diff --git "a/data/hamilton/QA/Base/Vision_Text_train.json" "b/data/hamilton/QA/Base/Vision_Text_train.json" --- "a/data/hamilton/QA/Base/Vision_Text_train.json" +++ "b/data/hamilton/QA/Base/Vision_Text_train.json" @@ -1,8822 +1,3 @@ -[ - { - "id": "hamilton-easy-graph208", - "image": "data/hamilton/graph_visual/Base/easy/graph208.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,8) (9,0) (2,3) (6,7) (4,8) (1,7) (9,2) (6,2) (4,2) (3,6) (6,1) (5,1) (4,9) (3,5) (3,7) (8,5) (4,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->2->3->8->4->7->6->1->5." - } - ] - }, - { - "id": "hamilton-easy-graph3", - "image": "data/hamilton/graph_visual/Base/easy/graph3.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (3,4) (1,2) (1,3) (2,0) (1,0) (3,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->1->3->4." - } - ] - }, - { - "id": "hamilton-easy-graph296", - "image": "data/hamilton/graph_visual/Base/easy/graph296.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,7) (3,9) (6,1) (0,1) (9,1) (2,7) (6,8) (0,8) (4,8) (2,6) (0,3) (2,4) (9,5) (4,0) (8,2) (8,1) (0,5) (5,6) (4,6) (6,9) (0,9) (3,8) (7,9) (0,7) (1,2) (3,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->6->7->2->4->8->3->9->5." - } - ] - }, - { - "id": "hamilton-easy-graph91", - "image": "data/hamilton/graph_visual/Base/easy/graph91.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,0) (3,6) (0,2) (1,5) (3,5) (1,3) (7,3) (0,6) (0,1) (1,4) (7,6) (4,2) (2,3) (3,4) (5,2) (7,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->1->5->2->3->6->7." - } - ] - }, - { - "id": "hamilton-easy-graph38", - "image": "data/hamilton/graph_visual/Base/easy/graph38.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (4,1) (3,5) (6,5) (0,1) (3,0) (2,4) (0,4) (0,6) (2,3) (2,1) (6,2) (3,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->4->2->3->5->6." - } - ] - }, - { - "id": "hamilton-easy-graph259", - "image": "data/hamilton/graph_visual/Base/easy/graph259.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,1) (7,5) (2,8) (6,5) (1,6) (4,7) (7,9) (9,2) (6,2) (4,6) (0,9) (1,7) (4,2) (2,0) (8,4) (1,2) (3,0) (0,7) (2,3) (9,3) (6,7) (5,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->7->5->1->6->4->8->2->3." - } - ] - }, - { - "id": "hamilton-easy-graph10", - "image": "data/hamilton/graph_visual/Base/easy/graph10.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,4) (5,1) (3,1) (2,4) (5,3) (1,2) (4,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->2->1->5->3." - } - ] - }, - { - "id": "hamilton-easy-graph172", - "image": "data/hamilton/graph_visual/Base/easy/graph172.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,6) (0,1) (6,0) (0,5) (4,5) (3,4) (1,6) (0,4) (8,5) (3,2) (6,7) (4,6) (0,3) (8,2) (6,5) (1,8) (2,1) (3,1) (4,8) (3,7) (1,5) (5,2) (6,2) (7,0) (8,7) (7,2) (7,1) (4,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->6->8->5->4->3->2->7." - } - ] - }, - { - "id": "hamilton-easy-graph15", - "image": "data/hamilton/graph_visual/Base/easy/graph15.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (2,1) (3,1) (4,1) (0,1) (5,3) (2,3) (4,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->2->3->5->4." - } - ] - }, - { - "id": "hamilton-easy-graph267", - "image": "data/hamilton/graph_visual/Base/easy/graph267.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,9) (4,0) (2,4) (3,9) (5,7) (7,0) (5,1) (6,4) (1,8) (3,7) (6,0) (9,2) (6,5) (2,7) (6,2) (2,8) (1,0) (8,6) (7,4) (9,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->3->7->5->1->8->2->4->6." - } - ] - }, - { - "id": "hamilton-easy-graph247", - "image": "data/hamilton/graph_visual/Base/easy/graph247.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,6) (7,9) (2,1) (3,9) (7,4) (6,8) (0,1) (8,5) (0,3) (6,4) (0,2) (4,1) (1,5) (7,2) (5,0) (5,2) (2,6) (8,2) (1,6) (2,3) (9,1) (6,3) (7,5) (0,8) (9,2) (9,8) (9,5) (7,0) (7,6) (7,3) (9,0) (2,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->8->5->1->2->3->9->7->4." - } - ] - }, - { - "id": "hamilton-easy-graph250", - "image": "data/hamilton/graph_visual/Base/easy/graph250.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,2) (8,4) (5,7) (7,4) (6,5) (1,8) (1,9) (2,4) (6,7) (4,5) (8,9) (5,1) (6,9) (4,0) (6,8) (2,0) (9,5) (3,6) (2,7) (6,1) (4,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->8->1->9->5->7->2->6->3." - } - ] - }, - { - "id": "hamilton-easy-graph273", - "image": "data/hamilton/graph_visual/Base/easy/graph273.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,8) (9,8) (6,8) (1,7) (2,0) (0,5) (8,2) (8,4) (7,3) (1,4) (5,9) (1,0) (3,4) (5,4) (5,8) (1,3) (9,6) (4,9) (1,9) (0,7) (7,2) (4,2) (2,5) (3,2) (3,0) (9,3) (8,1) (7,6) (6,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->8->7->1->4->3->9->5->6." - } - ] - }, - { - "id": "hamilton-easy-graph149", - "image": "data/hamilton/graph_visual/Base/easy/graph149.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,7) (1,2) (8,5) (4,6) (5,7) (4,1) (3,0) (4,3) (3,5) (1,6) (3,8) (8,7) (2,7) (6,2) (3,1) (2,3) (0,2) (0,6) (6,8) (4,5) (2,8) (5,2) (7,0) (6,3) (2,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->4->6->7->5->8->2->1." - } - ] - }, - { - "id": "hamilton-easy-graph113", - "image": "data/hamilton/graph_visual/Base/easy/graph113.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,4) (4,8) (3,0) (2,1) (1,0) (3,8) (3,7) (5,6) (2,3) (3,6) (5,4) (6,2) (1,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->8->4->5->6->2->1->7." - } - ] - }, - { - "id": "hamilton-easy-graph48", - "image": "data/hamilton/graph_visual/Base/easy/graph48.