,9) (5,9) (22,20) (4,13) (2,10) (23,6) (29,6) (8,14) (6,15) (5,27) (27,3) (0,15) (15,25) (0,1) (1,18) (12,16) (1,26) (12,1) (22,30) (14,4) (24,6) (4,11) (27,7) (13,1) (28,2) (9,17) (20,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1002", "image": "data/cycle/graph_visual/hard/graph1002.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,17) (10,25) (13,0) (25,16) (5,2) (2,4) (0,3) (20,12) (18,6) (0,14) (14,22) (19,16) (19,15) (7,0) (0,2) (16,23) (6,8) (9,11) (9,19) (12,21) (1,12) (0,1) (24,7) (1,8) (20,4) (5,19) (20,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph16", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (13,20) (7,6) (11,15) (23,17) (7,1) (5,17) (18,0) (22,15) (8,19) (15,0) (14,18) (2,16) (7,21) (10,19) (20,25) (3,18) (8,17) (15,12) (15,17) (17,24) (9,4) (20,12) (6,22) (19,2) (11,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph644", "image": "data/cycle/graph_visual/hard/graph644.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (28,1) (10,9) (17,18) (14,24) (13,4) (19,11) (1,7) (2,29) (14,23) (6,30) (24,5) (28,9) (14,28) (28,15) (21,3) (31,18) (20,22) (0,16) (13,19) (0,20) (25,19) (29,21) (24,11) (4,8) (1,27) (12,10) (18,22) (27,22) (21,11) (30,15) (26,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1408", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (8,15) (27,13) (25,6) (0,8) (26,11) (14,8) (3,25) (7,26) (24,10) (17,29) (1,16) (25,15) (23,6) (1,0) (9,2) (17,28) (2,0) (3,0) (0,24) (15,18) (18,5) (29,13) (4,21) (19,4) (15,2) (11,10) (12,24) (0,4) (22,23) (23,27) (24,21) (18,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1318", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (0,26) (15,22) (0,7) (8,4) (0,14) (13,22) (0,1) (19,0) (12,15) (20,2) (28,21) (5,23) (18,23) (27,4) (24,5) (17,27) (9,11) (28,25) (19,20) (9,24) (10,18) (12,26) (3,2) (7,1) (21,16) (14,6) (9,17) (21,10) (25,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph265", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (10,22) (15,18) (4,3) (19,27) (25,9) (6,27) (13,0) (25,13) (18,23) (10,15) (16,8) (5,24) (13,6) (8,21) (10,4) (20,17) (0,5) (13,14) (26,2) (4,12) (2,3) (24,11) (1,23) (21,7) (3,20) (18,14) (21,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1329", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (3,0) (9,25) (0,4) (19,8) (17,13) (21,27) (13,7) (20,6) (0,2) (19,16) (8,12) (0,5) (13,11) (14,5) (15,3) (1,5) (6,22) (20,1) (5,24) (14,26) (1,0) (2,3) (4,24) (14,10) (9,1) (3,21) (18,19) (28,8) (5,3) (13,15) (15,28) (21,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1042", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (22,11) (11,20) (0,17) (2,0) (9,16) (19,4) (8,12) (8,23) (6,0) (11,8) (21,7) (13,23) (0,1) (22,4) (21,18) (14,10) (3,7) (15,1) (12,24) (1,25) (0,4) (5,7) (10,3) (0,3) (14,22) (2,6) (25,11) (16,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1303", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (4,24) (2,28) (12,25) (19,4) (17,4) (3,1) (0,1) (26,4) (3,23) (13,21) (24,14) (4,8) (26,5) (9,17) (20,18) (20,14) (22,6) (13,7) (6,19) (13,0) (6,0) (10,19) (15,5) (22,11) (23,6) (16,7) (2,7) (27,6) (12,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1380", "image": "data/cycle/graph_visual/hard/graph1380.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,23) (6,7) (20,14) (27,25) (2,5) (18,1) (8,22) (5,12) (15,6) (25,16) (4,21) (5,9) (18,14) (6,25) (27,13) (3,21) (26,14) (14,10) (12,6) (26,19) (12,28) (11,24) (0,1) (25,11) (8,7) (14,21) (2,0) (26,15) (23,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph643", "image": "data/cycle/graph_visual/hard/graph643.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (27,20) (8,5) (8,16) (1,27) (4,17) (21,17) (16,10) (0,27) (0,24) (22,25) (15,23) (1,23) (14,31) (18,19) (10,29) (22,28) (17,7) (12,1) (22,13) (30,17) (19,30) (5,19) (4,31) (2,13) (7,6) (9,19) (27,11) (29,26) (11,3) (26,2) (29,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1951", "image": "data/cycle/graph_visual/hard/graph1951.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (20,34) (8,24) (27,14) (28,10) (31,0) (28,14) (29,4) (24,11) (8,7) (2,10) (13,17) (12,13) (25,9) (19,26) (5,6) (19,12) (29,20) (1,0) (30,29) (30,12) (21,19) (22,9) (32,22) (22,24) (11,18) (3,26) (5,3) (15,2) (1,29) (33,30) (1,2) (5,23) (1,31) (3,16) (11,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1245", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (15,23) (20,0) (6,18) (16,6) (22,11) (27,2) (14,24) (11,5) (4,9) (14,0) (22,20) (18,15) (4,17) (8,12) (13,1) (12,21) (6,26) (25,7) (4,7) (12,14) (26,12) (10,6) (2,1) (25,15) (2,12) (7,3) (0,1) (19,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1049", "image": "data/cycle/graph_visual/hard/graph1049.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,23) (14,24) (12,6) (10,18) (7,14) (15,9) (8,15) (25,17) (15,1) (3,14) (0,1) (6,22) (11,12) (19,2) (2,0) (14,19) (1,6) (2,17) (9,5) (15,25) (4,0) (17,4) (18,23) (13,7) (10,16) (23,21) (12,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph651", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (18,13) (29,4) (28,3) (16,21) (29,10) (1,5) (5,25) (30,26) (5,30) (4,11) (19,13) (8,0) (17,21) (20,5) (27,14) (15,26) (10,23) (22,4) (25,17) (21,8) (16,2) (22,7) (4,26) (6,8) (31,0) (20,3) (24,0) (9,29) (9,14) (19,21) (9,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph238", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (0,8) (15,18) (2,9) (2,15) (4,21) (0,24) (7,26) (6,23) (13,26) (13,27) (6,25) (5,18) (12,24) (10,24) (25,15) (14,8) (23,27) (25,3) (24,20) (22,11) (8,15) (18,19) (0,1) (4,17) (16,1) (21,23) (10,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1544", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (26,2) (27,18) (11,23) (7,8) (8,12) (7,14) (28,2) (7,16) (0,19) (6,17) (18,13) (23,28) (19,16) (0,10) (20,30) (4,15) (24,3) (17,0) (17,25) (0,1) (3,21) (20,22) (2,0) (6,22) (3,9) (20,5) (7,29) (4,23) (6,2) (21,23) (1,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1298", "image": "data/cycle/graph_visual/hard/graph1298.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,1) (16,5) (24,5) (26,4) (19,25) (10,16) (2,24) (1,13) (8,21) (23,1) (4,0) (18,26) (15,18) (4,3) (26,12) (9,17) (8,5) (21,22) (9,11) (3,27) (15,7) (3,24) (6,9) (14,25) (2,0) (20,5) (3,0) (25,6) (17,26) (13,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph317", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (10,11) (1,20) (12,23) (19,10) (28,18) (1,19) (5,18) (3,13) (14,11) (22,10) (20,0) (26,11) (2,11) (21,5) (21,25) (15,9) (23,9) (18,24) (27,8) (22,8) (22,16) (15,24) (7,24) (13,6) (14,17) (2,3) (23,19) (4,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1048", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (16,9) (19,8) (25,11) (13,20) (12,15) (13,9) (13,11) (22,13) (0,23) (0,7) (19,18) (0,1) (0,21) (9,5) (0,2) (8,17) (25,24) (3,8) (13,6) (23,14) (15,11) (1,17) (0,3) (3,4) (2,5) (0,17) (21,10) (14,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph731", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (31,16) (4,22) (12,1) (19,22) (15,31) (24,27) (3,29) (32,6) (19,11) (6,24) (23,5) (28,8) (31,5) (18,9) (14,10) (28,16) (17,15) (7,12) (2,21) (1,20) (7,31) (26,23) (6,29) (11,26) (13,22) (0,9) (10,15) (29,21) (30,25) (4,9) (5,3) (2,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph757", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (1,11) (28,23) (20,29) (10,11) (2,17) (28,22) (19,7) (23,29) (19,32) (4,5) (27,24) (0,3) (23,5) (31,15) (12,2) (13,10) (25,18) (16,8) (3,5) (1,14) (20,11) (15,14) (25,32) (17,26) (13,9) (27,10) (21,23) (2,1) (16,27) (6,10) (32,20) (30,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph468", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (19,7) (6,10) (19,23) (16,21) (25,5) (8,27) (15,28) (14,26) (20,21) (3,18) (10,11) (24,27) (15,9) (0,8) (16,0) (17,22) (4,17) (26,6) (7,4) (6,13) (8,2) (0,26) (17,20) (7,12) (25,26) (25,1) (6,29) (9,3) (15,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph863", "image": "data/cycle/graph_visual/hard/graph863.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,3) (19,7) (3,5) (25,18) (28,22) (16,27) (13,10) (23,28) (32,15) (15,14) (31,10) (20,33) (23,5) (25,32) (10,11) (29,20) (17,2) (12,2) (29,23) (17,26) (24,30) (16,8) (4,5) (10,6) (13,9) (1,14) (2,1) (19,32) (27,24) (27,33) (1,11) (21,23) (20,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1918", "image": "data/cycle/graph_visual/hard/graph1918.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (1,2) (7,27) (5,24) (7,33) (3,1) (30,25) (23,26) (9,13) (8,18) (28,34) (0,1) (3,20) (15,34) (4,29) (30,29) (0,2) (8,1) (21,32) (10,2) (31,4) (9,23) (33,18) (4,17) (11,14) (19,20) (21,14) (25,5) (25,6) (12,33) (4,0) (16,2) (34,29) (22,21) (14,27) (32,28) (30,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1728", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (28,31) (0,1) (7,31) (3,4) (24,10) (14,28) (0,21) (0,2) (24,18) (3,0) (20,6) (11,13) (30,9) (1,16) (23,17) (24,13) (7,5) (31,15) (1,20) (12,6) (27,19) (25,6) (27,1) (16,4) (27,13) (4,0) (28,8) (0,24) (1,29) (28,22) (14,17) (26,1) (31,32) (0,30) (8,2) (14,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1071", "image": "data/cycle/graph_visual/hard/graph1071.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (1,12) (6,3) (24,4) (6,15) (22,21) (4,7) (14,2) (21,16) (0,1) (2,19) (22,17) (10,5) (13,6) (23,13) (12,0) (5,7) (25,19) (11,7) (12,20) (23,19) (12,16) (8,23) (2,17) (19,9) (15,24) (18,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph609", "image": "data/cycle/graph_visual/hard/graph609.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (16,9) (20,16) (28,12) (20,19) (2,0) (12,7) (7,2) (5,25) (24,4) (17,6) (27,6) (13,6) (30,26) (26,1) (14,16) (11,9) (25,31) (23,4) (1,6) (21,20) (25,27) (7,29) (22,12) (1,19) (4,6) (22,8) (12,3) (18,10) (29,24) (18,17) (26,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph15", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (17,18) (0,22) (11,10) (0,1) (15,18) (8,12) (13,23) (25,13) (0,8) (2,7) (21,11) (25,3) (4,21) (15,8) (15,2) (23,6) (16,4) (9,24) (23,20) (1,14) (10,24) (19,24) (15,25) (6,24) (18,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1551", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (10,2) (14,0) (7,24) (22,16) (9,19) (17,8) (26,21) (9,17) (25,18) (24,27) (22,24) (30,14) (28,5) (28,15) (7,21) (28,4) (13,18) (29,4) (6,5) (29,10) (23,20) (18,0) (1,12) (30,23) (8,12) (23,4) (1,0) (3,7) (11,12) (12,27) (26,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1144", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (9,24) (2,0) (17,21) (15,23) (12,16) (3,11) (13,21) (23,1) (15,16) (4,18) (14,6) (25,8) (26,20) (5,13) (8,24) (0,1) (26,23) (2,24) (22,19) (10,2) (1,7) (22,10) (15,8) (3,0) (21,11) (21,14) (0,14) (18,21) (0,4) (22,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph555", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (9,14) (30,20) (27,12) (12,2) (1,15) (8,24) (1,9) (23,26) (13,3) (29,27) (16,20) (3,18) (18,28) (29,5) (9,18) (30,26) (25,13) (0,11) (26,10) (18,21) (19,27) (3,27) (29,6) (26,7) (24,4) (0,6) (8,1) (23,21) (22,24) (15,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1558", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (19,16) (1,0) (0,7) (3,0) (11,9) (19,9) (24,16) (6,21) (3,17) (2,5) (8,6) (29,26) (8,1) (20,12) (0,13) (26,19) (26,18) (0,14) (1,12) (25,10) (2,0) (15,19) (23,14) (20,4) (26,28) (22,12) (20,17) (25,29) (7,27) (5,29) (4,2) (30,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph743", "image": "data/cycle/graph_visual/hard/graph743.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (25,27) (20,7) (31,32) (22,19) (27,15) (11,28) (19,16) (32,15) (7,28) (9,20) (18,30) (8,32) (17,26) (4,23) (6,11) (7,23) (18,13) (30,10) (12,18) (5,30) (3,29) (19,31) (24,3) (0,10) (4,14) (21,26) (20,3) (20,17) (4,13) (1,14) (2,17) (20,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1823", "image": "data/cycle/graph_visual/hard/graph1823.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,6) (7,22) (12,1) (27,4) (3,0) (2,0) (19,18) (26,21) (3,16) (13,20) (32,10) (9,28) (17,22) (14,11) (21,6) (32,27) (4,0) (33,13) (30,5) (6,29) (16,23) (23,31) (3,24) (23,14) (9,33) (5,3) (1,8) (18,24) (15,4) (25,19) (9,0) (1,0) (19,10) (33,2) (20,24) (0,22) (1,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1100", "image": "data/cycle/graph_visual/hard/graph1100.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (15,19) (8,11) (22,10) (0,3) (21,3) (9,1) (16,0) (19,11) (4,14) (22,5) (12,13) (18,25) (11,18) (24,17) (25,20) (17,19) (12,26) (2,0) (22,15) (3,14) (9,21) (2,1) (0,4) (14,19) (1,0) (6,24) (24,13) (4,7) (16,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1243", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (22,4) (3,0) (23,15) (3,8) (23,18) (27,21) (14,21) (24,3) (8,7) (21,2) (25,12) (7,11) (13,8) (9,14) (23,12) (26,27) (24,12) (19,2) (7,27) (6,20) (9,17) (20,14) (16,10) (16,8) (5,24) (1,0) (22,9) (19,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph313", "image": "data/cycle/graph_visual/hard/graph313.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (12,19) (13,2) (18,12) (13,20) (17,6) (3,0) (5,2) (18,9) (11,4) (12,16) (8,25) (23,17) (24,8) (27,28) (16,14) (19,1) (23,15) (10,11) (14,7) (26,28) (0,21) (1,25) (15,25) (22,3) (10,8) (17,0) (13,21) (0,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1825", "image": "data/cycle/graph_visual/hard/graph1825.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (31,7) (23,4) (13,20) (6,31) (29,32) (27,1) (0,13) (8,23) (19,3) (30,33) (29,11) (25,29) (4,2) (27,5) (24,8) (24,7) (11,17) (2,0) (22,10) (15,16) (9,15) (0,1) (18,33) (19,8) (3,0) (1,23) (30,20) (6,16) (28,33) (4,0) (29,13) (14,18) (26,10) (12,28) (21,4) (26,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1660", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (28,8) (24,2) (1,7) (0,13) (9,2) (29,23) (15,28) (1,29) (6,7) (18,13) (17,21) (6,27) (0,2) (5,30) (20,19) (4,22) (22,14) (1,0) (9,25) (24,23) (3,11) (16,31) (23,17) (26,6) (13,7) (0,3) (4,3) (11,8) (18,30) (10,5) (4,31) (19,16) (19,12) (27,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1663", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (20,28) (0,3) (5,0) (2,0) (2,31) (18,30) (10,21) (0,4) (20,31) (25,4) (13,6) (3,11) (8,9) (21,28) (18,25) (0,1) (22,17) (22,16) (29,1) (15,31) (19,4) (14,1) (22,29) (10,24) (27,1) (18,12) (21,18) (5,11) (20,13) (25,8) (11,21) (26,0) (23,21) (7,20) (27,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph705", "image": "data/cycle/graph_visual/hard/graph705.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (8,25) (16,26) (3,32) (6,27) (9,13) (9,16) (10,22) (17,6) (12,23) (6,14) (18,11) (20,19) (1,6) (29,24) (17,21) (4,24) (18,20) (2,7) (30,12) (28,4) (20,22) (32,25) (7,12) (16,15) (7,29) (2,0) (4,6) (26,1) (1,19) (5,12) (31,26) (27,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph549", "image": "data/cycle/graph_visual/hard/graph549.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,6) (10,25) (20,23) (24,12) (0,11) (10,28) (28,6) (21,10) (16,15) (19,24) (2,24) (0,8) (22,29) (8,12) (14,3) (9,26) (22,17) (28,11) (22,27) (26,7) (23,4) (26,15) (13,17) (26,2) (1,4) (30,16) (3,28) (20,17) (18,8) (29,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1053", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (8,5) (0,15) (9,13) (3,22) (10,14) (9,23) (25,21) (1,0) (10,0) (23,20) (6,13) (18,9) (17,15) (8,4) (4,2) (19,1) (2,0) (1,20) (3,0) (8,11) (2,12) (9,3) (2,19) (7,15) (24,25) (8,25) (2,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph562", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (22,13) (20,0) (2,12) (3,7) (2,15) (17,1) (15,27) (14,0) (8,30) (6,16) (12,9) (6,28) (25,7) (28,26) (20,23) (4,10) (15,30) (6,11) (15,24) (12,22) (18,29) (18,6) (16,21) (4,19) (1,2) (7,4) (5,11) (14,12) (25,14) (26,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1393", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (15,6) (18,7) (28,17) (4,15) (3,28) (16,12) (27,21) (20,3) (28,10) (5,23) (21,19) (0,27) (1,19) (3,25) (1,0) (23,8) (3,0) (2,11) (11,12) (13,3) (19,26) (5,4) (9,11) (22,25) (2,14) (11,26) (12,3) (0,2) (18,1) (18,5) (17,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1889", "image": "data/cycle/graph_visual/hard/graph1889.