diff --git "a/data/cycle/QA/Base/Text_Only_test.json" "b/data/cycle/QA/Base/Text_Only_test.json" --- "a/data/cycle/QA/Base/Text_Only_test.json" +++ "b/data/cycle/QA/Base/Text_Only_test.json" @@ -1,15992 +1,3 @@ -[ - { - "id": "cycle-easy-graph290", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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", - "conversations": [ - { - "from": "human", - "value": "In an 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." - } - ] - } -] \ No newline at end of file +version https://git-lfs.github.com/spec/v1 +oid sha256:5e3ea95335c5e16c372d22194bf2d8e083e19fae4cbd3116ea2650afba5d712b +size 781066