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (4,2) (6,2) (6,4) (5,2) (1,6) (0,3) (1,2) (3,2) (3,4) (3,5) (6,3) (1,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->4->6->1->2->5." - } - ] - }, - { - "id": "hamilton-easy-graph52", - "image": "data/hamilton/graph_visual/Base/easy/graph52.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,6) (3,6) (1,0) (3,5) (3,2) (3,0) (5,4) (2,1) (5,1) (6,1) (3,1) (0,2) (4,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->2->6->3->5->4." - } - ] - }, - { - "id": "hamilton-easy-graph255", - "image": "data/hamilton/graph_visual/Base/easy/graph255.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,9) (7,3) (5,2) (4,8) (3,8) (4,7) (6,4) (6,9) (3,6) (7,8) (0,7) (6,1) (6,5) (3,4) (8,5) (1,4) (6,8) (0,1) (3,5) (9,7) (7,6) (8,0) (3,2) (6,0) (5,1) (3,0) (7,1) (6,2) (9,0) (9,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->3->8->9->6->4->1->5->2." - } - ] - }, - { - "id": "hamilton-easy-graph18", - "image": "data/hamilton/graph_visual/Base/easy/graph18.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (2,3) (2,5) (1,2) (0,2) (1,4) (3,1) (4,0) (0,5) (5,3) (5,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->2->3->5->4." - } - ] - }, - { - "id": "hamilton-easy-graph28", - "image": "data/hamilton/graph_visual/Base/easy/graph28.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (5,4) (0,6) (1,2) (4,2) (0,4) (1,3) (6,4) (4,1) (6,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->5->4->2->1->3." - } - ] - }, - { - "id": "hamilton-easy-graph204", - "image": "data/hamilton/graph_visual/Base/easy/graph204.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,5) (3,2) (4,2) (3,6) (8,6) (4,6) (0,3) (6,0) (5,2) (8,7) (1,2) (4,0) (5,9) (7,3) (3,4) (9,2) (6,7) (1,4) (1,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->2->4->1->6->7->8->5->9." - } - ] - }, - { - "id": "hamilton-easy-graph244", - "image": "data/hamilton/graph_visual/Base/easy/graph244.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,2) (5,2) (0,7) (7,2) (1,0) (9,7) (6,2) (7,8) (2,1) (0,3) (3,1) (4,2) (1,7) (8,6) (5,6) (8,3) (6,4) (6,3) (8,0) (1,6) (4,8) (7,4) (9,3) (9,4) (6,9) (8,2) (7,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->2->9->4->8->3->1->6->5." - } - ] - }, - { - "id": "hamilton-easy-graph253", - "image": "data/hamilton/graph_visual/Base/easy/graph253.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,2) (4,1) (0,8) (5,1) (1,6) (8,1) (4,7) (3,9) (0,4) (9,8) (3,8) (4,3) (1,2) (4,2) (4,9) (7,5) (4,6) (6,7) (2,3) (0,7) (2,0) (6,0) (9,5) (4,5) (2,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->1->4->7->5->9->3->2->6." - } - ] - }, - { - "id": "hamilton-easy-graph232", - "image": "data/hamilton/graph_visual/Base/easy/graph232.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,9) (4,1) (6,4) (6,3) (1,5) (8,9) (3,7) (2,6) (9,7) (5,0) (0,8) (4,2) (9,4) (9,6) (4,0) (2,7) (4,3) (0,3) (2,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->1->4->6->3->2->7->9->8." - } - ] - }, - { - "id": "hamilton-easy-graph7", - "image": "data/hamilton/graph_visual/Base/easy/graph7.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (3,1) (2,4) (1,2) (4,0) (3,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->2->1->3." - } - ] - }, - { - "id": "hamilton-easy-graph176", - "image": "data/hamilton/graph_visual/Base/easy/graph176.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,6) (0,1) (6,5) (8,2) (5,7) (6,1) (4,1) (3,1) (8,4) (6,2) (4,3) (7,6) (1,2) (3,2) (2,0) (0,3) (4,5) (5,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->6->7->5->4->8->2->3." - } - ] - }, - { - "id": "hamilton-easy-graph299", - "image": "data/hamilton/graph_visual/Base/easy/graph299.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,9) (5,4) (2,9) (0,2) (8,1) (3,8) (5,9) (7,0) (0,1) (5,7) (4,3) (2,5) (4,7) (1,2) (8,0) (3,0) (6,3) (4,1) (4,0) (1,9) (5,1) (5,0) (2,6) (9,4) (6,1) (3,2) (8,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->9->7->5->4->3->8->1->6." - } - ] - }, - { - "id": "hamilton-easy-graph70", - "image": "data/hamilton/graph_visual/Base/easy/graph70.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,7) (0,2) (4,1) (5,6) (7,3) (6,2) (6,7) (5,2) (7,1) (1,3) (0,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->5->6->7->4->1->3." - } - ] - }, - { - "id": "hamilton-easy-graph243", - "image": "data/hamilton/graph_visual/Base/easy/graph243.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,3) (9,4) (3,0) (8,7) (6,1) (4,6) (4,2) (8,1) (6,2) (4,5) (4,7) (2,0) (9,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->5->9->4->2->6->1->8->7." - } - ] - }, - { - "id": "hamilton-easy-graph62", - "image": "data/hamilton/graph_visual/Base/easy/graph62.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,2) (5,1) (4,1) (7,4) (1,3) (2,1) (7,5) (3,7) (2,6) (6,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->6->4->1->5->7->3." - } - ] - }, - { - "id": "hamilton-easy-graph245", - "image": "data/hamilton/graph_visual/Base/easy/graph245.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,7) (0,4) (8,2) (1,8) (9,7) (5,1) (5,2) (2,1) (9,8) (7,4) (1,9) (9,2) (1,4) (1,6) (0,9) (5,4) (3,7) (8,4) (7,8) (0,2) (7,5) (9,6) (5,9) (0,6) (3,6) (2,7) (6,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->7->1->8->2->5->9->6->3." - } - ] - }, - { - "id": "hamilton-easy-graph55", - "image": "data/hamilton/graph_visual/Base/easy/graph55.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (4,5) (3,0) (3,2) (6,5) (2,5) (4,3) (5,1) (4,2) (6,0) (5,0) (6,3) (6,1) (4,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->2->4->5->6->1." - } - ] - }, - { - "id": "hamilton-easy-graph205", - "image": "data/hamilton/graph_visual/Base/easy/graph205.