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (22,16) (0,3) (1,5) (1,0) (4,15) (7,4) (20,14) (10,9) (31,17) (29,19) (25,26) (7,21) (20,22) (6,2) (33,13) (16,11) (17,5) (12,18) (15,6) (16,28) (14,29) (19,24) (7,25) (17,8) (30,9) (21,1) (18,28) (4,0) (0,10) (32,10) (5,0) (16,23) (27,25) (0,2) (23,33) (13,17) (33,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph22", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (0,2) (3,13) (9,10) (24,8) (22,24) (5,24) (17,12) (4,15) (7,6) (23,14) (2,4) (20,2) (15,19) (1,23) (11,17) (16,17) (9,25) (11,8) (9,21) (16,7) (0,12) (1,7) (3,5) (18,12) (25,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph959", "image": "data/cycle/graph_visual/hard/graph959.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (20,13) (0,5) (25,4) (28,5) (29,6) (28,7) (24,19) (13,23) (23,12) (2,16) (14,15) (30,19) (29,8) (22,24) (9,29) (31,17) (2,34) (16,10) (33,21) (3,10) (27,32) (18,13) (23,24) (22,31) (25,24) (13,16) (11,1) (28,34) (24,11) (11,21) (29,5) (27,11) (12,15) (5,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1892", "image": "data/cycle/graph_visual/hard/graph1892.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (10,21) (7,33) (13,3) (5,27) (0,16) (1,31) (2,0) (5,25) (1,0) (13,28) (5,14) (22,8) (24,15) (9,11) (33,27) (32,14) (17,20) (28,9) (18,23) (1,3) (4,32) (26,23) (9,0) (21,25) (3,32) (10,23) (17,29) (12,4) (24,0) (19,30) (12,29) (14,22) (30,21) (2,30) (17,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph642", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (6,25) (13,19) (27,16) (29,1) (27,15) (29,17) (30,11) (23,22) (11,9) (2,29) (4,11) (18,7) (28,21) (25,13) (12,22) (24,10) (12,9) (7,20) (26,23) (24,17) (3,16) (26,13) (21,14) (3,13) (8,22) (29,5) (10,31) (14,19) (29,25) (7,5) (0,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1692", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (26,0) (4,1) (0,3) (19,11) (18,17) (12,3) (30,3) (14,19) (21,14) (20,28) (15,16) (6,9) (27,5) (29,7) (31,6) (23,14) (2,23) (9,25) (21,5) (28,19) (24,26) (21,29) (25,4) (1,29) (15,21) (24,15) (24,8) (26,13) (18,19) (12,10) (22,31) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1399", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (11,7) (22,19) (1,26) (10,0) (25,2) (28,21) (19,6) (17,10) (16,20) (19,17) (28,13) (13,23) (4,8) (14,23) (12,27) (2,10) (12,5) (24,19) (5,22) (0,18) (22,14) (8,9) (16,14) (0,2) (4,5) (3,14) (21,15) (27,11) (0,1) (23,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph799", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (30,19) (18,8) (23,1) (27,5) (17,11) (6,16) (6,31) (14,18) (0,13) (23,8) (24,7) (11,29) (4,2) (29,31) (27,1) (4,23) (13,20) (7,28) (26,10) (26,32) (20,30) (1,0) (3,19) (13,29) (15,16) (25,29) (8,24) (28,12) (22,10) (19,32) (9,15) (21,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph741", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (19,16) (30,10) (19,31) (31,32) (15,20) (18,30) (23,4) (12,18) (3,20) (14,1) (6,11) (10,0) (13,18) (4,13) (5,30) (15,32) (15,27) (8,32) (22,19) (26,17) (14,4) (25,27) (3,24) (23,7) (29,3) (7,28) (21,26) (20,7) (20,9) (17,2) (20,17) (28,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1256", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (6,10) (11,7) (19,0) (15,26) (12,16) (9,21) (14,20) (19,25) (1,16) (12,15) (26,2) (14,3) (11,23) (24,22) (17,13) (26,24) (5,18) (27,4) (0,10) (9,10) (4,5) (7,9) (0,2) (14,21) (21,4) (17,0) (8,17) (23,26) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1640", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (23,30) (11,13) (25,26) (6,24) (2,23) (14,29) (26,1) (17,12) (20,0) (6,5) (8,19) (0,14) (4,18) (10,19) (22,3) (28,2) (1,21) (18,22) (31,23) (12,8) (24,16) (27,15) (9,1) (1,27) (5,7) (0,1) (11,29) (13,23) (2,0) (27,22) (13,3) (5,31) (28,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph373", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (2,17) (12,15) (8,17) (26,15) (16,20) (23,20) (0,1) (11,17) (19,2) (13,20) (10,25) (1,4) (6,25) (3,10) (7,8) (28,9) (9,14) (13,18) (23,24) (26,13) (5,7) (18,2) (12,28) (0,16) (25,11) (5,22) (21,0) (27,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph417", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (18,0) (1,27) (7,11) (22,14) (4,8) (5,4) (29,17) (25,2) (10,17) (2,10) (16,14) (13,29) (8,9) (10,0) (15,21) (19,22) (19,6) (12,28) (5,12) (19,24) (14,3) (16,20) (5,22) (1,23) (26,19) (23,14) (28,21) (11,27) (23,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph770", "image": "data/cycle/graph_visual/hard/graph770.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (20,16) (18,17) (15,22) (28,16) (8,19) (24,23) (30,13) (2,11) (11,19) (25,6) (10,12) (28,12) (31,0) (30,2) (26,0) (19,18) (13,5) (29,4) (6,8) (18,31) (7,12) (32,11) (14,25) (4,28) (21,26) (22,18) (27,13) (12,1) (3,6) (2,9) (3,23) (28,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph209", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (24,21) (3,10) (8,22) (23,6) (4,14) (22,3) (18,15) (9,14) (12,7) (5,0) (17,20) (19,5) (25,5) (2,21) (8,6) (6,7) (13,15) (11,10) (10,16) (1,3) (15,9) (20,15) (27,26) (14,8) (27,5) (16,21) (25,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1226", "image": "data/cycle/graph_visual/hard/graph1226.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (0,3) (16,26) (13,9) (17,7) (24,0) (14,0) (1,0) (16,18) (8,3) (23,4) (19,11) (2,21) (15,26) (4,24) (11,8) (2,0) (6,18) (12,11) (26,4) (22,18) (27,24) (10,9) (3,10) (1,16) (19,0) (20,12) (5,11) (2,13) (25,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph883", "image": "data/cycle/graph_visual/hard/graph883.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (23,31) (17,1) (18,12) (6,2) (19,3) (28,7) (12,25) (33,21) (2,32) (24,5) (13,6) (26,8) (22,24) (2,21) (4,5) (15,17) (16,30) (18,9) (27,14) (21,8) (14,3) (30,27) (1,2) (15,28) (10,14) (29,10) (23,27) (19,4) (13,31) (16,11) (5,20) (0,28) (4,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1479", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (12,25) (5,10) (4,17) (1,0) (20,29) (8,29) (10,13) (5,3) (9,17) (24,11) (9,10) (11,2) (26,5) (28,0) (6,25) (0,27) (1,15) (2,20) (10,14) (14,12) (6,7) (21,0) (11,15) (22,16) (18,25) (22,2) (10,20) (22,19) (28,16) (15,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1852", "image": "data/cycle/graph_visual/hard/graph1852.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (22,9) (7,10) (12,11) (17,15) (8,31) (0,3) (33,9) (28,24) (26,6) (32,22) (30,18) (12,29) (5,3) (4,0) (20,28) (30,2) (0,33) (7,14) (3,21) (27,15) (6,21) (30,27) (2,7) (23,25) (1,9) (0,1) (23,10) (4,29) (5,11) (21,16) (24,33) (19,16) (2,0) (28,27) (1,8) (12,0) (32,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1472", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (4,0) (12,16) (14,23) (2,8) (11,29) (12,27) (22,27) (7,26) (9,5) (2,0) (5,18) (23,19) (12,26) (1,0) (24,17) (3,4) (23,4) (23,13) (23,10) (2,9) (12,10) (2,11) (16,28) (6,9) (3,0) (29,24) (6,1) (13,17) (21,25) (15,21) (29,20) (17,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1584", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (21,22) (30,7) (8,14) (27,26) (0,2) (11,0) (17,9) (22,16) (27,4) (15,26) (2,3) (29,0) (5,23) (10,18) (19,21) (18,23) (29,12) (19,0) (25,28) (17,28) (24,9) (12,15) (1,0) (7,1) (14,9) (6,20) (0,20) (29,2) (13,4) (25,15) (24,5) (0,3) (30,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1590", "image": "data/cycle/graph_visual/hard/graph1590.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (6,29) (30,13) (8,28) (14,9) (7,12) (27,30) (6,8) (5,27) (10,16) (22,28) (20,18) (5,0) (8,26) (19,15) (24,25) (24,21) (15,23) (1,0) (10,3) (3,1) (6,7) (5,25) (5,20) (10,11) (15,17) (0,3) (2,0) (16,21) (28,14) (15,9) (14,4) (21,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1213", "image": "data/cycle/graph_visual/hard/graph1213.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (12,24) (7,5) (4,5) (18,21) (23,22) (16,20) (26,1) (27,19) (16,2) (15,8) (0,7) (25,17) (9,7) (11,12) (17,22) (20,10) (3,17) (26,7) (26,6) (23,14) (18,10) (16,17) (8,27) (1,0) (11,21) (12,8) (17,13) (26,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph449", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (5,9) (23,19) (17,15) (23,4) (29,24) (16,28) (5,18) (13,23) (0,2) (14,23) (15,21) (3,4) (29,11) (29,20) (17,13) (11,2) (25,21) (6,1) (26,7) (27,22) (12,10) (9,2) (12,27) (12,26) (17,24) (9,6) (2,8) (23,10) (16,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1702", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (7,17) (3,4) (0,3) (10,27) (25,23) (30,4) (6,5) (7,8) (0,1) (22,1) (4,31) (30,13) (24,7) (10,3) (26,14) (31,0) (6,10) (10,19) (12,5) (20,2) (9,11) (13,21) (14,30) (2,0) (16,9) (2,7) (22,15) (25,13) (21,18) (28,18) (5,32) (11,25) (18,29) (22,23) (7,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph734", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (17,3) (23,6) (14,3) (25,31) (21,5) (32,7) (3,11) (4,12) (26,23) (20,0) (15,5) (27,5) (3,27) (18,8) (2,13) (25,10) (4,15) (6,16) (9,7) (22,27) (13,20) (14,2) (1,9) (26,9) (24,4) (14,29) (7,28) (25,3) (8,2) (30,3) (26,18) (19,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1138", "image": "data/cycle/graph_visual/hard/graph1138.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (15,3) (0,14) (1,11) (22,16) (21,4) (25,10) (13,15) (14,12) (6,13) (21,10) (4,23) (11,7) (7,8) (17,8) (20,7) (5,9) (19,23) (19,9) (7,0) (22,9) (18,20) (15,2) (0,9) (21,13) (9,26) (24,26) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph619", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (18,21) (28,2) (13,22) (13,12) (24,11) (23,17) (21,19) (24,20) (3,12) (28,14) (2,24) (18,26) (27,5) (16,6) (31,3) (0,23) (9,29) (8,30) (6,9) (17,31) (28,4) (30,28) (0,24) (26,17) (7,19) (8,1) (31,10) (21,5) (14,15) (28,25) (16,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph45", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (14,21) (18,10) (19,16) (8,4) (22,17) (15,12) (22,11) (10,21) (9,17) (5,23) (9,4) (5,24) (0,7) (19,0) (18,23) (1,7) (2,20) (21,25) (0,15) (3,2) (13,0) (6,14) (24,9) (25,15) (20,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph572", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (13,30) (7,14) (18,10) (27,28) (12,24) (14,19) (4,3) (14,17) (0,29) (15,9) (28,12) (1,15) (7,21) (6,1) (12,20) (16,15) (18,23) (25,15) (28,11) (22,10) (4,14) (6,28) (25,17) (8,9) (2,30) (5,17) (2,19) (23,29) (26,29) (23,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1984", "image": "data/cycle/graph_visual/hard/graph1984.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (21,25) (2,30) (28,34) (0,2) (16,0) (23,10) (21,31) (13,29) (8,22) (25,5) (9,11) (15,24) (30,19) (32,3) (22,14) (20,17) (14,5) (18,23) (28,9) (24,0) (7,33) (27,5) (30,12) (0,1) (33,1) (3,13) (3,1) (17,6) (4,12) (9,0) (28,27) (21,10) (26,23) (32,14) (17,29) (4,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1219", "image": "data/cycle/graph_visual/hard/graph1219.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (3,22) (2,5) (27,20) (15,6) (2,0) (4,1) (1,21) (4,23) (19,11) (8,15) (14,24) (8,9) (26,18) (9,25) (11,2) (15,26) (20,16) (13,9) (8,11) (14,18) (21,7) (10,18) (20,21) (3,0) (12,18) (22,25) (17,2) (1,0) (17,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph279", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (26,1) (5,17) (6,20) (25,11) (18,23) (14,15) (19,16) (19,0) (4,13) (6,19) (27,12) (1,18) (16,7) (4,25) (4,17) (27,20) (23,16) (25,6) (23,9) (2,22) (8,24) (20,2) (3,24) (15,0) (17,10) (0,21) (8,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1112", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (17,9) (15,25) (16,20) (6,15) (25,17) (26,2) (15,0) (11,9) (1,0) (5,9) (11,4) (1,14) (1,12) (4,8) (18,6) (25,20) (26,20) (7,2) (10,12) (1,13) (3,14) (21,5) (13,4) (0,2) (19,6) (2,22) (24,6) (1,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph7", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (13,1) (21,20) (16,25) (15,7) (6,9) (2,24) (23,18) (6,24) (0,4) (12,25) (16,10) (17,9) (3,18) (3,15) (25,15) (14,5) (5,19) (4,17) (1,22) (3,4) (9,11) (15,13) (5,24) (8,21) (5,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph499", "image": "data/cycle/graph_visual/hard/graph499.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (13,25) (8,28) (5,11) (16,15) (27,20) (15,27) (24,25) (1,6) (10,16) (20,0) (26,5) (21,1) (3,8) (9,23) (11,18) (1,17) (0,7) (22,29) (14,0) (19,13) (5,4) (12,17) (4,23) (14,11) (29,2) (26,13) (2,7) (14,12) (28,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1946", "image": "data/cycle/graph_visual/hard/graph1946.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (10,7) (33,21) (17,27) (28,9) (23,24) (16,32) (6,23) (12,19) (30,34) (11,25) (6,7) (8,0) (23,26) (11,29) (4,32) (16,25) (20,2) (18,1) (5,0) (14,8) (17,24) (30,23) (10,32) (21,11) (12,6) (31,25) (3,34) (1,8) (22,12) (11,9) (13,34) (15,31) (5,17) (33,2) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1679", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (4,29) (17,2) (27,26) (31,15) (30,16) (0,4) (23,25) (14,21) (27,5) (15,25) (21,18) (28,3) (5,4) (8,16) (22,28) (13,4) (0,1) (0,2) (30,1) (0,30) (12,10) (22,0) (15,11) (8,21) (20,23) (16,17) (6,9) (19,16) (6,31) (3,26) (3,0) (24,11) (4,12) (18,7) (9,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph593", "image": "data/cycle/graph_visual/hard/graph593.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (1,10) (16,23) (2,7) (15,17) (11,18) (1,26) (24,2) (3,30) (26,18) (25,13) (5,30) (0,10) (2,28) (8,4) (3,18) (1,13) (20,11) (14,26) (7,29) (2,17) (19,3) (13,27) (12,2) (6,1) (22,29) (20,9) (6,16) (12,4) (13,17) (1,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1673", "image": "data/cycle/graph_visual/hard/graph1673.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (18,13) (6,7) (6,27) (4,31) (16,31) (5,10) (17,21) (4,3) (26,6) (29,1) (13,0) (18,30) (30,5) (22,14) (2,0) (11,8) (1,7) (19,20) (9,25) (9,2) (1,0) (17,23) (24,23) (7,13) (2,24) (27,4) (29,23) (19,12) (28,8) (16,19) (28,15) (11,3) (22,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph296", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (26,14) (27,24) (6,19) (1,21) (6,17) (26,11) (16,6) (10,0) (11,16) (8,18) (24,15) (20,16) (0,23) (3,10) (5,16) (26,0) (24,14) (19,7) (16,22) (9,25) (26,4) (19,1) (6,2) (8,2) (8,12) (4,13) (25,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph169", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (25,5) (15,9) (19,5) (14,8) (6,8) (4,14) (15,18) (3,10) (15,13) (12,7) (20,17) (23,6) (2,21) (22,8) (15,20) (0,5) (9,14) (21,24) (22,3) (11,10) (6,7) (10,16) (3,1) (16,21) (25,24) (5,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1056", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (18,17) (0,2) (21,17) (16,2) (7,6) (7,9) (15,0) (7,10) (11,5) (3,24) (4,0) (10,15) (2,6) (0,1) (23,4) (4,11) (3,0) (12,22) (3,11) (11,10) (14,24) (10,19) (13,15) (20,8) (21,22) (7,20) (25,2) (2,17) (1,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1964", "image": "data/cycle/graph_visual/hard/graph1964.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (24,18) (27,16) (2,0) (10,32) (25,33) (15,19) (28,14) (9,23) (17,21) (6,31) (26,4) (11,7) (2,10) (3,7) (5,29) (7,6) (15,25) (0,28) (10,9) (12,17) (14,34) (11,27) (0,4) (8,26) (28,26) (0,3) (17,13) (23,33) (11,22) (1,0) (13,2) (0,33) (25,31) (4,1) (0,30) (19,29) (18,2) (31,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1578", "image": "data/cycle/graph_visual/hard/graph1578.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,20) (14,0) (24,30) (30,25) (26,4) (11,12) (28,21) (11,5) (28,7) (13,30) (29,18) (19,11) (2,0) (2,13) (0,1) (8,3) (3,4) (15,26) (0,19) (8,11) (30,23) (12,22) (16,26) (18,6) (2,27) (28,9) (18,16) (9,10) (3,10) (16,1) (24,0) (7,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph300", "image": "data/cycle/graph_visual/hard/graph300.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (22,9) (5,11) (24,5) (3,7) (3,10) (22,6) (1,13) (25,16) (18,12) (20,22) (12,13) (17,4) (16,2) (15,9) (12,24) (14,7) (23,0) (5,3) (20,12) (8,27) (24,28) (18,21) (18,27) (0,17) (16,22) (9,26) (7,19) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph855", "image": "data/cycle/graph_visual/hard/graph855.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (1,31) (19,4) (9,27) (11,21) (10,26) (31,15) (9,8) (25,4) (5,30) (3,11) (14,1) (29,22) (2,31) (22,16) (12,18) (21,28) (27,1) (18,32) (10,21) (23,33) (24,21) (13,6) (11,5) (17,22) (18,21) (20,23) (20,7) (28,20) (13,20) (25,18) (0,29) (0,32) (8,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph221", "image": "data/cycle/graph_visual/hard/graph221.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (9,11) (2,3) (15,22) (27,21) (7,0) (8,4) (25,15) (5,23) (1,7) (0,19) (25,17) (20,2) (21,16) (26,12) (12,15) (4,27) (0,26) (0,14) (10,21) (14,6) (13,22) (10,18) (24,9) (5,24) (20,19) (23,18) (17,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph466", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (7,19) (25,4) (24,22) (14,23) (2,0) (14,16) (4,1) (13,16) (5,3) (12,1) (8,24) (11,21) (7,4) (18,3) (24,4) (17,3) (28,21) (22,20) (23,26) (15,4) (1,27) (6,13) (1,21) (15,0) (12,9) (6,29) (23,17) (7,17) (4,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph408", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (19,16) (18,6) (25,15) (3,7) (20,0) (12,8) (23,15) (9,4) (14,24) (20,22) (12,14) (12,2) (12,26) (5,11) (15,2) (0,14) (4,17) (6,28) (29,15) (25,7) (10,6) (4,7) (1,13) (21,12) (18,27) (11,22) (1,2) (26,28) (16,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph658", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (13,22) (24,2) (24,20) (24,0) (14,15) (4,28) (30,8) (28,14) (24,11) (17,31) (6,16) (9,29) (10,31) (8,1) (25,28) (5,27) (23,0) (17,23) (6,9) (28,2) (21,19) (26,18) (17,26) (21,18) (30,28) (3,31) (17,16) (21,5) (12,13) (19,7) (3,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph662", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (17,1) (27,25) (9,24) (11,4) (30,12) (21,30) (2,10) (9,14) (23,9) (25,22) (19,1) (4,0) (5,8) (24,30) (3,15) (0,13) (14,26) (16,18) (25,28) (7,30) (28,8) (17,30) (19,2) (31,8) (4,10) (16,14) (30,15) (20,12) (27,24) (6,23) (29,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph892", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (22,18) (27,24) (15,18) (8,2) (25,23) (6,29) (1,5) (4,33) (9,20) (4,26) (30,0) (28,19) (26,29) (3,5) (28,11) (32,0) (14,6) (17,27) (31,0) (32,13) (2,27) (7,32) (23,4) (18,23) (33,12) (4,21) (26,5) (16,24) (10,23) (23,32) (13,28) (9,3) (33,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1346", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (21,27) (14,0) (19,25) (27,1) (12,14) (15,20) (16,24) (9,14) (18,22) (11,14) (17,7) (13,16) (6,5) (0,3) (16,15) (28,25) (27,8) (18,6) (23,25) (5,3) (26,5) (20,19) (17,25) (4,2) (9,4) (2,0) (17,2) (24,10) (1,0) (28,27) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1669", "image": "data/cycle/graph_visual/hard/graph1669.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,14) (8,7) (29,14) (4,18) (3,18) (23,22) (20,12) (16,7) (26,0) (2,16) (26,7) (29,9) (4,0) (12,30) (11,28) (2,21) (31,30) (0,2) (13,21) (30,28) (10,24) (10,8) (25,14) (16,19) (15,27) (28,6) (4,29) (25,28) (8,22) (0,1) (1,18) (23,27) (23,14) (14,17) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph321", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (16,19) (27,22) (24,27) (0,23) (23,21) (13,7) (5,11) (13,15) (2,22) (3,12) (1,14) (11,26) (16,9) (20,24) (15,8) (3,25) (23,4) (28,3) (10,21) (25,24) (14,10) (18,7) (23,8) (6,26) (17,20) (17,5) (19,18) (17,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1215", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (15,13) (17,14) (25,27) (26,24) (1,0) (23,0) (14,1) (6,26) (3,12) (18,7) (22,21) (24,20) (25,24) (5,11) (18,16) (8,23) (19,3) (20,17) (22,2) (23,4) (23,11) (2,0) (16,9) (14,10) (21,10) (27,19) (7,13) (15,8) (5,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1288", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (17,10) (25,8) (24,3) (17,4) (14,15) (1,0) (23,9) (0,15) (4,25) (23,18) (2,0) (19,16) (2,20) (22,2) (16,23) (6,25) (25,11) (27,20) (7,16) (0,3) (8,24) (4,13) (0,19) (12,27) (17,5) (26,1) (6,19) (20,6) (21,0) (18,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1125", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (19,13) (9,13) (23,8) (2,18) (20,14) (22,25) (15,26) (25,14) (12,21) (3,0) (18,9) (12,11) (6,1) (6,15) (4,6) (1,17) (6,25) (3,18) (6,16) (0,1) (5,6) (7,23) (0,15) (24,19) (11,9) (8,14) (10,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1407", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (15,14) (13,12) (19,24) (28,24) (27,26) (4,1) (9,24) (3,6) (16,24) (6,23) (28,25) (20,18) (19,13) (15,3) (24,0) (21,25) (29,22) (26,12) (4,18) (0,1) (0,22) (2,8) (20,12) (17,14) (15,0) (27,5) (11,15) (0,2) (8,3) (2,10) (25,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph859", "image": "data/cycle/graph_visual/hard/graph859.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (27,4) (14,11) (29,14) (27,19) (12,29) (14,32) (32,9) (5,20) (16,24) (28,30) (27,28) (9,24) (2,14) (26,7) (24,0) (7,20) (31,8) (10,0) (22,7) (15,14) (33,2) (6,3) (6,12) (26,8) (30,14) (30,25) (12,1) (23,4) (0,21) (22,10) (14,17) (13,22) (18,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1063", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (11,9) (20,14) (25,18) (19,4) (1,15) (21,3) (21,19) (11,16) (15,8) (5,16) (25,14) (2,0) (1,0) (0,12) (17,7) (0,21) (15,11) (23,22) (14,4) (2,8) (6,21) (8,20) (4,10) (24,7) (19,22) (13,12) (0,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph961", "image": "data/cycle/graph_visual/hard/graph961.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (19,32) (14,1) (20,34) (11,1) (7,19) (25,18) (27,33) (21,23) (28,25) (29,23) (20,11) (10,6) (24,27) (11,10) (10,32) (5,3) (8,16) (30,23) (10,13) (3,0) (5,23) (34,22) (15,33) (28,17) (17,2) (9,13) (4,5) (1,2) (2,12) (26,32) (16,27) (29,20) (24,31) (14,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph571", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (12,11) (16,26) (26,4) (18,6) (19,11) (2,13) (11,5) (25,30) (19,0) (30,13) (0,20) (2,27) (4,3) (9,28) (24,30) (7,17) (0,14) (9,10) (29,18) (21,28) (28,7) (26,15) (0,24) (22,12) (10,3) (3,8) (30,23) (1,16) (16,18) (8,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1934", "image": "data/cycle/graph_visual/hard/graph1934.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (1,7) (3,2) (7,5) (5,30) (8,22) (25,1) (32,12) (25,21) (30,0) (19,34) (14,20) (14,8) (13,12) (26,29) (0,3) (33,28) (13,34) (4,0) (0,5) (8,17) (9,2) (26,13) (14,34) (24,9) (28,27) (25,23) (13,15) (21,31) (2,16) (33,21) (15,23) (7,6) (1,0) (3,8) (10,25) (0,2) (9,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph207", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (20,19) (0,26) (26,12) (9,17) (25,17) (0,19) (8,4) (14,0) (14,6) (18,10) (9,24) (5,24) (27,4) (22,15) (18,23) (16,21) (0,7) (3,2) (9,11) (5,23) (1,7) (27,21) (2,20) (21,10) (12,15) (22,13) (25,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1103", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (11,13) (2,0) (23,2) (17,25) (0,1) (8,14) (7,26) (19,12) (12,23) (2,3) (14,4) (15,24) (16,13) (0,4) (14,23) (6,10) (3,17) (7,10) (3,24) (1,21) (22,11) (8,1) (14,9) (3,0) (6,20) (5,0) (16,25) (22,5) (5,18) (20,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph133", "image": "data/cycle/graph_visual/hard/graph133.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (26,6) (12,19) (25,14) (11,12) (0,7) (26,8) (8,12) (7,26) (17,16) (14,23) (21,18) (5,7) (21,11) (5,4) (22,17) (17,24) (23,22) (20,10) (18,10) (13,17) (7,9) (3,17) (1,26) (2,16) (20,16) (8,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1900", "image": "data/cycle/graph_visual/hard/graph1900.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,16) (24,5) (34,3) (10,16) (2,0) (9,29) (2,27) (7,32) (13,18) (21,12) (6,7) (24,21) (11,3) (24,0) (1,8) (1,7) (10,14) (28,9) (4,23) (6,9) (14,19) (13,4) (20,10) (0,15) (17,25) (15,1) (30,8) (17,24) (28,26) (9,11) (18,27) (0,1) (2,33) (18,22) (23,30) (31,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph523", "image": "data/cycle/graph_visual/hard/graph523.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (20,23) (6,12) (4,25) (23,9) (5,6) (26,24) (0,24) (15,6) (0,3) (14,28) (27,14) (22,1) (10,18) (9,22) (26,8) (17,2) (20,3) (5,21) (4,19) (2,22) (12,7) (0,30) (13,5) (27,23) (25,29) (5,11) (24,18) (22,21) (21,16) (14,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1001", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (13,7) (18,10) (15,25) (10,16) (1,6) (0,1) (2,0) (17,4) (23,21) (18,23) (7,14) (6,22) (14,19) (8,15) (12,20) (11,12) (0,4) (25,17) (5,9) (12,6) (19,2) (14,24) (15,1) (2,17) (17,23) (14,3) (9,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1925", "image": "data/cycle/graph_visual/hard/graph1925.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (29,7) (1,25) (23,14) (29,21) (3,21) (8,19) (0,15) (26,32) (20,27) (17,21) (11,0) (8,27) (14,11) (7,10) (9,15) (29,18) (3,0) (16,0) (19,10) (2,12) (8,25) (1,0) (20,26) (13,33) (14,12) (2,0) (15,34) (0,6) (11,5) (8,22) (7,24) (28,12) (28,31) (33,28) (11,30) (4,21) (3,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph728", "image": "data/cycle/graph_visual/hard/graph728.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (7,14) (30,4) (15,0) (18,6) (14,11) (29,10) (4,6) (0,6) (32,7) (31,17) (28,21) (20,17) (22,27) (24,9) (20,6) (23,32) (4,22) (3,26) (25,20) (12,18) (10,7) (5,7) (2,32) (24,19) (18,21) (14,1) (18,2) (11,8) (1,13) (26,19) (25,24) (10,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph100", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (10,6) (0,17) (21,18) (7,3) (10,21) (0,11) (5,8) (13,21) (14,5) (4,23) (20,14) (19,5) (7,24) (19,4) (16,12) (2,6) (16,22) (25,10) (24,15) (0,10) (26,13) (20,9) (22,4) (22,3) (14,13) (12,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1644", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (27,23) (10,24) (9,5) (20,25) (15,22) (13,0) (0,1) (12,28) (22,8) (14,8) (30,6) (10,3) (8,18) (2,10) (26,31) (13,1) (16,19) (29,4) (23,14) (5,26) (2,1) (8,30) (21,3) (9,17) (16,3) (3,25) (29,28) (12,14) (7,23) (11,29) (20,22) (17,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1020", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (22,3) (4,24) (1,16) (20,2) (18,16) (0,2) (2,13) (1,0) (14,0) (18,21) (11,12) (0,24) (11,8) (18,6) (0,7) (19,11) (23,4) (15,7) (25,24) (19,0) (12,17) (11,5) (10,9) (9,13) (16,4) (8,3) (10,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1314", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (2,27) (1,15) (24,20) (24,19) (13,14) (20,17) (9,12) (17,10) (2,4) (20,3) (26,24) (8,22) (6,21) (23,28) (7,19) (14,6) (25,16) (11,21) (0,6) (1,0) (13,27) (25,18) (25,22) (20,4) (26,22) (2,0) (5,3) (12,0) (15,8) (6,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph99", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (8,10) (19,0) (15,1) (24,5) (22,16) (5,3) (11,23) (11,15) (9,13) (12,14) (15,21) (10,5) (25,22) (11,2) (0,16) (25,6) (17,25) (4,17) (0,20) (22,18) (9,10) (10,14) (7,6) (12,2) (10,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1905", "image": "data/cycle/graph_visual/hard/graph1905.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,6) (4,11) (30,24) (0,4) (3,33) (2,33) (30,12) (19,9) (0,1) (1,2) (0,29) (10,34) (19,32) (31,18) (4,13) (15,14) (5,21) (0,31) (7,33) (5,28) (3,22) (6,20) (16,1) (21,7) (9,13) (8,27) (28,12) (34,26) (31,15) (0,2) (10,7) (3,0) (18,12) (32,2) (23,25) (0,23) (21,20) (8,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph364", "image": "data/cycle/graph_visual/hard/graph364.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (17,26) (13,18) (18,11) (0,26) (6,25) (5,1) (16,5) (14,9) (24,25) (28,24) (6,19) (11,0) (5,22) (23,16) (13,10) (3,13) (22,8) (7,16) (4,2) (2,13) (15,9) (25,4) (20,15) (7,25) (15,25) (12,20) (21,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph756", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (19,27) (12,30) (10,14) (4,18) (32,8) (22,3) (4,0) (27,12) (7,5) (17,32) (25,11) (6,2) (2,1) (5,20) (21,22) (26,21) (14,31) (31,5) (6,28) (17,19) (32,26) (12,23) (27,28) (24,28) (13,26) (16,14) (22,9) (15,1) (29,26) (22,18) (25,10) (14,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1415", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (27,26) (21,7) (25,24) (23,17) (9,8) (2,17) (15,8) (21,1) (18,28) (16,20) (1,0) (29,20) (22,3) (5,2) (0,6) (8,11) (4,23) (2,11) (18,14) (12,18) (6,15) (19,28) (21,20) (9,13) (28,15) (14,25) (18,10) (26,9) (22,11) (4,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1480", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (25,1) (19,23) (0,1) (26,3) (2,17) (26,13) (3,12) (22,23) (9,26) (24,15) (16,3) (3,0) (0,2) (9,20) (29,0) (14,13) (24,4) (23,26) (18,16) (14,0) (25,28) (8,10) (17,6) (23,10) (24,12) (0,11) (27,28) (27,16) (5,0) (22,2) (26,7) (20,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph211", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (24,9) (15,27) (1,5) (8,6) (16,19) (5,3) (14,25) (24,4) (14,10) (11,13) (13,17) (13,7) (3,15) (9,1) (2,3) (20,6) (13,15) (5,14) (21,3) (8,12) (26,21) (22,21) (2,0) (18,19) (19,8) (23,5) (1,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph631", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (29,7) (23,8) (14,12) (9,3) (9,15) (2,12) (18,14) (11,24) (20,27) (26,30) (13,0) (26,20) (8,27) (0,6) (8,17) (31,11) (10,7) (19,8) (10,19) (21,0) (12,28) (7,22) (21,4) (28,15) (14,11) (5,11) (25,28) (21,3) (1,25) (21,29) (16,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1466", "image": "data/cycle/graph_visual/hard/graph1466.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (16,24) (9,19) (0,1) (0,2) (23,14) (1,8) (17,20) (8,6) (16,29) (17,3) (20,12) (13,0) (22,12) (26,19) (7,0) (4,2) (0,14) (25,10) (25,7) (15,19) (9,11) (4,20) (28,26) (26,18) (29,19) (12,1) (5,2) (29,5) (21,6) (27,26) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph779", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (29,21) (8,24) (13,26) (1,4) (25,4) (24,15) (10,12) (29,1) (19,18) (31,22) (14,19) (5,27) (16,15) (2,23) (28,20) (3,30) (14,23) (17,18) (28,19) (3,12) (7,29) (6,15) (26,24) (11,19) (0,26) (25,9) (15,32) (6,9) (21,14) (21,31) (5,21) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1240", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (11,21) (5,7) (11,8) (8,25) (15,1) (12,8) (18,21) (1,0) (25,1) (20,22) (11,22) (16,5) (10,14) (7,27) (0,6) (0,3) (27,4) (0,17) (11,7) (6,2) (16,9) (23,13) (19,4) (0,2) (23,7) (22,14) (26,12) (10,3) (24,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph665", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (26,1) (27,13) (13,11) (23,17) (19,27) (20,1) (28,22) (2,8) (12,6) (0,21) (15,31) (7,31) (14,28) (16,4) (3,4) (0,30) (1,16) (24,13) (24,0) (25,6) (6,20) (28,8) (14,1) (5,7) (29,1) (1,27) (10,24) (9,30) (24,18) (28,31) (17,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph690", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (2,19) (17,10) (22,25) (4,7) (26,10) (1,22) (6,31) (14,25) (10,3) (8,7) (10,6) (9,15) (7,23) (30,4) (18,28) (5,22) (7,2) (5,12) (18,21) (9,11) (31,0) (29,4) (25,11) (27,18) (4,3) (20,23) (30,14) (7,16) (21,13) (24,13) (30,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1085", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (15,12) (4,9) (13,0) (23,18) (12,20) (10,21) (5,24) (0,1) (5,23) (21,25) (7,1) (0,7) (25,15) (14,6) (18,10) (2,20) (16,19) (17,9) (3,2) (19,0) (22,17) (4,8) (9,24) (15,0) (21,14) (22,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph292", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (2,0) (1,9) (25,7) (8,9) (11,22) (27,8) (16,14) (17,19) (27,23) (23,3) (24,15) (25,22) (2,26) (14,5) (6,13) (25,18) (3,17) (4,16) (4,25) (14,12) (10,7) (23,11) (15,5) (27,20) (22,2) (9,13) (26,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1412", "image": "data/cycle/graph_visual/hard/graph1412.