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,9) (8,0) (3,8) (0,6) (9,4) (4,8) (0,1) (9,5) (5,2) (8,5) (2,8) (7,1) (6,7) (4,3) (9,7) (7,4) (7,2) (5,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->2->5->3->4->9->1->7->6." - } - ] - }, - { - "id": "hamilton-easy-graph249", - "image": "data/hamilton/graph_visual/Base/easy/graph249.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,3) (3,8) (4,6) (8,1) (8,7) (5,9) (0,4) (1,5) (6,9) (7,0) (8,4) (9,8) (2,6) (5,8) (3,9) (6,0) (0,2) (6,7) (2,9) (2,4) (9,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->8->1->5->9->2->4->6->7." - } - ] - }, - { - "id": "hamilton-easy-graph73", - "image": "data/hamilton/graph_visual/Base/easy/graph73.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,1) (0,7) (4,6) (4,5) (6,7) (4,2) (4,0) (0,2) (5,2) (1,7) (1,3) (5,7) (3,6) (6,2) (6,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->6->3->1->4->5->2." - } - ] - }, - { - "id": "hamilton-easy-graph57", - "image": "data/hamilton/graph_visual/Base/easy/graph57.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,4) (4,1) (6,1) (0,2) (0,7) (4,7) (3,1) (7,3) (1,2) (0,4) (5,3) (7,6) (6,3) (6,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->1->4->3->7->6->5." - } - ] - }, - { - "id": "hamilton-easy-graph189", - "image": "data/hamilton/graph_visual/Base/easy/graph189.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,9) (0,1) (8,0) (6,8) (4,5) (1,4) (6,9) (7,4) (6,5) (3,6) (3,1) (3,4) (3,7) (2,9) (2,7) (3,8) (5,8) (6,7) (5,9) (4,2) (2,3) (6,2) (0,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->4->5->6->8->9->2->7->3." - } - ] - }, - { - "id": "hamilton-easy-graph63", - "image": "data/hamilton/graph_visual/Base/easy/graph63.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,2) (0,3) (4,1) (4,6) (2,0) (4,7) (5,2) (6,2) (4,0) (3,5) (5,6) (1,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->5->6->2->1->4->7." - } - ] - }, - { - "id": "hamilton-easy-graph215", - "image": "data/hamilton/graph_visual/Base/easy/graph215.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,4) (5,6) (9,7) (9,1) (3,7) (4,9) (6,9) (2,5) (9,8) (3,6) (7,0) (4,2) (1,7) (0,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->9->1->7->4->2->5->6->3." - } - ] - }, - { - "id": "hamilton-easy-graph107", - "image": "data/hamilton/graph_visual/Base/easy/graph107.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,4) (2,1) (8,1) (2,6) (7,4) (6,4) (1,5) (6,8) (2,4) (7,8) (0,8) (3,4) (1,4) (7,5) (6,1) (3,0) (3,6) (3,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->2->1->8->6->3->7->5." - } - ] - }, - { - "id": "hamilton-easy-graph20", - "image": "data/hamilton/graph_visual/Base/easy/graph20.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (5,1) (4,1) (0,3) (2,3) (1,3) (3,5) (0,4) (2,4) (1,2) (0,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->2->4->1->5." - } - ] - }, - { - "id": "hamilton-easy-graph146", - "image": "data/hamilton/graph_visual/Base/easy/graph146.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,5) (5,0) (4,7) (2,0) (3,0) (4,8) (7,2) (4,6) (6,7) (3,8) (4,2) (3,2) (4,3) (5,4) (6,2) (7,0) (4,0) (5,3) (8,5) (6,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->7->4->8->3->2->6->1." - } - ] - }, - { - "id": "hamilton-easy-graph89", - "image": "data/hamilton/graph_visual/Base/easy/graph89.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (5,3) (6,5) (1,4) (6,0) (2,7) (4,3) (5,7) (4,0) (0,7) (7,4) (6,7) (7,1) (6,3) (7,3) (5,0) (0,1) (6,4) (2,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->5->3->4->1->7->2." - } - ] - }, - { - "id": "hamilton-easy-graph17", - "image": "data/hamilton/graph_visual/Base/easy/graph17.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,1) (4,5) (5,0) (4,0) (2,1) (1,0) (5,1) (2,3) (2,4) (4,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->4->2->1->3." - } - ] - }, - { - "id": "hamilton-easy-graph46", - "image": "data/hamilton/graph_visual/Base/easy/graph46.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (4,3) (6,5) (1,5) (3,0) (2,4) (1,0) (2,5) (0,4) (2,3) (2,0) (6,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->4->2->6->5->1." - } - ] - }, - { - "id": "hamilton-easy-graph163", - "image": "data/hamilton/graph_visual/Base/easy/graph163.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,3) (1,3) (4,7) (7,8) (2,8) (8,4) (3,2) (1,8) (0,4) (8,3) (6,5) (6,0) (4,5) (1,7) (7,6) (8,5) (1,4) (6,2) (7,3) (5,0) (2,1) (0,1) (7,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->1->8->7->4->5->6->2." - } - ] - }, - { - "id": "hamilton-easy-graph56", - "image": "data/hamilton/graph_visual/Base/easy/graph56.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (7,4) (5,0) (1,0) (7,0) (3,0) (5,2) (2,4) (6,4) (0,4) (7,6) (6,3) (1,4) (4,5) (3,2) (1,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->2->4->1->7->6->3." - } - ] - }, - { - "id": "hamilton-easy-graph221", - "image": "data/hamilton/graph_visual/Base/easy/graph221.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,6) (5,6) (0,9) (2,7) (4,9) (4,5) (9,7) (5,0) (2,9) (1,5) (3,5) (6,0) (7,0) (7,5) (4,3) (8,7) (1,6) (4,6) (9,8) (3,8) (2,0) (2,3) (1,3) (7,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->6->1->5->4->3->8->7->2." - } - ] - }, - { - "id": "hamilton-easy-graph284", - "image": "data/hamilton/graph_visual/Base/easy/graph284.