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (12,2) (6,16) (3,24) (18,28) (9,28) (23,15) (1,0) (10,13) (16,8) (22,9) (27,0) (12,17) (29,26) (25,20) (2,0) (8,1) (27,6) (11,18) (0,3) (25,29) (15,11) (16,4) (4,9) (1,13) (29,12) (24,4) (7,28) (14,15) (24,5) (21,26) (19,3) (25,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph775", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (2,19) (16,17) (30,13) (16,1) (13,1) (25,26) (27,3) (28,17) (5,9) (12,10) (3,14) (15,0) (12,17) (23,14) (6,16) (22,4) (32,24) (32,31) (10,19) (25,8) (15,30) (9,20) (6,11) (18,19) (24,21) (18,23) (4,1) (23,5) (11,29) (6,7) (5,21) (25,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph826", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (26,8) (16,24) (15,14) (7,20) (2,14) (29,14) (23,4) (32,14) (26,7) (14,30) (10,0) (2,33) (22,7) (27,4) (29,18) (13,22) (27,19) (24,0) (12,1) (30,25) (9,24) (21,0) (31,8) (5,20) (28,27) (11,14) (6,3) (17,14) (32,9) (28,30) (10,22) (12,6) (29,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph781", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (32,31) (19,10) (6,7) (30,15) (23,5) (12,10) (0,15) (18,25) (8,25) (26,25) (16,17) (30,13) (1,4) (24,21) (28,17) (4,22) (17,12) (24,32) (23,18) (19,2) (16,6) (11,29) (9,20) (27,3) (6,11) (5,21) (19,18) (5,9) (16,1) (14,3) (13,1) (14,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph829", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (28,14) (25,21) (14,8) (23,15) (25,10) (27,26) (2,9) (1,7) (23,25) (30,0) (5,28) (9,11) (1,25) (29,21) (24,33) (13,32) (18,7) (8,17) (5,7) (21,31) (13,33) (13,26) (19,14) (7,6) (12,13) (12,30) (13,15) (8,20) (9,22) (3,8) (0,4) (2,16) (3,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1633", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (17,3) (5,27) (11,3) (22,26) (21,27) (15,5) (30,25) (4,15) (9,7) (10,25) (24,3) (26,9) (20,0) (2,14) (3,29) (7,31) (20,5) (13,19) (8,18) (9,1) (23,6) (6,16) (1,0) (23,4) (12,4) (28,14) (25,3) (13,2) (8,2) (27,7) (2,0) (26,18) (3,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph149", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (0,7) (17,7) (25,3) (21,2) (22,18) (0,24) (10,3) (18,16) (0,19) (10,9) (23,4) (0,14) (8,3) (18,6) (26,16) (19,11) (11,12) (15,26) (16,1) (13,9) (24,4) (13,2) (26,4) (20,12) (11,8) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph498", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (15,22) (27,7) (19,7) (14,8) (28,14) (16,11) (23,6) (0,3) (2,21) (16,12) (3,2) (29,1) (5,24) (10,9) (26,0) (18,9) (20,26) (4,23) (22,2) (0,24) (13,9) (8,6) (0,28) (11,4) (17,28) (19,14) (13,12) (29,15) (18,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph684", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (24,6) (1,29) (5,17) (5,22) (15,10) (15,3) (29,20) (28,27) (11,0) (25,10) (7,8) (4,8) (10,27) (9,23) (4,24) (7,3) (17,31) (26,14) (19,11) (14,13) (13,18) (21,2) (21,23) (12,17) (18,6) (24,2) (0,21) (16,8) (28,29) (10,30) (26,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph127", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (5,3) (17,7) (9,14) (16,23) (3,8) (12,20) (24,9) (21,0) (0,3) (17,4) (5,10) (12,18) (18,25) (13,1) (24,5) (7,3) (16,2) (0,15) (7,13) (18,19) (12,26) (22,20) (11,12) (22,6) (22,9) (16,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1154", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (5,14) (24,14) (11,13) (6,8) (9,1) (13,7) (22,5) (9,23) (21,3) (5,1) (14,10) (17,13) (20,6) (0,1) (13,15) (18,8) (5,3) (19,15) (0,2) (2,3) (25,21) (16,19) (21,20) (24,4) (26,3) (19,1) (12,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1885", "image": "data/cycle/graph_visual/hard/graph1885.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (12,33) (9,19) (19,24) (14,33) (29,1) (28,6) (26,25) (14,32) (12,28) (32,16) (17,12) (20,28) (22,30) (11,6) (4,30) (12,2) (29,8) (13,28) (21,32) (0,33) (15,31) (28,7) (1,15) (0,10) (27,10) (29,20) (25,28) (0,2) (3,4) (11,23) (2,3) (18,11) (0,1) (5,9) (2,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph131", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (11,1) (5,24) (7,16) (2,1) (19,6) (18,26) (23,26) (16,19) (12,3) (9,13) (11,12) (25,12) (13,20) (15,10) (0,22) (0,23) (21,12) (20,23) (3,20) (14,7) (9,15) (17,10) (0,8) (4,18) (19,11) (16,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph595", "image": "data/cycle/graph_visual/hard/graph595.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (24,8) (24,10) (1,3) (12,30) (21,22) (17,10) (16,2) (16,10) (26,4) (2,20) (3,18) (26,21) (9,5) (22,6) (19,27) (20,29) (13,25) (19,6) (3,4) (15,14) (13,21) (9,22) (29,0) (7,28) (8,12) (7,12) (25,12) (21,23) (14,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph465", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (9,20) (12,0) (15,11) (21,19) (13,23) (27,10) (11,13) (29,25) (17,8) (15,18) (8,5) (26,0) (11,25) (9,6) (14,28) (21,16) (24,13) (27,29) (3,4) (19,26) (1,17) (7,13) (8,22) (9,13) (0,17) (5,2) (0,23) (26,3) (14,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph418", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (4,12) (10,2) (9,1) (13,17) (16,22) (2,7) (17,2) (28,7) (16,6) (13,25) (18,11) (1,20) (6,1) (18,3) (18,26) (4,5) (3,15) (14,17) (27,2) (0,10) (1,13) (19,11) (26,1) (12,26) (20,8) (29,3) (29,21) (23,2) (24,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph981", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (10,24) (15,9) (5,25) (34,32) (0,27) (26,30) (18,21) (29,31) (8,21) (3,20) (4,33) (4,23) (17,21) (9,14) (0,1) (28,14) (9,1) (4,26) (0,8) (13,19) (7,8) (16,26) (11,22) (13,22) (30,5) (10,29) (21,19) (4,12) (6,16) (5,2) (29,3) (20,5) (25,17) (32,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph482", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (2,20) (3,5) (2,11) (16,22) (10,5) (22,19) (4,17) (9,17) (8,29) (10,14) (9,10) (25,18) (10,13) (15,1) (15,23) (29,20) (11,15) (2,22) (27,0) (10,20) (6,25) (24,11) (28,16) (7,6) (12,14) (0,28) (26,5) (0,21) (12,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1379", "image": "data/cycle/graph_visual/hard/graph1379.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (21,13) (4,25) (5,14) (16,24) (3,7) (6,10) (22,4) (5,19) (19,4) (11,20) (7,26) (28,8) (24,14) (28,13) (20,10) (17,22) (0,12) (1,12) (9,5) (18,0) (27,0) (3,22) (10,21) (15,16) (21,23) (14,13) (27,10) (0,1) (6,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1332", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (1,0) (11,5) (13,15) (7,18) (12,3) (19,18) (10,14) (8,23) (16,19) (26,11) (5,17) (24,25) (17,20) (4,0) (26,6) (21,10) (0,2) (4,23) (7,13) (27,22) (0,3) (0,23) (27,24) (16,9) (28,3) (22,2) (1,14) (20,24) (21,23) (17,14) (3,25) (15,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph801", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (24,23) (6,30) (17,20) (24,28) (5,6) (24,17) (20,14) (29,10) (31,7) (31,2) (25,4) (13,26) (32,27) (4,31) (9,13) (26,15) (16,1) (29,20) (7,0) (32,22) (11,28) (28,16) (7,28) (22,18) (18,8) (19,6) (9,21) (25,15) (12,8) (18,3) (8,1) (4,33) (2,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1643", "image": "data/cycle/graph_visual/hard/graph1643.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (28,1) (29,21) (14,23) (1,7) (8,26) (22,27) (10,9) (0,3) (28,15) (9,28) (0,2) (8,4) (10,12) (6,30) (0,1) (21,3) (19,13) (14,28) (0,16) (21,11) (24,14) (0,4) (22,18) (31,18) (29,2) (19,25) (27,1) (19,11) (17,18) (15,30) (5,24) (13,4) (0,20) (11,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1148", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (6,20) (16,23) (2,21) (20,2) (11,16) (24,3) (7,10) (1,0) (21,14) (19,23) (10,26) (3,0) (21,12) (7,13) (4,22) (3,8) (1,19) (9,23) (8,7) (14,22) (15,8) (17,8) (12,24) (14,9) (12,25) (24,5) (2,0) (18,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1588", "image": "data/cycle/graph_visual/hard/graph1588.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (12,20) (9,14) (28,0) (30,21) (26,17) (0,27) (29,18) (25,7) (11,29) (13,2) (24,30) (0,1) (15,9) (25,6) (5,16) (22,16) (0,4) (11,0) (25,24) (10,13) (22,8) (5,23) (20,15) (4,2) (0,3) (3,13) (25,15) (18,13) (7,16) (2,0) (16,26) (6,19) (25,4) (5,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1363", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (23,8) (16,21) (19,5) (6,8) (13,15) (4,0) (0,3) (11,10) (18,15) (14,28) (21,2) (9,15) (15,20) (1,0) (22,27) (10,16) (4,14) (0,5) (22,3) (28,8) (0,2) (20,17) (6,26) (5,25) (28,5) (7,6) (24,21) (14,9) (3,1) (10,3) (24,25) (12,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1105", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (21,2) (4,23) (13,2) (2,0) (0,19) (11,8) (4,24) (18,22) (4,26) (3,8) (18,16) (10,3) (16,1) (19,11) (0,24) (26,16) (26,15) (9,10) (1,0) (20,12) (11,5) (25,3) (0,4) (9,13) (18,6) (3,0) (11,12) (0,7) (14,0) (17,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1322", "image": "data/cycle/graph_visual/hard/graph1322.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (9,3) (8,12) (19,16) (23,17) (17,0) (28,6) (22,28) (20,3) (13,18) (0,10) (0,3) (21,23) (4,15) (2,26) (16,7) (24,2) (2,6) (8,7) (23,11) (19,0) (25,18) (0,1) (17,6) (27,7) (21,3) (14,7) (5,0) (0,4) (13,1) (20,5) (0,2) (4,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1715", "image": "data/cycle/graph_visual/hard/graph1715.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (30,3) (2,16) (0,31) (29,1) (0,2) (28,5) (22,26) (0,4) (0,5) (14,12) (15,1) (27,8) (18,13) (24,12) (10,7) (29,25) (28,23) (0,3) (4,11) (2,6) (25,13) (6,11) (19,13) (26,1) (17,12) (30,25) (21,9) (12,5) (9,5) (1,0) (27,32) (1,5) (16,14) (20,17) (7,25) (8,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1734", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (19,1) (22,12) (17,1) (21,24) (4,29) (26,17) (0,2) (28,20) (0,1) (19,5) (6,17) (6,8) (27,20) (11,16) (10,20) (31,24) (9,2) (30,12) (14,7) (32,18) (3,0) (3,12) (7,23) (25,32) (26,27) (30,18) (0,17) (21,9) (5,23) (0,15) (13,28) (4,12) (31,16) (13,22) (5,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1462", "image": "data/cycle/graph_visual/hard/graph1462.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (8,7) (6,15) (25,16) (5,9) (6,25) (23,19) (18,14) (5,2) (3,0) (24,12) (14,26) (19,26) (5,0) (1,0) (20,14) (25,28) (12,6) (27,13) (12,5) (14,10) (11,26) (4,0) (0,2) (6,7) (21,4) (25,11) (23,17) (24,29) (27,15) (22,8) (1,18) (14,21) (21,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph18", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (0,11) (3,11) (13,8) (23,9) (1,10) (16,21) (25,24) (6,12) (15,6) (12,1) (18,4) (1,20) (24,0) (15,19) (21,22) (11,7) (17,2) (22,24) (20,25) (11,23) (9,14) (13,15) (18,17) (1,5) (25,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1511", "image": "data/cycle/graph_visual/hard/graph1511.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,1) (29,15) (14,6) (17,29) (21,16) (14,0) (13,21) (7,1) (30,8) (11,26) (28,3) (3,11) (14,27) (15,18) (16,12) (22,25) (4,18) (28,21) (19,21) (21,20) (27,23) (5,13) (22,28) (8,24) (27,26) (10,29) (2,24) (9,24) (23,1) (2,29) (22,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1896", "image": "data/cycle/graph_visual/hard/graph1896.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (13,17) (4,7) (33,3) (29,14) (9,30) (33,13) (0,4) (27,25) (20,22) (16,11) (9,10) (12,18) (14,20) (18,28) (26,25) (17,5) (22,16) (29,19) (31,17) (7,21) (2,0) (1,0) (0,5) (19,24) (0,3) (7,25) (6,2) (15,6) (1,21) (8,17) (23,16) (15,4) (10,0) (10,32) (28,16) (1,5) (33,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph81", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (14,17) (16,23) (11,19) (24,6) (5,2) (15,22) (21,3) (21,19) (6,12) (20,14) (23,25) (7,6) (5,12) (11,25) (8,14) (2,0) (10,14) (4,21) (12,25) (6,15) (9,5) (7,8) (13,25) (18,14) (18,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1525", "image": "data/cycle/graph_visual/hard/graph1525.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (18,23) (8,3) (1,0) (11,17) (5,26) (19,12) (28,24) (27,1) (14,3) (7,10) (30,6) (2,4) (5,24) (8,6) (2,21) (25,9) (25,24) (17,16) (15,4) (2,0) (15,20) (29,30) (8,11) (0,12) (26,3) (16,7) (13,9) (9,23) (1,7) (17,12) (29,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph403", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (24,14) (6,11) (25,15) (14,28) (13,3) (16,2) (27,4) (25,16) (9,5) (18,28) (5,14) (21,29) (27,20) (14,3) (29,26) (22,6) (10,12) (5,10) (7,3) (27,8) (11,3) (9,17) (16,8) (8,10) (19,16) (19,1) (23,25) (0,27) (29,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1822", "image": "data/cycle/graph_visual/hard/graph1822.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (31,15) (30,9) (0,24) (7,5) (25,6) (0,1) (3,4) (23,17) (0,2) (14,28) (13,11) (2,8) (31,28) (28,8) (22,28) (16,4) (10,24) (0,21) (1,26) (1,33) (7,31) (29,1) (32,14) (20,1) (13,24) (12,6) (19,27) (6,20) (33,31) (27,1) (17,14) (13,27) (0,30) (24,18) (1,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph456", "image": "data/cycle/graph_visual/hard/graph456.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (25,3) (18,5) (24,0) (7,26) (25,15) (24,21) (27,13) (25,6) (29,17) (16,1) (13,29) (21,4) (8,14) (8,15) (10,24) (19,4) (10,11) (2,15) (28,17) (23,6) (1,0) (27,23) (2,9) (18,15) (23,22) (20,18) (12,24) (0,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1419", "image": "data/cycle/graph_visual/hard/graph1419.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,6) (15,0) (24,16) (1,4) (8,3) (2,8) (11,15) (28,24) (12,13) (12,20) (23,6) (3,0) (26,12) (14,15) (5,27) (24,9) (25,28) (19,24) (20,18) (2,0) (19,13) (26,27) (21,25) (15,3) (0,1) (29,22) (25,7) (0,22) (24,0) (17,14) (18,4) (10,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph865", "image": "data/cycle/graph_visual/hard/graph865.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (24,19) (29,1) (13,15) (30,4) (9,1) (28,16) (9,31) (1,30) (26,33) (5,18) (18,0) (6,26) (18,29) (26,11) (19,14) (23,2) (7,14) (14,15) (0,17) (25,1) (0,10) (29,32) (18,14) (19,20) (21,22) (26,16) (28,8) (23,16) (3,30) (12,16) (9,21) (19,23) (27,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1549", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (3,0) (18,20) (6,25) (17,29) (8,0) (4,21) (17,30) (8,14) (15,18) (15,8) (12,24) (2,9) (5,18) (0,1) (24,10) (11,28) (13,29) (30,21) (25,3) (4,0) (5,0) (19,4) (24,22) (26,23) (24,0) (0,2) (27,23) (6,23) (27,13) (15,2) (11,10) (7,26) (16,1) (15,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph948", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (17,16) (20,17) (33,32) (3,7) (29,20) (33,22) (0,31) (2,32) (24,28) (16,27) (20,4) (8,2) (6,19) (0,27) (29,21) (14,8) (5,7) (19,7) (9,26) (13,22) (1,32) (13,11) (9,28) (10,34) (11,18) (14,28) (17,15) (32,30) (28,7) (12,10) (25,10) (26,15) (0,12) (17,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1884", "image": "data/cycle/graph_visual/hard/graph1884.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (5,8) (7,30) (23,8) (4,11) (9,14) (33,9) (30,12) (24,31) (30,15) (30,21) (2,19) (1,19) (30,24) (20,12) (25,22) (10,2) (16,18) (17,1) (29,14) (32,0) (4,10) (25,28) (25,27) (0,13) (26,9) (30,17) (16,14) (3,15) (23,33) (8,28) (6,23) (0,4) (0,1) (24,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph788", "image": "data/cycle/graph_visual/hard/graph788.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,21) (5,32) (17,21) (4,29) (24,10) (18,8) (23,14) (30,20) (1,2) (25,31) (28,12) (28,27) (32,9) (32,20) (10,2) (3,25) (3,10) (11,29) (23,7) (22,32) (13,0) (1,13) (23,26) (16,19) (22,8) (15,22) (29,8) (8,14) (17,9) (3,16) (12,14) (30,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph958", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (29,15) (13,23) (4,24) (24,7) (14,6) (5,9) (27,21) (27,7) (1,18) (10,6) (9,28) (25,22) (32,17) (30,8) (25,3) (1,32) (31,32) (27,19) (12,29) (24,11) (18,2) (3,33) (6,26) (8,24) (4,3) (3,34) (2,0) (11,23) (11,17) (31,16) (31,29) (32,10) (20,23) (9,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph412", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (28,7) (4,15) (4,23) (2,27) (21,3) (19,16) (16,7) (3,20) (18,26) (6,22) (21,23) (9,3) (7,14) (17,0) (5,20) (6,2) (10,0) (22,29) (1,13) (18,13) (8,12) (23,28) (7,8) (6,17) (0,19) (24,17) (23,11) (25,2) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph262", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (13,0) (5,4) (23,9) (12,27) (2,17) (1,8) (21,27) (16,7) (4,19) (18,21) (13,4) (4,27) (15,20) (23,6) (25,2) (9,3) (22,7) (14,5) (6,26) (0,9) (23,20) (20,7) (10,21) (27,17) (25,11) (24,5) (21,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1390", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (9,12) (6,23) (13,27) (20,24) (8,22) (8,15) (27,2) (18,25) (26,22) (4,2) (20,4) (20,3) (0,6) (28,23) (24,19) (14,6) (10,17) (19,7) (22,25) (25,16) (15,1) (21,6) (1,0) (13,14) (17,20) (24,26) (5,3) (11,21) (12,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph837", "image": "data/cycle/graph_visual/hard/graph837.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (9,3) (5,19) (17,9) (13,31) (28,18) (7,19) (25,0) (15,5) (17,6) (11,20) (16,14) (1,4) (18,7) (8,17) (16,32) (9,26) (4,26) (0,7) (20,22) (4,29) (23,21) (16,22) (4,27) (11,2) (30,24) (21,1) (12,31) (27,13) (10,26) (8,30) (33,20) (3,2) (19,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph502", "image": "data/cycle/graph_visual/hard/graph502.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (9,30) (1,21) (29,21) (15,14) (26,11) (6,29) (20,30) (25,16) (12,23) (30,18) (13,16) (14,23) (25,3) (9,7) (13,11) (3,17) (6,10) (4,14) (12,22) (28,20) (5,24) (8,1) (5,22) (17,27) (2,3) (14,8) (23,2) (10,7) (0,4) (24,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph159", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (14,15) (6,0) (8,1) (18,9) (20,12) (23,26) (6,25) (24,17) (12,2) (26,7) (26,16) (26,5) (3,13) (18,3) (18,21) (9,1) (22,18) (24,3) (11,9) (4,24) (8,19) (0,10) (15,1) (23,21) (16,6) (13,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph849", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (28,5) (23,25) (3,22) (33,3) (12,18) (23,0) (33,8) (30,18) (6,17) (2,1) (24,30) (33,2) (11,4) (28,12) (10,33) (31,15) (32,7) (4,13) (19,32) (31,0) (29,12) (21,7) (16,1) (6,20) (13,9) (14,15) (31,2) (21,20) (26,8) (5,21) (7,10) (9,19) (27,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1649", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (31,28) (3,0) (29,5) (26,11) (0,23) (15,19) (4,1) (25,15) (29,0) (7,6) (26,4) (1,0) (2,10) (7,3) (27,19) (2,18) (26,8) (28,0) (18,22) (13,17) (17,12) (30,25) (2,0) (25,10) (21,11) (20,17) (14,27) (4,0) (31,6) (7,11) (23,9) (10,9) (28,24) (31,16) (13,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1149", "image": "data/cycle/graph_visual/hard/graph1149.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (16,14) (10,2) (10,0) (20,19) (13,23) (5,12) (26,13) (4,5) (7,11) (19,17) (23,1) (14,23) (14,3) (8,9) (5,22) (21,2) (16,18) (19,22) (0,15) (19,6) (4,8) (0,2) (12,25) (1,0) (24,1) (11,21) (22,14) (0,3) (10,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph851", "image": "data/cycle/graph_visual/hard/graph851.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (27,0) (14,8) (19,6) (11,13) (28,9) (20,4) (9,26) (12,33) (32,2) (28,7) (29,32) (18,11) (16,17) (5,7) (0,30) (33,22) (28,24) (20,10) (29,21) (14,28) (15,17) (0,12) (10,25) (17,23) (17,20) (16,27) (32,31) (3,7) (26,15) (19,7) (13,22) (8,2) (32,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph243", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (12,15) (23,18) (8,4) (2,3) (5,24) (19,0) (4,27) (26,12) (23,5) (16,21) (15,25) (20,19) (18,10) (9,17) (11,9) (17,25) (7,0) (13,22) (14,6) (24,9) (15,22) (7,1) (2,20) (14,0) (27,21) (26,0) (21,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph750", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (4,16) (8,17) (32,5) (25,30) (12,2) (2,15) (13,31) (20,26) (24,12) (6,12) (1,26) (3,16) (18,30) (10,1) (21,27) (6,7) (21,28) (9,20) (25,5) (20,8) (31,29) (21,20) (28,19) (4,6) (9,0) (6,5) (10,11) (26,14) (26,22) (27,5) (13,15) (23,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1686", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (7,11) (19,22) (20,19) (6,7) (11,21) (2,23) (21,10) (29,9) (5,12) (5,19) (20,26) (8,19) (10,24) (2,28) (1,15) (0,1) (27,5) (5,4) (0,2) (12,2) (31,0) (13,1) (31,6) (24,17) (3,0) (5,29) (16,19) (3,14) (18,31) (6,5) (8,14) (30,16) (23,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph618", "image": "data/cycle/graph_visual/hard/graph618.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (9,15) (12,24) (25,10) (2,22) (8,23) (10,2) (11,9) (27,28) (6,28) (1,6) (27,20) (14,16) (29,21) (22,1) (31,9) (30,9) (16,0) (12,3) (5,16) (26,24) (1,15) (20,4) (7,0) (1,18) (8,22) (3,17) (5,12) (12,9) (20,29) (12,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph947", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (17,27) (22,24) (23,3) (21,17) (29,21) (20,22) (32,27) (30,27) (30,8) (31,5) (5,11) (34,13) (31,1) (12,25) (0,14) (26,4) (27,6) (14,21) (16,14) (5,4) (4,21) (2,17) (15,20) (15,7) (9,22) (28,12) (0,33) (14,20) (34,28) (12,6) (18,5) (23,6) (21,10) (9,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph531", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (3,5) (27,15) (20,1) (19,23) (1,28) (22,10) (15,11) (16,0) (17,12) (7,26) (26,0) (4,8) (9,25) (8,11) (29,22) (11,3) (20,21) (7,12) (20,29) (24,30) (14,24) (28,5) (26,18) (2,19) (13,30) (17,30) (6,23) (16,23) (7,27) (14,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1860", "image": "data/cycle/graph_visual/hard/graph1860.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (2,17) (33,15) (0,6) (4,5) (2,32) (31,28) (1,0) (29,32) (16,24) (18,26) (4,27) (22,3) (0,20) (0,25) (23,2) (15,12) (14,15) (6,1) (22,21) (27,33) (30,22) (1,19) (16,30) (28,15) (29,7) (23,22) (13,25) (8,21) (14,26) (12,21) (10,32) (16,9) (24,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1433", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (24,8) (20,2) (3,0) (25,12) (11,14) (26,21) (12,20) (6,19) (2,16) (5,9) (10,17) (29,8) (12,7) (4,14) (21,22) (9,22) (0,1) (22,6) (15,14) (25,13) (21,13) (16,10) (1,3) (4,26) (23,21) (28,7) (2,0) (29,0) (0,4) (27,19) (3,4) (18,3) (24,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1818", "image": "data/cycle/graph_visual/hard/graph1818.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (6,22) (26,1) (24,29) (7,23) (12,14) (3,0) (11,3) (21,8) (15,22) (2,0) (29,23) (13,24) (22,17) (5,32) (18,5) (17,16) (15,32) (10,19) (9,19) (0,28) (16,26) (2,4) (23,14) (14,21) (31,33) (8,11) (25,0) (1,20) (31,22) (1,0) (18,4) (31,23) (9,1) (28,20) (4,0) (27,4) (30,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph83", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (25,17) (2,5) (0,21) (12,16) (1,25) (19,12) (0,8) (0,3) (13,20) (3,22) (18,9) (23,17) (25,8) (13,21) (15,23) (14,7) (10,8) (15,24) (14,16) (17,6) (19,1) (10,11) (4,11) (2,13) (18,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph298", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (21,26) (21,10) (14,23) (4,20) (22,18) (23,17) (4,9) (16,14) (15,0) (17,3) (17,7) (24,6) (24,23) (7,15) (27,16) (8,12) (0,2) (1,21) (4,22) (5,3) (3,13) (12,4) (1,25) (24,19) (1,4) (11,1) (4,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1200", "image": "data/cycle/graph_visual/hard/graph1200.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (13,2) (12,3) (0,1) (15,12) (12,11) (2,0) (5,23) (8,23) (3,10) (5,4) (11,9) (17,24) (11,26) (5,18) (26,19) (3,16) (21,19) (1,18) (22,25) (27,0) (1,19) (3,20) (4,14) (17,3) (6,15) (11,2) (20,27) (21,25) (7,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1758", "image": "data/cycle/graph_visual/hard/graph1758.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (24,20) (14,11) (4,7) (31,30) (29,5) (26,0) (32,16) (25,8) (24,15) (11,17) (9,30) (0,1) (5,32) (12,9) (4,19) (19,2) (7,17) (3,0) (23,6) (22,26) (8,12) (3,8) (13,21) (16,23) (26,32) (26,9) (18,1) (7,21) (1,15) (3,27) (18,10) (0,2) (26,19) (13,28) (25,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph965", "image": "data/cycle/graph_visual/hard/graph965.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,5) (26,16) (12,2) (12,32) (17,12) (27,31) (22,34) (6,2) (13,20) (11,23) (23,5) (31,15) (6,18) (2,8) (24,6) (19,26) (29,16) (1,14) (26,23) (6,28) (27,21) (5,21) (1,17) (16,28) (30,5) (0,10) (30,9) (20,34) (12,34) (33,18) (0,9) (25,12) (7,16) (4,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1058", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (19,13) (11,25) (10,17) (8,11) (2,5) (1,6) (20,14) (25,3) (25,12) (24,14) (13,21) (16,22) (14,18) (17,23) (19,2) (0,1) (4,25) (14,4) (7,5) (2,0) (15,17) (21,0) (18,13) (17,25) (1,3) (16,10) (10,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph132", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (2,6) (11,4) (2,17) (8,20) (17,21) (6,7) (24,14) (3,11) (0,15) (21,22) (16,2) (11,5) (26,2) (12,22) (7,10) (25,3) (24,26) (13,15) (9,7) (15,10) (11,10) (10,19) (7,20) (4,23) (1,8) (17,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph46", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (21,14) (20,10) (24,17) (18,1) (10,11) (21,5) (25,16) (0,24) (6,3) (8,4) (1,22) (11,7) (5,13) (10,23) (12,6) (25,0) (2,22) (20,13) (16,4) (19,0) (12,15) (11,8) (9,10) (8,2) (3,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1025", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (25,21) (8,9) (12,18) (18,9) (25,20) (0,2) (21,7) (6,15) (5,2) (2,11) (3,22) (19,11) (0,4) (4,1) (2,17) (21,1) (23,17) (8,11) (4,23) (0,3) (6,0) (22,14) (18,10) (9,13) (8,15) (0,1) (18,14) (20,16) (24,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph423", "image": "data/cycle/graph_visual/hard/graph423.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (4,16) (24,4) (15,11) (16,6) (7,28) (10,13) (24,3) (25,19) (28,18) (3,19) (0,27) (18,11) (23,15) (1,13) (8,1) (6,27) (12,2) (12,29) (26,29) (25,29) (22,9) (15,14) (16,8) (5,24) (12,17) (20,25) (26,21) (9,4) (9,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph406", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (9,3) (24,7) (20,10) (21,18) (14,6) (14,12) (17,4) (14,16) (16,0) (22,24) (23,2) (15,27) (1,9) (24,17) (27,24) (23,11) (17,26) (1,15) (8,22) (19,11) (8,16) (25,15) (5,29) (26,10) (4,19) (6,21) (13,0) (12,29) (23,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1847", "image": "data/cycle/graph_visual/hard/graph1847.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (8,12) (15,29) (20,26) (17,14) (33,0) (28,14) (24,12) (28,8) (14,7) (27,1) (1,0) (15,4) (22,13) (8,20) (17,32) (10,8) (16,8) (23,10) (0,2) (13,9) (26,1) (7,2) (26,6) (4,6) (4,0) (19,26) (0,3) (25,12) (13,21) (5,11) (32,11) (9,25) (30,11) (29,18) (3,8) (0,12) (31,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph551", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (2,19) (19,26) (14,6) (9,21) (4,19) (15,26) (17,12) (20,5) (23,11) (5,4) (4,21) (28,0) (29,23) (9,7) (10,8) (16,1) (17,13) (17,16) (22,14) (25,24) (10,9) (18,0) (10,28) (12,15) (21,14) (27,0) (26,3) (24,26) (11,7) (2,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1597", "image": "data/cycle/graph_visual/hard/graph1597.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (26,18) (16,11) (0,1) (13,1) (5,22) (9,17) (14,26) (17,26) (21,23) (5,8) (24,7) (4,0) (25,20) (15,13) (15,10) (1,25) (5,19) (6,9) (18,27) (3,28) (16,25) (21,8) (2,30) (29,6) (12,9) (4,26) (29,24) (15,2) (4,3) (15,3) (5,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1723", "image": "data/cycle/graph_visual/hard/graph1723.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,2) (17,20) (31,11) (0,3) (30,22) (11,19) (12,17) (1,0) (32,28) (18,16) (3,27) (24,22) (29,8) (25,2) (29,7) (4,0) (24,26) (10,13) (16,29) (26,2) (19,23) (20,4) (1,2) (8,27) (13,0) (23,21) (10,2) (9,31) (14,31) (15,28) (15,4) (30,5) (26,18) (15,29) (6,0) (23,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph527", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (18,30) (13,6) (8,24) (24,22) (4,15) (17,3) (4,7) (22,25) (1,12) (17,23) (0,15) (1,21) (4,10) (2,0) (4,1) (14,23) (3,5) (17,7) (26,4) (16,13) (29,21) (1,28) (23,27) (21,11) (24,4) (3,19) (6,30) (7,20) (14,16) (9,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph567", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (5,13) (8,2) (30,27) (10,9) (14,29) (13,20) (6,18) (26,5) (24,21) (23,1) (27,0) (25,0) (10,29) (19,10) (17,12) (28,2) (22,28) (12,29) (11,7) (1,22) (8,4) (26,3) (25,16) (24,0) (4,16) (10,11) (3,6) (20,10) (11,8) (15,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph394", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (18,12) (14,24) (9,26) (6,0) (1,4) (9,13) (15,8) (18,10) (15,6) (25,26) (8,11) (5,2) (21,1) (20,11) (20,16) (11,2) (2,17) (7,21) (3,22) (4,23) (22,25) (9,8) (28,19) (28,18) (28,21) (18,14) (23,17) (27,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1011", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (1,18) (7,5) (21,5) (12,25) (23,24) (19,1) (0,1) (16,23) (11,25) (14,25) (15,21) (22,6) (2,0) (5,13) (2,3) (9,8) (23,10) (16,11) (17,9) (21,18) (2,4) (20,13) (3,0) (19,8) (11,2) (6,19) (12,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1907", "image": "data/cycle/graph_visual/hard/graph1907.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (19,3) (22,5) (14,3) (23,27) (15,5) (32,25) (34,7) (17,6) (30,14) (6,23) (16,34) (33,7) (0,1) (32,20) (31,3) (2,8) (3,27) (3,25) (11,3) (26,24) (8,18) (4,15) (9,1) (34,9) (2,13) (5,27) (12,4) (10,25) (4,28) (7,29) (0,20) (18,26) (9,26) (0,2) (21,13) (14,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph795", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (3,22) (29,2) (15,27) (13,11) (6,5) (31,5) (21,1) (0,14) (32,23) (16,24) (1,9) (1,26) (17,12) (31,23) (14,29) (5,7) (3,13) (24,6) (17,28) (27,28) (4,18) (19,10) (20,0) (25,26) (23,2) (13,23) (22,27) (1,32) (18,22) (8,12) (8,19) (30,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1869", "image": "data/cycle/graph_visual/hard/graph1869.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (22,6) (17,32) (8,32) (12,13) (10,25) (31,2) (23,22) (2,5) (18,14) (30,3) (12,16) (7,26) (0,23) (25,18) (25,11) (10,29) (0,24) (1,0) (27,0) (8,13) (26,12) (9,3) (21,19) (31,4) (20,2) (11,32) (30,12) (1,22) (33,26) (21,2) (28,12) (31,17) (19,24) (15,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1844", "image": "data/cycle/graph_visual/hard/graph1844.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,15) (19,6) (5,7) (8,14) (20,10) (12,0) (14,28) (9,26) (0,27) (0,30) (0,4) (21,29) (4,20) (18,11) (32,29) (33,12) (2,0) (13,22) (0,3) (23,17) (10,25) (9,28) (26,15) (24,28) (28,7) (32,2) (32,1) (27,16) (1,0) (2,8) (17,20) (31,32) (3,7) (7,19) (11,13) (22,33) (17,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1406", "image": "data/cycle/graph_visual/hard/graph1406.