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,4) (1,5) (1,3) (6,8) (8,2) (4,9) (2,5) (1,7) (4,6) (8,5) (2,0) (6,7) (5,0) (4,7) (3,9) (1,8) (4,0) (4,5) (8,7) (8,4) (0,9) (8,3) (0,3) (2,7) (9,2) (7,0) (0,6) (2,6) (6,5) (3,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->4->9->3->1->5->8->6->7." - } - ] - }, - { - "id": "hamilton-easy-graph77", - "image": "data/hamilton/graph_visual/Base/easy/graph77.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (5,2) (5,4) (0,6) (2,3) (3,7) (7,6) (4,0) (7,1) (7,2) (2,0) (4,6) (5,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->4->5->2->3->7->1." - } - ] - }, - { - "id": "hamilton-easy-graph101", - "image": "data/hamilton/graph_visual/Base/easy/graph101.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,3) (6,3) (5,0) (1,4) (0,7) (5,4) (2,3) (6,2) (5,3) (7,2) (3,0) (6,5) (4,6) (6,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->4->1->3->6->2->7." - } - ] - }, - { - "id": "hamilton-easy-graph93", - "image": "data/hamilton/graph_visual/Base/easy/graph93.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,2) (2,1) (6,2) (2,5) (7,0) (7,2) (3,5) (6,1) (6,3) (1,0) (0,4) (6,5) (5,7) (1,4) (4,2) (5,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->2->3->5->6->1->4." - } - ] - }, - { - "id": "hamilton-easy-graph194", - "image": "data/hamilton/graph_visual/Base/easy/graph194.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,4) (4,8) (9,1) (5,7) (9,7) (3,1) (7,2) (7,8) (9,0) (2,1) (6,2) (1,6) (0,2) (8,0) (0,7) (5,3) (8,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->7->5->3->1->4->8->2->6." - } - ] - }, - { - "id": "hamilton-easy-graph119", - "image": "data/hamilton/graph_visual/Base/easy/graph119.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,4) (4,0) (2,0) (3,4) (3,1) (1,7) (6,5) (2,6) (5,2) (5,8) (1,6) (5,4) (7,5) (5,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->6->4->3->1->7->5->8." - } - ] - }, - { - "id": "hamilton-easy-graph87", - "image": "data/hamilton/graph_visual/Base/easy/graph87.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,1) (7,5) (4,3) (2,4) (6,3) (7,6) (6,4) (3,5) (6,5) (3,0) (1,5) (4,0) (4,7) (1,7) (0,2) (5,4) (7,2) (5,0) (3,1) (5,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->4->2->1->5->7->6." - } - ] - }, - { - "id": "hamilton-easy-graph6", - "image": "data/hamilton/graph_visual/Base/easy/graph6.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (2,1) (0,1) (1,3) (2,4) (0,3) (4,0) (4,3) (2,0) (4,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->2->4->3." - } - ] - }, - { - "id": "hamilton-easy-graph226", - "image": "data/hamilton/graph_visual/Base/easy/graph226.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,7) (1,0) (4,7) (2,6) (0,7) (3,4) (1,6) (7,3) (4,9) (1,8) (9,8) (3,1) (8,0) (7,1) (5,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->9->4->5->7->3->1->6->2." - } - ] - }, - { - "id": "hamilton-easy-graph138", - "image": "data/hamilton/graph_visual/Base/easy/graph138.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,0) (1,6) (0,2) (4,1) (6,3) (1,2) (7,6) (5,8) (5,7) (7,3) (0,1) (2,3) (8,4) (1,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->6->7->5->8->4->1->2." - } - ] - }, - { - "id": "hamilton-easy-graph59", - "image": "data/hamilton/graph_visual/Base/easy/graph59.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,0) (4,7) (6,2) (6,3) (4,1) (4,3) (5,2) (3,7) (6,1) (4,5) (1,2) (2,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->5->4->7->3->6->1." - } - ] - }, - { - "id": "hamilton-easy-graph54", - "image": "data/hamilton/graph_visual/Base/easy/graph54.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (5,1) (1,4) (3,1) (4,0) (3,2) (5,2) (5,4) (1,0) (6,5) (3,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->1->3->2->5->6." - } - ] - }, - { - "id": "hamilton-easy-graph130", - "image": "data/hamilton/graph_visual/Base/easy/graph130.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,6) (1,7) (1,3) (6,2) (1,4) (1,8) (3,7) (5,0) (2,8) (4,7) (6,0) (8,5) (7,8) (4,6) (7,0) (2,4) (8,0) (0,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->8->1->6->2->4->7->3." - } - ] - }, - { - "id": "hamilton-easy-graph82", - "image": "data/hamilton/graph_visual/Base/easy/graph82.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,1) (2,4) (3,6) (4,5) (3,5) (6,1) (5,7) (0,2) (7,0) (4,3) (0,1) (1,5) (7,2) (6,5) (7,3) (6,2) (0,5) (0,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->1->6->3->4->5->7." - } - ] - }, - { - "id": "hamilton-easy-graph298", - "image": "data/hamilton/graph_visual/Base/easy/graph298.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,4) (1,3) (1,7) (3,9) (0,9) (4,9) (5,4) (8,6) (2,5) (2,1) (4,6) (8,4) (7,2) (1,4) (0,8) (8,7) (8,9) (1,8) (2,3) (5,0) (6,3) (0,7) (2,4) (9,5) (8,3) (7,4) (7,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->9->3->6->8->7->1->2->5." - } - ] - }, - { - "id": "hamilton-easy-graph102", - "image": "data/hamilton/graph_visual/Base/easy/graph102.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (6,0) (5,4) (0,2) (4,0) (4,6) (3,5) (2,1) (4,7) (3,0) (3,7) (1,4) (5,6) (6,3) (2,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->5->4->7->3->2->1." - } - ] - }, - { - "id": "hamilton-easy-graph35", - "image": "data/hamilton/graph_visual/Base/easy/graph35.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,1) (0,3) (3,2) (1,2) (4,5) (6,5) (6,0) (5,2) (6,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->2->1->6->5->4." - } - ] - }, - { - "id": "hamilton-easy-graph230", - "image": "data/hamilton/graph_visual/Base/easy/graph230.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,5) (4,8) (4,5) (8,2) (9,2) (4,3) (3,0) (9,1) (9,7) (9,8) (6,8) (9,4) (7,0) (7,2) (5,0) (5,1) (3,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->4->8->2->7->9->1->5->6." - } - ] - }, - { - "id": "hamilton-easy-graph136", - "image": "data/hamilton/graph_visual/Base/easy/graph136.