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (5,1) (8,12) (16,19) (3,5) (14,27) (28,21) (6,23) (11,13) (4,24) (25,5) (15,29) (3,15) (0,1) (5,14) (5,0) (18,19) (3,21) (13,7) (26,9) (10,14) (28,22) (15,13) (2,3) (24,21) (19,8) (1,9) (0,2) (1,20) (13,17) (8,29) (6,20) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1989", "image": "data/cycle/graph_visual/hard/graph1989.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (3,24) (22,5) (21,11) (18,33) (26,12) (12,4) (11,6) (13,26) (11,29) (16,15) (23,31) (8,14) (25,1) (13,9) (15,10) (34,0) (7,14) (13,24) (23,24) (17,2) (5,21) (33,32) (8,5) (25,20) (30,5) (5,33) (0,1) (24,16) (30,20) (17,0) (9,29) (19,34) (28,12) (31,27) (25,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph283", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (0,21) (25,11) (1,18) (13,4) (1,26) (27,20) (27,12) (8,25) (25,4) (20,6) (17,10) (18,23) (0,19) (2,22) (3,24) (6,19) (19,16) (5,17) (2,20) (7,16) (4,17) (15,0) (24,8) (15,14) (16,23) (6,25) (9,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1757", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (23,30) (31,2) (0,2) (11,21) (13,18) (9,6) (17,22) (1,8) (21,18) (12,14) (28,25) (26,9) (10,16) (32,9) (0,24) (30,8) (6,7) (3,16) (19,24) (20,29) (10,20) (15,0) (1,7) (13,4) (27,2) (9,28) (1,0) (24,17) (15,1) (18,27) (5,24) (7,3) (23,4) (14,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph724", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (6,27) (27,28) (25,3) (9,1) (29,5) (4,25) (25,1) (29,19) (18,5) (15,17) (21,1) (15,0) (13,11) (16,8) (22,4) (22,26) (10,25) (8,19) (2,18) (24,10) (4,23) (31,19) (15,1) (12,16) (8,30) (7,31) (17,6) (20,0) (19,32) (3,13) (17,7) (14,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph830", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (1,25) (11,0) (15,33) (22,8) (0,16) (9,20) (4,20) (27,28) (10,31) (9,12) (28,6) (26,33) (6,1) (32,21) (10,2) (16,17) (29,8) (30,23) (5,12) (5,16) (32,7) (13,9) (2,22) (3,19) (22,1) (12,14) (27,20) (18,32) (3,12) (15,1) (29,23) (12,24) (24,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1059", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (19,2) (11,15) (6,3) (3,0) (7,16) (16,23) (5,1) (13,16) (19,5) (21,23) (1,23) (0,18) (11,1) (11,20) (6,14) (22,9) (17,14) (14,23) (8,4) (12,22) (4,22) (2,0) (0,1) (24,5) (25,11) (23,8) (10,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1529", "image": "data/cycle/graph_visual/hard/graph1529.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (18,21) (17,12) (4,26) (18,19) (22,1) (13,14) (15,24) (2,0) (3,10) (27,16) (20,29) (24,7) (8,28) (28,27) (7,23) (3,5) (26,12) (29,27) (6,10) (21,24) (7,6) (19,2) (7,17) (11,22) (3,0) (27,17) (9,30) (24,14) (6,0) (19,30) (21,25) (11,18) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph31", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (20,14) (3,21) (15,21) (0,1) (11,8) (22,1) (14,15) (9,11) (17,19) (0,11) (7,25) (25,12) (17,24) (20,2) (10,7) (0,18) (4,6) (23,24) (16,18) (13,1) (3,10) (25,6) (2,0) (13,5) (23,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1255", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (2,26) (17,8) (14,20) (27,4) (26,23) (6,10) (11,23) (1,16) (17,0) (21,9) (26,24) (10,0) (5,4) (19,25) (16,12) (19,0) (21,4) (0,1) (26,15) (22,24) (9,10) (17,13) (12,15) (7,11) (7,9) (21,14) (18,5) (14,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1720", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (28,11) (10,0) (9,20) (7,20) (26,17) (22,19) (12,18) (30,18) (1,14) (11,6) (15,32) (31,19) (32,31) (29,3) (14,4) (28,7) (30,10) (4,23) (26,21) (23,7) (17,20) (3,24) (2,17) (2,0) (4,13) (3,20) (1,0) (5,30) (8,32) (18,13) (15,20) (27,25) (27,15) (16,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1518", "image": "data/cycle/graph_visual/hard/graph1518.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (14,21) (19,4) (0,2) (21,9) (9,7) (1,0) (28,10) (17,16) (7,11) (30,2) (26,19) (23,11) (1,16) (6,14) (15,12) (0,18) (17,13) (0,28) (22,14) (12,17) (9,10) (27,0) (4,5) (21,4) (24,26) (20,5) (8,10) (15,26) (25,24) (0,3) (2,19) (23,29) (3,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph817", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (10,12) (22,4) (11,6) (21,24) (19,2) (18,25) (15,30) (5,21) (17,29) (9,20) (31,13) (5,23) (14,33) (27,3) (18,23) (15,0) (32,24) (25,8) (12,17) (14,3) (26,25) (16,6) (4,1) (18,19) (1,13) (1,16) (10,19) (28,23) (11,30) (5,9) (7,6) (17,16) (32,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1956", "image": "data/cycle/graph_visual/hard/graph1956.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,3) (0,20) (23,22) (9,16) (26,0) (20,27) (2,17) (1,6) (22,3) (28,15) (10,32) (8,21) (14,15) (32,28) (27,4) (11,24) (33,29) (5,4) (0,2) (16,24) (32,30) (22,31) (12,15) (18,26) (25,34) (13,25) (29,7) (33,2) (0,6) (21,22) (1,0) (15,34) (12,21) (16,30) (2,23) (1,19) (27,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1831", "image": "data/cycle/graph_visual/hard/graph1831.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (33,9) (11,16) (20,3) (12,11) (26,29) (0,4) (0,3) (0,2) (11,22) (26,12) (19,25) (14,5) (19,32) (11,8) (23,27) (21,16) (32,9) (1,16) (22,13) (7,33) (7,30) (28,6) (3,17) (0,1) (20,21) (4,1) (17,14) (0,8) (1,27) (2,15) (28,19) (10,7) (31,3) (20,18) (5,15) (11,25) (24,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1246", "image": "data/cycle/graph_visual/hard/graph1246.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (17,14) (12,13) (0,24) (19,24) (22,6) (12,20) (11,15) (6,3) (4,1) (21,25) (0,2) (8,2) (0,3) (26,24) (10,2) (0,4) (24,9) (4,18) (13,19) (1,0) (16,24) (20,18) (14,15) (23,26) (3,15) (27,5) (0,27) (25,12) (8,3) (0,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph652", "image": "data/cycle/graph_visual/hard/graph652.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (6,2) (4,18) (20,21) (0,4) (5,7) (27,25) (22,8) (11,26) (10,24) (22,12) (5,31) (14,26) (26,21) (1,2) (14,10) (17,19) (1,13) (9,25) (19,27) (28,6) (17,14) (22,16) (26,30) (12,27) (26,28) (3,22) (18,5) (14,15) (12,29) (30,31) (23,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph10", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (4,19) (21,24) (13,3) (17,23) (24,6) (0,2) (15,0) (23,25) (8,12) (24,16) (17,3) (12,4) (14,7) (1,22) (9,4) (22,15) (1,11) (4,1) (7,4) (20,23) (21,10) (5,3) (21,1) (18,4) (7,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1539", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (15,29) (11,23) (10,16) (11,16) (27,3) (2,19) (17,22) (18,16) (21,0) (1,0) (8,28) (1,23) (0,27) (0,2) (4,29) (20,14) (23,19) (23,14) (1,24) (27,11) (30,5) (8,4) (9,6) (13,15) (12,22) (28,7) (26,5) (22,29) (6,14) (23,28) (25,29) (1,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1763", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (1,18) (32,19) (2,31) (7,18) (23,24) (29,0) (20,32) (0,2) (5,13) (10,21) (13,8) (8,3) (12,1) (3,11) (15,1) (9,8) (26,25) (10,27) (26,12) (1,0) (4,12) (7,32) (30,16) (28,24) (17,2) (23,15) (15,22) (3,0) (6,27) (30,1) (30,13) (14,9) (20,29) (27,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph827", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (9,15) (33,18) (24,8) (28,33) (3,19) (4,23) (29,11) (0,13) (23,1) (1,0) (6,16) (22,10) (7,31) (20,13) (23,8) (32,29) (20,30) (25,29) (6,31) (4,2) (19,8) (27,5) (4,21) (18,14) (7,24) (33,30) (26,10) (17,11) (1,27) (16,15) (32,26) (29,13) (28,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1569", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (28,7) (25,30) (3,0) (29,15) (2,26) (20,5) (4,18) (15,16) (24,30) (14,9) (3,27) (14,13) (1,0) (26,8) (11,5) (28,15) (7,12) (1,29) (5,22) (16,19) (8,20) (23,0) (27,5) (0,24) (9,28) (18,11) (5,21) (16,0) (21,17) (5,6) (10,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1275", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (23,2) (17,24) (17,21) (8,22) (9,0) (4,19) (4,17) (13,10) (1,7) (24,22) (23,11) (15,20) (5,24) (16,0) (15,1) (23,26) (15,27) (1,0) (21,12) (6,14) (10,26) (6,18) (14,27) (14,16) (8,16) (9,3) (11,19) (25,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1128", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (16,9) (20,17) (1,14) (3,12) (23,0) (20,24) (2,0) (8,15) (3,19) (2,22) (25,26) (5,17) (23,8) (21,19) (26,6) (21,10) (7,18) (13,7) (18,16) (10,14) (25,24) (23,24) (1,0) (22,11) (23,4) (14,17) (15,13) (5,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph873", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (2,24) (23,9) (7,3) (10,29) (10,27) (17,33) (0,21) (5,23) (27,28) (7,8) (24,6) (14,13) (6,18) (11,19) (20,32) (26,5) (21,2) (12,17) (11,0) (29,1) (32,8) (29,22) (21,25) (31,10) (28,30) (24,4) (17,5) (8,16) (13,18) (26,14) (32,4) (15,10) (15,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph2", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (18,3) (22,6) (20,12) (16,2) (4,11) (19,8) (9,4) (23,17) (15,22) (18,14) (10,19) (6,7) (7,21) (5,17) (11,15) (15,12) (24,17) (17,15) (20,13) (2,19) (15,0) (20,25) (7,1) (0,18) (8,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph47", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (11,4) (6,7) (16,2) (14,24) (15,0) (19,10) (20,7) (8,20) (17,2) (15,13) (22,21) (23,4) (7,9) (10,11) (15,10) (22,12) (17,21) (5,11) (3,24) (17,18) (11,3) (8,1) (2,25) (2,6) (7,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1370", "image": "data/cycle/graph_visual/hard/graph1370.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (10,6) (0,1) (27,17) (4,14) (10,7) (20,6) (22,12) (13,16) (24,11) (2,23) (13,11) (1,21) (4,0) (12,23) (9,26) (25,3) (16,25) (7,9) (5,22) (15,14) (24,18) (2,0) (8,1) (17,3) (0,5) (14,8) (3,2) (19,5) (14,23) (20,21) (28,26) (3,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph632", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (8,24) (1,3) (18,12) (11,27) (9,27) (23,27) (14,23) (20,5) (17,25) (25,31) (23,2) (10,1) (14,15) (17,15) (23,10) (2,0) (22,6) (31,6) (21,25) (30,11) (24,20) (24,18) (29,8) (30,7) (4,14) (16,26) (9,28) (8,16) (9,24) (19,1) (27,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph739", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (25,21) (22,20) (19,7) (19,32) (2,23) (28,0) (8,5) (14,29) (3,24) (5,1) (13,22) (27,12) (5,14) (2,16) (6,9) (2,14) (32,5) (26,32) (18,24) (25,16) (3,30) (0,29) (30,15) (11,9) (11,5) (32,12) (24,14) (20,27) (27,31) (19,10) (12,4) (17,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1179", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (6,9) (16,12) (5,18) (15,20) (24,17) (4,23) (14,23) (9,5) (8,2) (0,1) (23,10) (21,19) (17,13) (11,23) (9,2) (12,21) (0,2) (10,12) (6,1) (7,26) (17,15) (4,3) (2,11) (23,13) (24,26) (12,22) (4,0) (3,0) (16,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1102", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (4,15) (22,24) (9,25) (2,4) (12,17) (0,1) (1,23) (24,8) (10,9) (21,9) (3,13) (17,16) (0,2) (2,20) (14,23) (6,7) (25,3) (5,24) (7,16) (19,15) (5,26) (3,26) (0,12) (12,18) (11,8) (11,17) (1,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph201", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (9,11) (8,21) (26,16) (22,15) (3,0) (20,27) (25,10) (9,6) (4,25) (5,9) (19,17) (2,13) (7,12) (26,12) (24,5) (3,22) (23,24) (20,10) (7,0) (22,18) (16,25) (8,13) (16,1) (21,17) (13,23) (27,8) (11,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph98", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (4,23) (23,21) (0,10) (4,15) (17,2) (2,6) (23,18) (16,7) (18,13) (9,3) (13,1) (20,5) (24,2) (7,8) (19,0) (0,1) (7,14) (23,11) (16,19) (20,3) (7,6) (8,12) (25,0) (21,3) (17,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph828", "image": "data/cycle/graph_visual/hard/graph828.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (11,23) (11,15) (24,20) (28,11) (26,11) (25,14) (12,9) (33,16) (4,6) (16,7) (5,19) (12,17) (23,30) (3,23) (27,21) (29,18) (8,27) (0,24) (0,15) (31,29) (12,1) (2,10) (32,16) (27,22) (6,12) (26,21) (22,25) (3,13) (30,19) (13,6) (9,2) (9,18) (9,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1268", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (6,17) (14,2) (21,24) (14,26) (13,20) (8,11) (10,1) (25,14) (23,8) (18,4) (20,6) (12,7) (11,24) (19,6) (1,0) (27,22) (26,0) (4,23) (1,4) (23,16) (21,9) (19,22) (0,16) (7,9) (20,1) (21,15) (5,16) (18,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph628", "image": "data/cycle/graph_visual/hard/graph628.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (9,30) (0,30) (8,28) (4,16) (19,27) (7,5) (6,25) (1,14) (2,8) (31,15) (1,20) (27,1) (13,27) (17,23) (20,6) (4,3) (6,12) (0,21) (1,29) (16,1) (31,28) (17,14) (14,28) (24,0) (26,1) (22,28) (24,10) (13,11) (13,24) (7,31) (24,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph150", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (1,26) (2,17) (23,2) (4,5) (15,3) (4,12) (25,26) (6,1) (1,18) (13,21) (14,17) (7,2) (20,2) (22,13) (2,10) (10,0) (11,18) (1,9) (3,11) (17,13) (12,26) (24,7) (20,8) (16,6) (1,13) (16,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph657", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (11,23) (5,21) (30,12) (21,27) (22,12) (8,2) (0,9) (16,7) (6,2) (31,15) (29,27) (5,25) (0,10) (26,19) (18,6) (6,20) (30,9) (17,1) (26,16) (20,13) (5,23) (3,5) (23,26) (4,31) (28,16) (12,18) (16,24) (14,1) (2,31) (6,28) (12,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1185", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (18,21) (2,11) (8,25) (26,9) (6,3) (24,22) (1,0) (8,4) (15,1) (20,17) (17,11) (10,24) (1,23) (5,13) (19,9) (21,1) (13,25) (4,14) (16,17) (12,16) (3,10) (1,20) (7,19) (7,16) (2,0) (23,14) (24,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph495", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (15,17) (8,5) (1,20) (21,25) (29,23) (12,2) (8,4) (3,22) (28,25) (10,0) (27,9) (15,7) (13,9) (28,23) (0,3) (11,8) (19,2) (2,16) (0,15) (2,4) (23,24) (9,18) (20,26) (19,27) (10,14) (6,13) (28,1) (25,8) (3,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph805", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (1,23) (17,11) (24,8) (1,0) (31,7) (30,33) (11,29) (15,16) (1,27) (4,21) (9,15) (33,28) (3,19) (13,0) (16,6) (2,4) (8,19) (20,13) (4,23) (22,10) (32,29) (12,28) (14,18) (30,20) (5,27) (13,29) (23,8) (33,18) (7,24) (32,26) (26,10) (29,25) (6,31)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1471", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (2,15) (12,26) (3,0) (17,29) (18,27) (4,0) (20,14) (2,11) (29,10) (3,1) (0,1) (20,7) (11,25) (11,6) (14,27) (7,25) (13,0) (2,9) (5,2) (19,21) (27,3) (23,16) (10,15) (24,11) (0,5) (9,22) (0,2) (19,17) (19,8) (4,17) (19,28) (29,16) (12,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph807", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (24,2) (17,26) (8,1) (30,9) (31,28) (3,31) (25,28) (6,9) (4,28) (0,33) (31,10) (23,32) (12,13) (6,16) (14,15) (24,11) (19,21) (20,24) (12,3) (24,0) (22,13) (19,7) (17,23) (18,29) (14,28) (0,17) (5,27) (18,26) (2,28) (30,8) (16,17) (21,33) (5,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1073", "image": "data/cycle/graph_visual/hard/graph1073.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (13,0) (4,11) (0,23) (9,6) (1,10) (0,2) (20,7) (18,15) (21,5) (1,7) (3,0) (12,4) (25,20) (4,0) (2,22) (16,8) (21,2) (25,17) (3,9) (24,25) (14,15) (1,12) (8,7) (13,25) (9,18) (10,14) (4,5) (19,25) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1234", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (0,3) (11,23) (5,15) (25,18) (21,26) (7,10) (4,25) (8,9) (17,19) (0,1) (24,15) (22,25) (12,14) (2,22) (9,13) (27,23) (20,27) (16,14) (5,14) (26,2) (1,9) (13,6) (4,0) (25,7) (11,22) (3,23) (2,0) (16,4) (3,17) (27,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1421", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (6,19) (11,12) (4,18) (0,3) (29,28) (11,19) (12,3) (1,2) (8,0) (12,27) (1,11) (10,17) (13,9) (0,1) (0,2) (13,20) (12,22) (3,20) (26,19) (29,16) (15,9) (16,7) (0,27) (14,7) (28,20) (25,23) (18,26) (24,0) (15,10) (21,28) (23,5) (16,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph359", "image": "data/cycle/graph_visual/hard/graph359.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (24,23) (4,19) (7,9) (16,10) (15,20) (26,14) (1,20) (24,21) (23,27) (21,17) (11,22) (1,12) (21,9) (7,13) (28,5) (8,11) (18,3) (28,8) (0,26) (0,16) (25,14) (4,1) (28,16) (6,18) (23,4) (20,6) (14,2) (28,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph585", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (20,30) (6,10) (30,18) (2,3) (1,8) (28,20) (17,27) (14,8) (23,2) (11,26) (5,22) (13,11) (16,25) (12,22) (13,16) (14,4) (24,19) (23,14) (0,4) (1,21) (7,10) (3,17) (30,9) (3,25) (9,7) (5,24) (14,15) (23,12) (29,21) (29,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1514", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (5,18) (22,8) (11,14) (1,25) (17,22) (3,2) (28,8) (30,15) (14,20) (2,11) (9,15) (3,16) (12,30) (9,23) (1,19) (5,21) (27,11) (0,20) (23,13) (21,26) (10,11) (2,0) (7,24) (13,6) (13,4) (12,18) (3,0) (23,19) (18,24) (19,10) (22,10) (29,24) (0,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph253", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (20,14) (18,3) (23,7) (6,4) (5,6) (1,6) (27,9) (27,15) (25,14) (10,20) (9,13) (12,11) (14,8) (0,15) (11,9) (25,22) (8,23) (17,1) (26,6) (0,3) (21,12) (6,15) (18,25) (19,13) (24,19) (16,6) (2,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph470", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (1,0) (20,2) (21,15) (11,7) (1,24) (0,11) (4,6) (23,27) (21,3) (26,23) (25,28) (3,26) (2,0) (12,26) (19,18) (6,25) (13,25) (0,18) (14,20) (8,28) (9,29) (26,29) (13,5) (14,15) (8,11) (16,1) (26,10) (24,17) (22,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph880", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (17,21) (13,33) (27,15) (27,16) (3,1) (9,11) (0,32) (32,18) (29,31) (12,15) (14,17) (4,17) (10,33) (26,4) (11,31) (20,31) (5,8) (11,18) (22,24) (19,23) (10,25) (7,28) (2,21) (3,6) (26,24) (20,10) (15,25) (18,1) (22,25) (5,0) (31,23) (7,32) (13,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph804", "image": "data/cycle/graph_visual/hard/graph804.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (27,6) (7,32) (11,3) (15,1) (2,31) (13,5) (19,32) (17,2) (20,32) (8,9) (22,15) (13,30) (29,0) (10,21) (1,18) (26,12) (23,24) (8,3) (27,14) (2,0) (13,8) (30,16) (20,29) (30,1) (25,26) (1,12) (14,9) (23,15) (27,10) (33,20) (7,18) (4,12) (28,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1277", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (6,1) (7,20) (4,15) (12,5) (3,0) (1,0) (10,20) (19,25) (18,8) (9,27) (1,21) (2,3) (0,2) (12,27) (0,4) (1,25) (17,9) (13,7) (24,10) (26,0) (18,16) (23,2) (16,14) (22,0) (4,17) (26,1) (18,17) (2,25) (26,20) (18,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph558", "image": "data/cycle/graph_visual/hard/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 30, and the edges are: (28,17) (24,5) (16,22) (21,19) (30,10) (23,18) (23,5) (30,7) (25,28) (29,0) (19,0) (2,3) (27,26) (6,20) (7,1) (27,4) (26,15) (29,2) (8,14) (11,0) (15,12) (10,18) (22,21) (9,17) (25,15) (12,29) (14,9) (20,0) (4,13) (24,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1977", "image": "data/cycle/graph_visual/hard/graph1977.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (32,33) (34,5) (28,14) (34,0) (30,15) (29,19) (24,10) (25,9) (14,17) (0,12) (13,9) (25,12) (7,2) (0,1) (20,8) (0,2) (4,6) (1,26) (8,12) (26,20) (10,8) (16,14) (4,15) (11,32) (33,17) (8,28) (21,26) (22,13) (26,6) (1,29) (27,12) (18,8) (11,31) (7,11) (8,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph822", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (14,0) (19,22) (1,32) (3,13) (1,24) (6,5) (3,22) (0,21) (4,18) (8,12) (27,15) (1,26) (26,28) (24,16) (20,8) (14,29) (27,29) (23,33) (7,5) (11,31) (30,2) (9,1) (13,23) (17,28) (22,27) (23,32) (12,17) (33,18) (31,5) (23,2) (6,25) (13,11) (19,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1801", "image": "data/cycle/graph_visual/hard/graph1801.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (24,11) (8,7) (16,0) (6,18) (4,31) (20,6) (18,13) (29,21) (14,1) (10,23) (0,3) (25,20) (17,20) (0,6) (24,25) (1,0) (30,10) (14,7) (5,33) (0,4) (11,9) (7,32) (18,2) (26,32) (6,4) (17,32) (19,24) (12,14) (15,1) (33,2) (3,26) (10,7) (22,4) (21,18) (27,19) (2,0) (28,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph461", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (6,25) (20,15) (26,17) (16,5) (8,22) (13,18) (26,0) (18,28) (22,5) (24,29) (11,29) (15,25) (25,24) (10,13) (0,11) (15,9) (0,27) (23,16) (5,1) (6,19) (21,16) (25,7) (16,7) (2,13) (9,14) (4,25) (20,12) (2,4) (13,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1824", "image": "data/cycle/graph_visual/hard/graph1824.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (24,7) (0,18) (2,13) (4,33) (32,23) (30,5) (27,28) (10,11) (20,21) (0,2) (19,4) (0,28) (8,13) (10,12) (7,1) (13,20) (2,23) (21,4) (14,12) (15,5) (22,29) (29,31) (19,28) (11,6) (0,1) (10,25) (10,20) (16,10) (19,31) (26,31) (17,9) (33,1) (3,0) (5,16) (3,24) (18,9)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1495", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (27,7) (1,13) (21,6) (27,2) (9,17) (16,12) (29,22) (15,0) (24,5) (22,20) (6,28) (20,25) (0,1) (14,8) (4,13) (6,23) (2,26) (25,17) (1,18) (4,14) (11,9) (15,6) (1,26) (19,20) (27,3) (12,1) (10,2) (15,25) (5,9) (4,11)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1882", "image": "data/cycle/graph_visual/hard/graph1882.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (10,12) (24,11) (16,8) (21,14) (25,23) (30,16) (9,6) (15,11) (4,13) (19,16) (1,30) (28,3) (9,32) (27,5) (15,29) (21,18) (31,4) (28,22) (20,23) (0,1) (12,4) (16,17) (22,0) (6,25) (33,25) (2,17) (15,31) (30,0) (4,5) (26,3) (26,27) (8,21) (18,7) (14,33)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1153", "image": "data/cycle/graph_visual/hard/graph1153.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (20,7) (17,13) (18,19) (25,7) (25,11) (5,0) (9,21) (12,23) (2,0) (2,9) (10,15) (3,1) (26,13) (24,0) (19,8) (2,11) (17,19) (2,5) (17,4) (0,4) (14,20) (3,14) (16,22) (3,0) (0,1) (6,11) (11,16) (15,2) (10,19) (13,12)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1118", "image": "data/cycle/graph_visual/hard/graph1118.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (9,26) (19,9) (13,15) (19,23) (0,3) (11,7) (22,9) (1,11) (14,12) (7,20) (16,22) (21,13) (15,3) (21,4) (10,21) (24,26) (8,17) (25,10) (18,20) (13,6) (0,14) (0,9) (8,7) (4,23) (0,1) (15,2) (7,0) (0,2) (9,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1864", "image": "data/cycle/graph_visual/hard/graph1864.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (15,3) (21,25) (26,5) (10,27) (10,31) (9,23) (28,30) (15,10) (0,11) (29,22) (7,3) (6,18) (0,1) (0,3) (21,2) (13,14) (4,24) (33,17) (24,2) (5,23) (28,27) (8,16) (26,14) (17,12) (18,13) (32,8) (20,32) (0,4) (1,29) (17,5) (19,11) (4,32) (0,2) (24,6) (7,8) (21,0) (29,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1193", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (25,6) (15,6) (16,6) (18,3) (0,3) (9,13) (13,19) (25,14) (26,15) (11,12) (18,9) (24,19) (0,1) (1,6) (17,1) (8,14) (2,18) (20,14) (4,0) (15,0) (6,5) (7,23) (4,6) (10,20) (0,2) (11,9) (12,21) (8,23) (25,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1434", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (5,24) (11,4) (28,17) (10,29) (1,7) (9,24) (0,2) (9,13) (2,3) (21,20) (0,8) (29,0) (9,17) (16,0) (15,25) (0,19) (15,12) (1,0) (26,22) (3,0) (25,28) (26,15) (14,7) (27,4) (23,18) (18,10) (27,12) (5,23) (21,19) (29,2) (14,22) (6,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1261", "image": "data/cycle/graph_visual/hard/graph1261.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (10,2) (1,0) (18,21) (7,2) (27,0) (3,27) (8,19) (11,26) (1,18) (19,1) (14,5) (13,5) (22,27) (0,2) (21,5) (25,12) (0,3) (20,13) (9,8) (11,2) (19,6) (20,12) (26,6) (23,25) (4,1) (23,15) (24,9) (17,21) (23,27) (16,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1199", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (1,0) (8,12) (26,16) (17,9) (2,24) (4,1) (23,10) (4,0) (2,26) (13,3) (3,11) (20,21) (15,25) (0,8) (3,22) (18,24) (23,4) (5,6) (19,10) (0,11) (17,22) (10,22) (2,0) (26,7) (12,24) (26,6) (20,17) (0,3) (16,15) (14,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph268", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (18,14) (4,11) (18,3) (17,5) (15,12) (21,8) (18,0) (15,11) (22,15) (27,20) (7,1) (19,2) (4,9) (16,2) (13,20) (26,17) (17,15) (26,0) (12,20) (22,6) (7,6) (25,26) (17,8) (7,23) (19,15) (19,10) (24,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph177", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (3,19) (15,8) (26,6) (21,10) (16,18) (23,0) (1,14) (20,24) (22,2) (12,3) (23,24) (18,7) (5,17) (24,25) (23,4) (17,20) (16,9) (13,15) (21,19) (8,23) (10,14) (11,22) (26,25) (7,13) (11,5) (17,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph914", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (27,14) (1,31) (9,25) (15,2) (20,34) (30,33) (30,29) (28,10) (8,7) (21,19) (26,19) (13,12) (22,24) (12,30) (1,2) (11,20) (5,6) (22,9) (5,3) (22,32) (26,3) (24,8) (23,5) (11,18) (12,19) (29,1) (2,10) (24,11) (4,29) (17,13) (14,28) (3,16) (0,31) (29,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1343", "image": "data/cycle/graph_visual/hard/graph1343.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (6,14) (25,20) (1,9) (18,3) (26,22) (10,2) (1,13) (12,13) (14,26) (25,5) (11,1) (7,2) (0,6) (0,18) (4,27) (4,28) (23,7) (20,8) (15,21) (1,5) (1,0) (18,19) (10,15) (27,13) (11,23) (26,16) (24,8) (15,16) (2,0) (17,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph876", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (10,32) (18,26) (24,16) (9,16) (0,25) (28,31) (2,17) (2,23) (0,6) (16,30) (15,14) (21,8) (21,22) (12,15) (32,29) (1,6) (24,11) (14,26) (27,20) (3,22) (29,7) (22,30) (1,19) (4,27) (13,25) (0,20) (33,15) (15,28) (5,4) (2,32) (27,33) (12,21) (22,23)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph189", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (9,2) (19,8) (16,11) (0,1) (24,0) (19,18) (1,3) (13,17) (17,19) (15,2) (7,25) (14,20) (12,23) (13,26) (9,21) (2,5) (13,12) (25,11) (6,11) (14,3) (10,15) (20,7) (22,16) (19,10) (4,17) (11,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1260", "image": "data/cycle/graph_visual/hard/graph1260.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (21,16) (15,20) (1,3) (13,15) (27,5) (3,0) (6,7) (14,4) (6,8) (10,3) (14,8) (25,24) (0,4) (2,0) (11,10) (3,22) (8,22) (5,19) (7,12) (14,9) (5,25) (26,27) (15,18) (0,1) (16,10) (20,17) (21,24) (21,2) (9,15) (0,5) (23,6)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1883", "image": "data/cycle/graph_visual/hard/graph1883.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (31,13) (22,5) (11,27) (10,29) (1,6) (32,30) (2,0) (9,21) (13,6) (23,33) (6,32) (17,20) (12,9) (14,28) (16,4) (19,9) (12,29) (25,27) (0,3) (26,22) (7,20) (18,9) (18,26) (26,8) (33,15) (13,19) (16,23) (0,1) (10,2) (3,4) (24,4) (24,6) (25,4) (28,26) (28,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph306", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (28,7) (10,2) (14,5) (3,24) (22,15) (4,23) (21,10) (28,25) (6,9) (19,12) (27,5) (13,10) (18,2) (20,2) (2,1) (14,19) (0,7) (24,13) (19,0) (9,22) (8,16) (4,8) (18,27) (11,27) (22,21) (26,6) (11,17) (27,4)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph64", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (12,15) (8,23) (6,21) (25,5) (0,17) (13,1) (21,24) (19,12) (3,9) (11,23) (14,8) (1,20) (22,15) (20,24) (0,7) (5,23) (10,3) (16,13) (20,4) (6,2) (23,7) (6,22) (18,4) (21,9) (12,17)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph119", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (12,15) (12,26) (19,15) (25,17) (26,24) (2,19) (7,6) (15,22) (17,8) (4,11) (18,3) (9,4) (21,7) (2,16) (0,18) (22,6) (5,17) (11,15) (10,19) (7,1) (15,17) (17,23) (20,8) (18,14) (20,13) (26,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1305", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (0,3) (1,0) (27,23) (23,9) (22,21) (2,0) (3,28) (12,7) (14,0) (25,4) (24,18) (26,14) (2,17) (24,25) (8,26) (5,21) (20,3) (2,22) (13,5) (0,24) (6,12) (19,4) (18,10) (5,6) (20,23) (22,9) (15,6) (11,5) (16,21) (27,14) (1,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1523", "image": "data/cycle/graph_visual/hard/graph1523.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (19,14) (3,0) (15,22) (24,5) (22,2) (26,18) (0,1) (0,27) (4,11) (12,13) (9,18) (26,21) (7,19) (2,24) (1,29) (23,6) (15,30) (7,29) (8,6) (17,9) (11,16) (28,0) (28,20) (14,8) (2,3) (25,0) (14,28) (13,9) (30,10) (23,4) (12,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph259", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (25,20) (9,6) (26,0) (4,5) (25,19) (14,10) (12,4) (12,1) (8,16) (18,15) (25,27) (14,15) (7,20) (9,3) (22,27) (24,5) (7,1) (23,2) (25,17) (9,18) (13,0) (2,21) (10,1) (7,8) (25,13) (4,11) (21,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph21", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (8,21) (1,13) (5,19) (9,17) (10,16) (7,15) (24,5) (11,9) (24,2) (4,0) (18,23) (3,18) (5,8) (17,4) (5,14) (25,16) (15,3) (21,20) (15,25) (1,22) (15,13) (12,25) (6,9) (6,24) (4,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1458", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (2,0) (26,23) (17,6) (3,12) (22,23) (0,5) (2,22) (27,16) (25,28) (0,29) (3,26) (10,8) (11,0) (14,0) (26,13) (1,25) (3,0) (3,16) (21,20) (7,26) (10,23) (23,19) (4,24) (20,9) (1,0) (15,24) (9,26) (27,28) (16,18) (17,2) (0,4) (24,12) (13,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph954", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (30,9) (14,11) (29,34) (23,9) (14,27) (4,29) (17,4) (5,24) (20,3) (31,4) (8,1) (33,12) (25,5) (21,32) (21,14) (21,22) (10,2) (6,25) (25,30) (28,34) (9,13) (15,34) (32,28) (2,16) (1,2) (4,0) (8,18) (30,29) (1,3) (27,7) (33,7) (33,18) (26,23) (20,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph737", "image": "data/cycle/graph_visual/hard/graph737.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (11,0) (23,1) (9,3) (5,30) (18,13) (16,18) (30,21) (6,12) (30,7) (24,6) (31,11) (4,31) (1,19) (11,14) (27,20) (8,25) (12,19) (9,32) (5,26) (29,31) (31,5) (22,19) (15,0) (10,2) (17,10) (20,22) (10,16) (32,28) (22,15) (8,7) (23,28) (27,2)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1491", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (25,29) (1,4) (27,12) (0,2) (22,13) (13,18) (17,21) (16,26) (10,8) (10,17) (14,23) (18,14) (0,1) (17,25) (0,21) (24,26) (27,13) (11,29) (20,27) (28,17) (3,25) (14,26) (25,19) (29,9) (11,7) (10,16) (19,2) (6,5) (5,2) (3,1) (25,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1606", "image": "data/cycle/graph_visual/hard/graph1606.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (30,13) (7,29) (14,24) (12,30) (26,27) (1,0) (2,21) (23,0) (20,4) (7,31) (28,2) (0,15) (14,22) (21,31) (27,19) (27,25) (23,30) (23,1) (0,18) (10,3) (11,17) (7,5) (9,4) (5,9) (16,13) (15,11) (18,10) (26,8) (1,9) (26,6) (14,2) (26,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1813", "image": "data/cycle/graph_visual/hard/graph1813.