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,6) (8,6) (3,0) (7,1) (8,7) (2,5) (6,5) (5,4) (5,0) (7,4) (4,2) (4,6) (1,4) (2,8) (5,8) (3,1) (2,7) (7,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->1->7->8->6->2->5->4." - } - ] - }, - { - "id": "hamilton-easy-graph180", - "image": "data/hamilton/graph_visual/Base/easy/graph180.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,0) (4,8) (2,3) (5,4) (1,6) (0,8) (2,4) (8,2) (1,8) (3,4) (7,4) (1,7) (5,6) (6,2) (3,6) (8,5) (6,7) (2,0) (2,7) (3,1) (4,0) (7,8) (5,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->4->8->2->3->6->1->7." - } - ] - }, - { - "id": "hamilton-easy-graph276", - "image": "data/hamilton/graph_visual/Base/easy/graph276.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,2) (8,7) (8,3) (2,7) (9,6) (1,4) (3,5) (8,5) (0,8) (1,7) (0,3) (1,5) (2,5) (3,9) (0,1) (0,7) (2,1) (4,3) (5,0) (3,6) (9,8) (6,2) (5,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->7->2->5->1->4->3->9->6." - } - ] - }, - { - "id": "hamilton-easy-graph33", - "image": "data/hamilton/graph_visual/Base/easy/graph33.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (3,1) (4,5) (5,2) (0,4) (2,4) (3,2) (3,5) (6,5) (3,4) (0,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->5->4->2->3->1." - } - ] - }, - { - "id": "hamilton-easy-graph195", - "image": "data/hamilton/graph_visual/Base/easy/graph195.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,3) (1,6) (2,9) (7,0) (2,8) (1,5) (8,7) (2,6) (4,2) (1,9) (2,7) (9,4) (3,4) (3,9) (7,9) (6,5) (0,8) (6,4) (1,0) (5,3) (9,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->8->3->4->2->9->1->6->5." - } - ] - }, - { - "id": "hamilton-easy-graph58", - "image": "data/hamilton/graph_visual/Base/easy/graph58.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,6) (0,7) (6,4) (3,4) (0,1) (2,3) (6,1) (4,0) (3,7) (2,1) (7,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->6->1->2->3->7->5." - } - ] - }, - { - "id": "hamilton-easy-graph241", - "image": "data/hamilton/graph_visual/Base/easy/graph241.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,4) (6,9) (2,6) (8,7) (7,0) (0,8) (2,9) (2,4) (8,9) (1,6) (0,4) (5,6) (6,8) (1,0) (3,8) (1,8) (0,9) (4,7) (5,7) (0,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->5->6->9->2->4->1->8->3." - } - ] - }, - { - "id": "hamilton-easy-graph264", - "image": "data/hamilton/graph_visual/Base/easy/graph264.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,0) (4,5) (5,2) (0,7) (9,2) (2,1) (1,3) (2,7) (1,8) (4,2) (4,0) (1,4) (0,5) (8,3) (6,2) (9,8) (6,3) (9,4) (3,9) (8,5) (5,7) (5,1) (1,6) (0,2) (4,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->1->8->9->4->5->7->2->6." - } - ] - }, - { - "id": "hamilton-easy-graph85", - "image": "data/hamilton/graph_visual/Base/easy/graph85.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,6) (5,6) (3,0) (6,3) (1,5) (4,0) (6,4) (2,5) (1,2) (4,7) (7,0) (4,2) (3,4) (3,1) (2,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->5->2->1->3->4->7." - } - ] - }, - { - "id": "hamilton-easy-graph211", - "image": "data/hamilton/graph_visual/Base/easy/graph211.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,9) (7,2) (1,9) (6,1) (7,4) (6,3) (7,9) (4,6) (2,1) (7,3) (9,2) (8,2) (3,4) (6,0) (7,1) (0,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->9->1->6->3->4->7->2->8." - } - ] - }, - { - "id": "hamilton-easy-graph278", - "image": "data/hamilton/graph_visual/Base/easy/graph278.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,6) (8,0) (0,4) (2,5) (4,9) (1,0) (7,5) (4,8) (8,9) (6,7) (8,3) (3,5) (9,0) (3,1) (1,5) (2,6) (8,5) (1,7) (4,5) (0,3) (8,1) (7,2) (1,4) (2,9) (5,9) (7,3) (6,3) (5,0) (9,7) (1,9) (7,4) (0,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->4->6->7->5->2->9->1->3." - } - ] - }, - { - "id": "hamilton-easy-graph294", - "image": "data/hamilton/graph_visual/Base/easy/graph294.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,3) (8,9) (4,8) (1,3) (7,8) (5,0) (3,5) (5,2) (7,5) (7,9) (1,7) (1,0) (7,4) (9,6) (5,4) (0,7) (2,4) (3,7) (2,8) (5,1) (4,1) (8,5) (3,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->3->8->2->4->1->7->9->6." - } - ] - }, - { - "id": "hamilton-easy-graph183", - "image": "data/hamilton/graph_visual/Base/easy/graph183.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,6) (2,1) (7,2) (0,5) (5,7) (8,4) (8,2) (7,0) (5,4) (1,4) (5,3) (5,6) (5,8) (3,2) (3,7) (3,1) (5,2) (3,8) (0,8) (3,6) (6,8) (1,8) (5,1) (7,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->5->7->2->1->4->8->3." - } - ] - }, - { - "id": "hamilton-easy-graph125", - "image": "data/hamilton/graph_visual/Base/easy/graph125.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,2) (0,1) (3,6) (5,1) (1,4) (6,0) (2,8) (2,7) (4,2) (3,2) (3,7) (5,4) (2,5) (1,7) (8,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->3->7->1->5->4->2->8." - } - ] - }, - { - "id": "hamilton-easy-graph31", - "image": "data/hamilton/graph_visual/Base/easy/graph31.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,3) (5,4) (5,1) (0,5) (6,4) (3,4) (1,6) (2,3) (0,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->1->6->4->3->2." - } - ] - }, - { - "id": "hamilton-easy-graph167", - "image": "data/hamilton/graph_visual/Base/easy/graph167.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,4) (5,8) (7,1) (3,2) (6,3) (4,2) (4,7) (4,6) (3,7) (5,0) (0,8) (3,5) (8,3) (4,1) (1,8) (2,0) (4,3) (6,0) (1,5) (8,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->8->1->7->4->2->3->6." - } - ] - }, - { - "id": "hamilton-easy-graph184", - "image": "data/hamilton/graph_visual/Base/easy/graph184.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,8) (0,6) (4,2) (1,8) (5,7) (2,0) (6,3) (6,1) (8,0) (6,8) (4,3) (7,4) (6,2) (7,2) (4,1) (5,0) (3,8) (5,2) (6,7) (0,4) (2,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->3->4->2->7->5->8->1." - } - ] - }, - { - "id": "hamilton-easy-graph266", - "image": "data/hamilton/graph_visual/Base/easy/graph266.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,4) (3,1) (2,7) (0,9) (5,0) (3,5) (2,8) (6,2) (1,0) (4,3) (7,1) (3,7) (0,3) (5,8) (1,2) (6,8) (4,1) (6,3) (9,1) (9,6) (6,1) (1,8) (1,5) (9,2) (8,7) (9,7) (0,6) (6,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->4->3->1->7->2->6->8->5." - } - ] - }, - { - "id": "hamilton-easy-graph74", - "image": "data/hamilton/graph_visual/Base/easy/graph74.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,0) (7,2) (6,7) (2,1) (6,1) (4,3) (5,4) (3,1) (5,0) (7,5) (0,4) (6,4) (7,0) (4,2) (4,7) (5,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->7->6->1->3->4->5." - } - ] - }, - { - "id": "hamilton-easy-graph94", - "image": "data/hamilton/graph_visual/Base/easy/graph94.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,4) (3,4) (0,7) (7,3) (5,1) (3,1) (6,0) (1,2) (7,6) (5,0) (6,5) (6,4) (6,3) (2,0) (5,4) (7,1) (2,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->4->3->6->5->1->2." - } - ] - }, - { - "id": "hamilton-easy-graph213", - "image": "data/hamilton/graph_visual/Base/easy/graph213.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,4) (6,9) (0,9) (5,8) (9,3) (3,4) (2,1) (4,6) (3,1) (9,7) (2,5) (3,0) (9,8) (6,5) (2,8) (8,3) (3,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->1->2->8->5->6->4->9->7." - } - ] - }, - { - "id": "hamilton-easy-graph128", - "image": "data/hamilton/graph_visual/Base/easy/graph128.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,5) (8,0) (0,1) (4,6) (0,7) (3,5) (2,5) (6,7) (2,0) (0,6) (1,4) (2,8) (8,7) (2,1) (7,1) (3,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->3->7->6->4->1->2->8." - } - ] - }, - { - "id": "hamilton-easy-graph24", - "image": "data/hamilton/graph_visual/Base/easy/graph24.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,6) (3,1) (0,3) (2,3) (6,3) (0,2) (6,2) (1,4) (3,4) (6,1) (5,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->1->4->3->2->5." - } - ] - }, - { - "id": "hamilton-easy-graph16", - "image": "data/hamilton/graph_visual/Base/easy/graph16.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (4,1) (1,5) (2,3) (4,2) (0,3) (5,4) (0,1) (3,5) (0,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->2->4->1->5." - } - ] - }, - { - "id": "hamilton-easy-graph277", - "image": "data/hamilton/graph_visual/Base/easy/graph277.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,5) (4,0) (2,6) (7,8) (1,7) (1,4) (6,0) (8,4) (3,2) (1,6) (8,5) (3,8) (7,6) (9,2) (9,8) (0,7) (0,8) (1,5) (1,8) (5,7) (6,3) (2,7) (2,5) (1,3) (9,6) (4,6) (3,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->5->8->7->1->6->3->2->9." - } - ] - }, - { - "id": "hamilton-easy-graph154", - "image": "data/hamilton/graph_visual/Base/easy/graph154.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,7) (8,5) (2,0) (0,8) (3,4) (2,8) (1,5) (4,5) (6,4) (8,6) (0,1) (5,6) (2,1) (7,1) (8,7) (0,4) (3,2) (5,7) (8,4) (8,3) (1,8) (7,4) (6,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->1->5->8->2->3->4->6." - } - ] - }, - { - "id": "hamilton-easy-graph27", - "image": "data/hamilton/graph_visual/Base/easy/graph27.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,3) (6,5) (1,3) (0,4) (2,5) (4,3) (5,3) (6,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->6->5->2->3->1." - } - ] - }, - { - "id": "hamilton-easy-graph217", - "image": "data/hamilton/graph_visual/Base/easy/graph217.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,5) (1,9) (0,6) (4,9) (8,3) (4,7) (7,1) (7,2) (2,8) (2,0) (2,6) (4,0) (9,0) (6,8) (1,6) (8,1) (2,4) (3,9) (1,4) (5,0) (1,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->7->4->9->1->3->8->6->5." - } - ] - }, - { - "id": "hamilton-easy-graph144", - "image": "data/hamilton/graph_visual/Base/easy/graph144.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,1) (3,7) (2,4) (8,6) (7,6) (3,8) (7,4) (0,1) (0,3) (2,8) (5,8) (8,4) (2,1) (5,0) (6,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->6->7->4->2->8->5." - } - ] - }, - { - "id": "hamilton-easy-graph206", - "image": "data/hamilton/graph_visual/Base/easy/graph206.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,4) (6,9) (6,8) (4,3) (1,8) (7,6) (0,5) (6,5) (4,7) (4,2) (9,4) (5,8) (3,1) (3,5) (9,7) (6,2) (8,3) (3,7) (1,6) (0,8) (8,2) (0,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->6->9->4->7->3->1->8->2." - } - ] - }, - { - "id": "hamilton-easy-graph290", - "image": "data/hamilton/graph_visual/Base/easy/graph290.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,7) (4,0) (0,5) (8,3) (0,2) (5,8) (5,4) (2,9) (9,8) (3,6) (5,9) (7,4) (9,6) (2,5) (2,7) (5,1) (8,6) (3,1) (3,5) (9,0) (7,9) (2,1) (6,7) (4,9) (4,2) (7,5) (6,1) (7,1) (1,8) (8,7) (4,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->5->8->3->7->2->9->6->1." - } - ] - }, - { - "id": "hamilton-easy-graph150", - "image": "data/hamilton/graph_visual/Base/easy/graph150.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,6) (0,1) (2,8) (0,8) (1,4) (0,5) (2,5) (6,8) (0,6) (3,6) (7,2) (8,1) (5,6) (6,2) (7,4) (0,3) (4,2) (3,8) (1,7) (8,4) (3,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->4->7->6->3->8->2->5." - } - ] - }, - { - "id": "hamilton-easy-graph229", - "image": "data/hamilton/graph_visual/Base/easy/graph229.