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,2) (28,22) (15,31) (17,14) (25,6) (3,4) (27,19) (28,31) (7,5) (31,33) (8,28) (0,1) (0,3) (30,0) (28,14) (32,14) (8,2) (10,24) (6,20) (31,7) (27,1) (4,0) (23,17) (16,4) (1,16) (13,11) (27,13) (0,24) (29,1) (1,20) (1,26) (21,0) (24,18) (6,12) (1,33) (30,9) (24,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1395", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (0,2) (1,15) (1,0) (23,2) (8,22) (3,0) (26,24) (9,3) (7,1) (17,24) (12,14) (22,24) (16,14) (24,5) (0,4) (19,4) (17,4) (26,10) (6,14) (23,27) (23,11) (25,17) (16,0) (13,21) (27,15) (21,15) (12,28) (6,20) (8,16) (9,0) (18,10) (11,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph84", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (1,5) (11,7) (25,20) (1,12) (11,23) (6,12) (2,25) (11,0) (24,25) (20,1) (17,18) (14,9) (13,8) (1,10) (23,9) (6,15) (3,11) (19,15) (16,21) (4,18) (2,17) (0,24) (22,24) (22,21) (15,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1651", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (28,30) (23,17) (22,13) (3,12) (1,8) (28,2) (21,5) (24,11) (12,13) (24,0) (18,26) (0,2) (6,16) (28,25) (28,4) (7,19) (14,15) (19,21) (24,20) (6,9) (31,3) (14,28) (16,17) (31,17) (24,2) (8,30) (21,18) (0,23) (26,17) (10,31) (9,29) (27,5) (1,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1198", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (0,6) (19,15) (16,7) (8,14) (6,3) (11,0) (3,23) (24,9) (2,4) (15,21) (12,19) (13,15) (7,17) (26,22) (22,23) (1,0) (22,18) (9,5) (2,11) (20,4) (4,1) (14,5) (23,7) (0,2) (10,11) (15,26) (3,0) (22,25) (5,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph949", "image": "data/cycle/graph_visual/hard/graph949.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (22,10) (16,34) (14,13) (14,31) (28,30) (11,29) (33,8) (24,0) (15,24) (21,7) (29,28) (24,9) (23,0) (20,27) (12,5) (7,22) (14,34) (2,6) (4,25) (29,19) (32,9) (0,10) (14,30) (14,18) (14,32) (7,26) (1,12) (34,17) (27,30) (14,6) (22,12) (3,20) (27,4) (26,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph820", "image": "data/cycle/graph_visual/hard/graph820.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (24,27) (1,19) (12,30) (16,18) (30,24) (19,2) (20,12) (0,32) (10,4) (30,21) (27,25) (11,4) (13,0) (8,5) (1,17) (8,23) (33,23) (2,10) (15,30) (9,33) (14,16) (9,14) (30,17) (30,7) (28,8) (4,0) (25,22) (29,14) (31,24) (25,28) (9,26) (23,6) (15,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph821", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (8,25) (29,18) (11,14) (11,0) (20,27) (13,33) (0,16) (21,4) (3,21) (26,32) (24,7) (6,0) (15,28) (17,21) (7,29) (27,8) (1,25) (14,12) (11,30) (21,29) (9,3) (11,5) (19,8) (22,8) (14,23) (28,12) (2,12) (20,26) (9,15) (31,28) (0,33) (10,7) (10,19)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1441", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (15,29) (6,23) (15,22) (3,0) (18,25) (7,27) (9,18) (9,13) (9,10) (3,2) (4,11) (28,14) (29,1) (23,4) (24,0) (8,6) (2,22) (1,0) (7,19) (0,26) (28,17) (0,28) (4,0) (8,14) (12,16) (20,26) (11,16) (13,12) (2,0) (2,21) (5,24) (19,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph752", "image": "data/cycle/graph_visual/hard/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 32, and the edges are: (13,11) (0,12) (20,17) (2,8) (7,3) (14,28) (19,6) (2,31) (9,28) (26,15) (22,17) (29,21) (28,7) (32,25) (28,23) (24,10) (27,16) (32,30) (27,0) (11,18) (7,5) (17,15) (1,32) (4,20) (8,14) (0,29) (16,17) (32,12) (19,7) (13,22) (10,20) (9,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph228", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (27,24) (15,17) (5,18) (16,26) (1,6) (12,25) (21,15) (14,23) (10,12) (23,11) (12,16) (7,26) (11,2) (24,17) (4,23) (21,20) (9,5) (0,2) (8,2) (13,17) (23,13) (3,4) (12,22) (9,6) (2,9) (10,23) (19,27)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph287", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (7,24) (23,19) (6,13) (22,16) (15,9) (4,13) (23,9) (2,3) (1,19) (11,2) (21,25) (14,11) (18,11) (5,18) (3,13) (10,19) (10,22) (22,8) (1,20) (24,27) (14,17) (20,0) (23,12) (21,5) (15,24) (10,11) (8,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph383", "image": "data/cycle/graph_visual/hard/graph383.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (27,8) (20,16) (0,1) (15,12) (25,6) (10,3) (9,14) (17,8) (28,12) (1,4) (23,20) (7,8) (2,19) (15,26) (18,2) (24,23) (28,9) (13,26) (25,11) (17,2) (20,13) (0,21) (0,16) (11,17) (5,7) (5,22) (10,25) (18,13)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1117", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (3,10) (20,24) (3,9) (15,12) (2,26) (20,1) (5,6) (25,7) (9,21) (14,8) (26,0) (24,21) (13,16) (21,6) (12,19) (22,15) (8,23) (23,11) (18,4) (17,12) (22,6) (23,26) (0,17) (0,1) (13,1) (4,20) (23,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph72", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (12,8) (19,0) (3,21) (6,2) (10,0) (11,23) (4,15) (24,2) (1,13) (23,18) (7,14) (7,16) (18,13) (0,25) (0,1) (5,20) (17,22) (4,23) (17,2) (21,23) (6,7) (3,9) (20,3) (7,8) (19,16)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph816", "image": "data/cycle/graph_visual/hard/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 33, and the edges are: (32,5) (16,21) (26,16) (19,1) (30,4) (29,7) (16,9) (17,23) (12,31) (7,12) (17,6) (6,18) (12,28) (3,7) (25,20) (19,20) (9,15) (33,13) (12,8) (33,2) (26,32) (0,2) (25,10) (33,27) (24,4) (1,26) (29,24) (6,4) (6,1) (22,11) (27,6) (22,20) (14,18)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph366", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (22,25) (0,6) (8,14) (3,23) (6,3) (0,24) (9,27) (19,12) (22,18) (16,7) (22,11) (19,28) (19,11) (7,17) (11,2) (11,10) (15,13) (13,5) (4,21) (15,20) (23,15) (4,2) (22,26) (5,9) (14,5) (26,15) (4,1) (23,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1589", "image": "data/cycle/graph_visual/hard/graph1589.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (17,9) (1,29) (3,25) (2,18) (17,7) (12,18) (16,15) (8,13) (2,26) (25,11) (6,18) (3,0) (0,2) (4,0) (18,21) (16,4) (16,27) (8,25) (15,5) (30,17) (30,1) (24,25) (0,13) (21,22) (28,26) (10,20) (25,14) (1,0) (24,23) (18,3) (19,28) (20,21) (1,10) (5,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph744", "image": "data/cycle/graph_visual/hard/graph744.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (29,31) (26,1) (13,31) (4,6) (32,5) (9,20) (30,18) (1,10) (20,8) (24,12) (20,21) (25,5) (20,26) (2,15) (27,21) (0,9) (23,13) (7,6) (14,26) (16,3) (12,6) (25,30) (19,28) (11,10) (5,6) (8,17) (13,15) (5,27) (12,2) (4,16) (22,26) (21,28)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph920", "image": "data/cycle/graph_visual/hard/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 34, and the edges are: (15,11) (0,22) (2,17) (6,25) (23,25) (7,18) (21,14) (3,26) (24,23) (13,4) (30,1) (21,19) (27,5) (25,34) (8,21) (33,14) (6,9) (26,27) (20,16) (4,31) (30,16) (0,30) (8,16) (18,34) (28,3) (4,12) (5,4) (32,15) (33,9) (31,15) (28,22) (10,12) (16,17) (11,29)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1624", "image": "data/cycle/graph_visual/hard/graph1624.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (12,31) (7,0) (30,13) (1,0) (26,10) (4,28) (4,27) (0,24) (16,20) (29,8) (26,4) (7,18) (5,15) (19,2) (5,19) (16,14) (3,0) (9,17) (0,2) (1,4) (21,22) (13,27) (8,17) (31,16) (20,11) (17,6) (3,2) (9,3) (9,26) (2,11) (21,1) (25,18) (7,19) (23,30)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1308", "image": "data/cycle/graph_visual/hard/graph1308.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (7,24) (4,0) (23,20) (0,3) (4,13) (5,15) (28,14) (0,2) (8,21) (7,18) (2,26) (27,17) (9,23) (27,6) (27,22) (17,2) (20,7) (5,4) (21,19) (20,16) (10,21) (9,0) (11,25) (13,0) (28,4) (9,3) (0,1) (6,23) (25,5) (8,1) (12,27) (4,21)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph334", "image": "data/cycle/graph_visual/hard/graph334.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (22,3) (5,2) (18,9) (0,3) (15,25) (12,16) (11,10) (11,4) (28,27) (20,13) (17,6) (12,19) (13,2) (12,18) (8,24) (17,23) (7,14) (25,8) (8,10) (13,21) (23,15) (0,17) (16,14) (0,26) (21,0) (19,1) (25,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1423", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (10,3) (14,0) (15,26) (22,12) (8,3) (18,16) (17,7) (16,1) (23,2) (18,25) (5,11) (13,9) (24,0) (26,16) (27,3) (10,9) (28,4) (20,0) (11,8) (0,1) (7,28) (19,0) (24,29) (4,26) (2,13) (11,12) (21,28) (18,6) (11,19) (4,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1840", "image": "data/cycle/graph_visual/hard/graph1840.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (15,20) (23,17) (25,32) (26,0) (0,1) (13,16) (8,7) (3,31) (21,28) (5,10) (16,33) (18,9) (18,17) (21,32) (11,9) (5,20) (0,3) (33,30) (31,6) (2,21) (4,30) (6,19) (27,23) (23,1) (1,15) (31,29) (10,4) (2,0) (21,10) (1,3) (21,8) (12,27) (3,14) (23,22) (0,6) (4,0) (0,24)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1608", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (15,12) (26,24) (1,3) (17,21) (9,11) (31,7) (13,29) (26,4) (31,0) (3,6) (25,15) (24,22) (15,27) (14,17) (0,10) (20,30) (4,17) (23,19) (18,1) (10,20) (25,10) (11,31) (18,13) (0,1) (23,31) (5,8) (16,27) (11,18) (21,2) (28,7) (5,0) (22,25)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1650", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (20,17) (28,21) (31,22) (6,18) (19,23) (20,25) (3,26) (18,12) (1,0) (7,14) (4,27) (3,0) (10,7) (5,7) (6,0) (17,30) (26,22) (2,0) (1,14) (21,18) (2,22) (9,24) (11,8) (4,6) (7,4) (16,10) (14,11) (25,24) (19,24) (1,13) (2,18) (20,6) (29,10) (0,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1876", "image": "data/cycle/graph_visual/hard/graph1876.png", "conversations": [ { "from": "human", "value": "\nIn this 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) (21,2) (0,26) (30,33) (0,24) (6,19) (7,8) (0,2) (15,1) (1,3) (12,27) (6,0) (11,9) (21,28) (0,1) (10,21) (31,29) (13,16) (25,32) (10,5) (3,14) (15,20) (1,23) (30,4) (17,23) (23,22) (33,16) (8,21) (31,3) (5,20) (6,31) (18,17) (9,18) (10,4) (21,32)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1392", "image": "data/cycle/graph_visual/hard/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 28, and the edges are: (0,4) (25,10) (28,3) (1,22) (13,28) (27,1) (16,15) (5,2) (12,27) (9,18) (4,16) (12,6) (24,2) (0,26) (0,1) (21,25) (20,7) (17,18) (2,25) (26,20) (5,0) (17,4) (2,0) (7,14) (18,19) (1,26) (10,20) (18,11) (3,0) (23,0) (28,17) (8,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1202", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (16,11) (12,14) (15,10) (23,13) (22,25) (2,7) (9,16) (7,0) (0,1) (19,1) (6,1) (27,2) (3,0) (5,4) (14,0) (14,11) (4,21) (23,8) (12,17) (25,20) (11,5) (26,13) (0,2) (5,24) (1,26) (15,27) (18,13) (20,0) (3,8) (17,1)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1082", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (11,15) (16,6) (24,4) (19,3) (8,17) (1,8) (13,5) (17,25) (0,12) (14,12) (0,1) (18,6) (9,20) (0,2) (3,0) (22,9) (8,24) (9,4) (18,11) (7,1) (15,21) (25,19) (16,10) (16,4) (2,24) (12,25) (3,23) (13,15)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1895", "image": "data/cycle/graph_visual/hard/graph1895.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (6,4) (11,15) (19,5) (20,24) (2,0) (14,25) (16,32) (18,29) (22,27) (29,31) (0,1) (21,27) (9,12) (26,21) (24,0) (12,6) (3,13) (33,9) (12,17) (0,4) (22,25) (7,16) (1,12) (23,3) (10,2) (11,28) (30,19) (27,8) (26,11) (16,33) (11,23) (6,13) (15,0) (23,30) (2,9) (18,9) (0,3)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1682", "image": "data/cycle/graph_visual/hard/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 31, and the edges are: (29,18) (15,29) (6,4) (28,8) (17,11) (12,25) (26,6) (0,31) (27,1) (21,13) (24,12) (26,19) (28,14) (2,7) (8,16) (3,8) (1,26) (13,22) (0,12) (20,8) (3,0) (13,9) (15,4) (1,0) (10,8) (11,30) (10,23) (25,9) (7,14) (17,14) (20,26) (2,0) (12,8) (11,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1012", "image": "data/cycle/graph_visual/hard/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 25, and the edges are: (19,15) (4,12) (17,14) (22,24) (20,0) (10,22) (18,21) (22,17) (0,2) (22,13) (4,20) (23,22) (9,11) (9,23) (0,1) (19,3) (3,0) (2,1) (6,23) (25,0) (25,2) (7,12) (7,10) (19,4) (11,5) (19,21) (11,16) (5,8)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1880", "image": "data/cycle/graph_visual/hard/graph1880.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (30,0) (16,27) (0,12) (14,8) (0,27) (10,20) (19,6) (23,17) (13,11) (28,24) (20,4) (2,8) (19,7) (32,1) (0,3) (15,17) (0,1) (13,22) (33,22) (32,29) (2,0) (17,20) (15,26) (18,11) (32,2) (29,21) (32,31) (28,7) (4,0) (25,10) (9,28) (33,12) (28,14) (17,16) (7,3) (9,26) (5,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph1942", "image": "data/cycle/graph_visual/hard/graph1942.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (33,32) (2,17) (1,0) (24,29) (9,28) (27,1) (13,11) (1,6) (23,19) (30,14) (4,25) (15,24) (17,13) (10,15) (3,31) (3,24) (0,3) (23,14) (11,22) (0,9) (5,16) (14,10) (28,8) (23,18) (7,34) (6,20) (33,0) (8,10) (12,26) (34,1) (16,17) (23,22) (21,34) (23,25) (0,2) (20,5) (25,26)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph167", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (4,13) (2,24) (14,20) (21,8) (20,23) (9,3) (21,16) (5,22) (9,0) (4,26) (1,8) (21,10) (5,12) (5,4) (18,4) (2,17) (7,19) (23,9) (25,11) (7,15) (25,21) (23,6) (0,13) (26,21) (17,6) (20,7)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph453", "image": "data/cycle/graph_visual/hard/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 29, and the edges are: (25,20) (4,9) (29,10) (23,12) (2,14) (20,9) (7,1) (15,12) (1,19) (27,21) (14,3) (14,0) (8,11) (21,18) (28,27) (2,26) (7,21) (6,9) (23,19) (2,16) (26,9) (17,2) (15,8) (29,5) (29,27) (24,2) (13,21) (23,26) (6,22)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph208", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (14,3) (23,6) (1,6) (10,16) (15,9) (17,25) (17,10) (17,2) (12,11) (23,24) (8,15) (4,17) (23,18) (5,9) (12,22) (26,14) (0,4) (19,2) (15,25) (16,27) (18,21) (6,12) (14,7) (10,20) (13,7) (1,15) (19,14)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1127", "image": "data/cycle/graph_visual/hard/graph1127.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (25,19) (16,5) (4,0) (24,5) (13,1) (10,16) (24,3) (4,25) (9,6) (26,17) (23,1) (17,9) (2,24) (4,26) (21,8) (25,14) (15,18) (22,21) (7,15) (11,9) (18,26) (20,5) (26,12) (1,0) (15,13) (3,6) (8,5)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph250", "image": "data/cycle/graph_visual/hard/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 27, and the edges are: (20,1) (2,19) (6,13) (12,2) (18,9) (2,4) (22,3) (14,10) (21,25) (0,3) (23,24) (23,25) (7,15) (23,27) (8,25) (8,5) (20,26) (9,3) (8,4) (8,11) (16,2) (9,27) (13,9) (17,15) (19,1) (0,15) (0,10)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] }, { "id": "cycle-hard-graph1038", "image": "data/cycle/graph_visual/hard/graph1038.png", "conversations": [ { "from": "human", "value": "\nIn this 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: (0,3) (18,15) (17,20) (23,12) (10,12) (7,6) (21,2) (1,0) (1,6) (16,0) (22,5) (3,25) (7,12) (8,4) (0,4) (6,14) (11,20) (9,24) (21,9) (2,11) (22,23) (2,0) (5,0) (13,0) (19,8) (18,25) (8,21) (11,0)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "Yes." } ] }, { "id": "cycle-hard-graph182", "image": "data/cycle/graph_visual/hard/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 26, and the edges are: (26,3) (12,10) (9,25) (2,21) (5,26) (11,0) (22,23) (7,12) (22,5) (0,13) (24,0) (18,15) (8,4) (14,6) (7,6) (3,0) (19,8) (6,1) (18,25) (9,21) (12,23) (0,16) (20,11) (8,21) (11,2) (17,20)<\nIs there a cycle in this undirected graph?" }, { "from": "gpt", "value": "No." } ] } ]