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,7) (2,7) (0,7) (5,2) (0,6) (9,3) (9,5) (0,2) (9,4) (5,0) (6,2) (9,8) (7,3) (6,7) (4,0) (2,8) (7,9) (5,3) (7,5) (1,6) (8,7) (3,2) (8,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->1->7->3->5->2->8->9->4." - } - ] - }, - { - "id": "hamilton-easy-graph104", - "image": "data/hamilton/graph_visual/Base/easy/graph104.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,6) (5,6) (1,4) (5,1) (6,0) (3,0) (7,4) (8,3) (4,5) (5,2) (0,7) (4,6) (7,8) (6,8) (5,7) (1,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->8->7->4->1->6->5->2." - } - ] - }, - { - "id": "hamilton-easy-graph88", - "image": "data/hamilton/graph_visual/Base/easy/graph88.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,7) (1,3) (0,2) (1,2) (7,2) (5,7) (6,1) (3,2) (5,6) (2,4) (6,7) (2,6) (2,5) (0,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->3->1->6->5->7->4." - } - ] - }, - { - "id": "hamilton-easy-graph8", - "image": "data/hamilton/graph_visual/Base/easy/graph8.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,0) (0,1) (4,3) (2,3) (0,5) (4,1) (5,4) (2,1) (5,2) (4,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->4->1->2->5." - } - ] - }, - { - "id": "hamilton-easy-graph92", - "image": "data/hamilton/graph_visual/Base/easy/graph92.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,4) (6,5) (0,7) (2,6) (4,0) (5,3) (0,3) (2,5) (1,0) (1,6) (0,6) (4,3) (2,3) (5,4) (6,3) (1,4) (6,7) (4,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->4->3->5->2->6->1." - } - ] - }, - { - "id": "hamilton-easy-graph231", - "image": "data/hamilton/graph_visual/Base/easy/graph231.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,8) (7,2) (5,2) (6,2) (3,0) (0,9) (1,8) (2,8) (5,6) (1,5) (5,0) (7,8) (8,5) (0,1) (9,4) (3,1) (2,3) (6,3) (7,9) (5,9) (6,0) (4,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->1->8->7->2->6->5->9->4." - } - ] - }, - { - "id": "hamilton-easy-graph47", - "image": "data/hamilton/graph_visual/Base/easy/graph47.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,4) (5,2) (1,0) (1,3) (5,3) (5,4) (5,0) (5,1) (6,1) (1,4) (2,0) (1,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->4->5->3->1->6." - } - ] - }, - { - "id": "hamilton-easy-graph185", - "image": "data/hamilton/graph_visual/Base/easy/graph185.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,8) (5,2) (4,2) (8,4) (2,0) (7,6) (1,2) (8,2) (6,2) (6,0) (8,3) (6,4) (0,3) (5,3) (5,1) (1,0) (2,3) (4,7) (1,3) (0,5) (8,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->5->3->1->8->6->7->4." - } - ] - }, - { - "id": "hamilton-easy-graph157", - "image": "data/hamilton/graph_visual/Base/easy/graph157.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,8) (5,2) (8,2) (1,5) (2,6) (1,7) (4,6) (3,0) (0,5) (7,6) (5,4) (6,3) (4,8) (3,8) (1,6) (5,7) (5,6) (1,2) (7,2) (8,7) (1,4) (1,0) (3,5) (2,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->6->2->5->1->7->8->4." - } - ] - }, - { - "id": "hamilton-easy-graph75", - "image": "data/hamilton/graph_visual/Base/easy/graph75.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,2) (6,4) (7,0) (6,2) (1,4) (1,3) (5,0) (1,5) (7,1) (2,1) (2,7) (6,5) (3,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->2->3->1->4->6->5." - } - ] - }, - { - "id": "hamilton-easy-graph72", - "image": "data/hamilton/graph_visual/Base/easy/graph72.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,0) (6,2) (5,4) (6,0) (1,4) (3,6) (5,6) (1,0) (7,5) (7,1) (4,6) (2,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->4->1->7->5->6->3." - } - ] - }, - { - "id": "hamilton-easy-graph156", - "image": "data/hamilton/graph_visual/Base/easy/graph156.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,1) (3,6) (2,6) (5,2) (1,7) (2,4) (5,6) (7,5) (1,5) (8,5) (0,2) (5,3) (0,8) (8,6) (2,8) (0,4) (5,4) (0,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->4->1->7->5->8->6->3." - } - ] - }, - { - "id": "hamilton-easy-graph39", - "image": "data/hamilton/graph_visual/Base/easy/graph39.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,2) (4,2) (1,4) (2,3) (3,6) (3,4) (6,5) (0,2) (3,0) (0,1) (1,6) (0,4) (2,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->3->4->1->6->5." - } - ] - }, - { - "id": "hamilton-easy-graph236", - "image": "data/hamilton/graph_visual/Base/easy/graph236.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,7) (4,8) (0,7) (6,3) (3,9) (7,9) (0,8) (8,1) (2,9) (0,3) (9,0) (1,4) (2,5) (8,2) (9,6) (8,6) (2,4) (2,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->1->4->8->6->3->9->2->5." - } - ] - }, - { - "id": "hamilton-easy-graph271", - "image": "data/hamilton/graph_visual/Base/easy/graph271.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,1) (8,0) (1,2) (0,2) (3,0) (6,9) (8,7) (5,6) (0,9) (3,2) (7,4) (1,5) (6,0) (9,8) (6,7) (2,4) (8,2) (5,0) (8,5) (3,8) (4,5) (9,1) (0,1) (6,8) (2,9) (9,4) (5,7) (8,4) (4,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->7->1->5->6->9->4->2->3." - } - ] - }, - { - "id": "hamilton-easy-graph79", - "image": "data/hamilton/graph_visual/Base/easy/graph79.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,3) (2,3) (5,6) (6,7) (0,7) (3,1) (0,6) (2,6) (4,0) (5,7) (1,4) (6,3) (5,0) (1,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->5->6->2->3->1->4." - } - ] - }, - { - "id": "hamilton-easy-graph262", - "image": "data/hamilton/graph_visual/Base/easy/graph262.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,3) (1,9) (0,7) (6,9) (7,5) (9,7) (1,8) (3,1) (2,1) (4,3) (8,2) (0,5) (9,4) (3,7) (5,3) (2,5) (0,4) (4,1) (0,2) (4,2) (6,1) (8,9) (6,4) (8,7) (5,6) (5,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->5->3->8->1->9->6->4->2." - } - ] - }, - { - "id": "hamilton-easy-graph261", - "image": "data/hamilton/graph_visual/Base/easy/graph261.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,8) (8,4) (4,6) (9,7) (2,7) (6,5) (8,3) (8,9) (6,3) (5,8) (4,2) (9,3) (1,6) (1,8) (3,0) (7,3) (5,3) (2,6) (9,0) (7,4) (9,5) (1,0) (3,2) (6,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->8->2->4->7->9->5->6->1." - } - ] - }, - { - "id": "hamilton-easy-graph181", - "image": "data/hamilton/graph_visual/Base/easy/graph181.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,5) (0,4) (8,6) (2,8) (5,7) (5,3) (7,8) (1,5) (3,1) (3,8) (7,3) (2,0) (0,3) (2,3) (3,6) (8,0) (5,8) (7,4) (4,6) (0,7) (4,2) (2,5) (6,2) (4,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->7->8->6->3->1->4->2." - } - ] - }, - { - "id": "hamilton-easy-graph5", - "image": "data/hamilton/graph_visual/Base/easy/graph5.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (1,2) (3,2) (3,0) (3,4) (1,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->2->3->4." - } - ] - }, - { - "id": "hamilton-easy-graph95", - "image": "data/hamilton/graph_visual/Base/easy/graph95.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,2) (1,5) (4,2) (6,4) (7,0) (3,4) (1,7) (1,2) (0,1) (5,6) (5,3) (6,2) (3,1) (0,5) (6,1) (3,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->2->4->6->5->1->3." - } - ] - }, - { - "id": "hamilton-easy-graph272", - "image": "data/hamilton/graph_visual/Base/easy/graph272.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,1) (6,1) (3,9) (4,1) (0,2) (8,7) (5,2) (4,3) (2,7) (5,4) (5,9) (8,6) (0,6) (4,7) (5,8) (8,1) (6,3) (9,6) (7,0) (6,7) (8,9) (4,0) (2,8) (0,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->5->4->1->9->3->6->8->7." - } - ] - }, - { - "id": "hamilton-easy-graph83", - "image": "data/hamilton/graph_visual/Base/easy/graph83.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,5) (7,1) (1,5) (7,2) (7,5) (6,5) (1,3) (6,1) (6,3) (0,6) (5,2) (5,4) (0,1) (4,7) (2,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->1->6->3->2->7->4." - } - ] - }, - { - "id": "hamilton-easy-graph114", - "image": "data/hamilton/graph_visual/Base/easy/graph114.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,1) (4,7) (2,1) (8,3) (3,4) (1,4) (0,6) (7,5) (0,5) (8,7) (6,4) (7,3) (2,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->2->5->7->8->3->4->6." - } - ] - }, - { - "id": "hamilton-easy-graph179", - "image": "data/hamilton/graph_visual/Base/easy/graph179.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,3) (4,1) (5,2) (7,6) (7,8) (6,4) (2,1) (6,3) (3,2) (8,1) (0,8) (2,6) (2,8) (5,1) (5,8) (1,3) (5,0) (2,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->7->3->6->4->1->2->5." - } - ] - }, - { - "id": "hamilton-easy-graph225", - "image": "data/hamilton/graph_visual/Base/easy/graph225.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,6) (7,0) (1,4) (3,1) (5,2) (2,0) (8,9) (3,7) (1,2) (1,7) (5,4) (5,3) (8,1) (8,5) (0,4) (2,4) (2,7) (4,6) (6,8) (5,7) (7,8) (5,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->6->4->2->5->3->1->8->9." - } - ] - }, - { - "id": "hamilton-easy-graph67", - "image": "data/hamilton/graph_visual/Base/easy/graph67.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,3) (5,1) (0,6) (5,6) (6,4) (0,2) (3,7) (1,2) (5,7) (7,6) (2,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->7->5->1->2->4->6." - } - ] - }, - { - "id": "hamilton-easy-graph115", - "image": "data/hamilton/graph_visual/Base/easy/graph115.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,1) (3,6) (1,4) (7,1) (5,8) (6,8) (3,8) (3,1) (3,7) (4,6) (6,5) (6,2) (0,2) (1,5) (3,2) (3,5) (7,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->6->1->4->7->3->8->5." - } - ] - }, - { - "id": "hamilton-easy-graph110", - "image": "data/hamilton/graph_visual/Base/easy/graph110.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,8) (3,2) (5,6) (7,5) (4,0) (4,3) (1,5) (2,0) (6,0) (7,4) (7,0) (4,6) (1,0) (6,2) (5,2) (7,3) (6,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->3->2->6->8->7->5->1." - } - ] - }, - { - "id": "hamilton-easy-graph201", - "image": "data/hamilton/graph_visual/Base/easy/graph201.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,7) (1,8) (3,5) (7,0) (0,9) (4,6) (0,2) (6,1) (9,1) (5,7) (9,2) (6,8) (0,8) (0,4) (3,0) (7,4) (7,8) (8,2) (5,6) (6,2) (8,9) (1,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->4->1->8->9->2->6->5->3." - } - ] - }, - { - "id": "hamilton-easy-graph166", - "image": "data/hamilton/graph_visual/Base/easy/graph166.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,3) (4,1) (1,0) (8,1) (3,7) (0,6) (5,2) (2,8) (7,1) (8,0) (6,5) (3,8) (7,8) (3,6) (5,1) (4,5) (2,7) (2,6) (2,3) (0,3) (0,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->4->3->7->8->2->5->6." - } - ] - }, - { - "id": "hamilton-easy-graph42", - "image": "data/hamilton/graph_visual/Base/easy/graph42.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,1) (5,1) (2,5) (5,3) (4,0) (5,0) (4,1) (0,1) (3,2) (4,2) (5,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->1->6->5->2->3." - } - ] - }, - { - "id": "hamilton-easy-graph212", - "image": "data/hamilton/graph_visual/Base/easy/graph212.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,9) (0,6) (4,0) (6,8) (8,5) (3,4) (7,4) (9,0) (7,0) (1,2) (1,4) (2,8) (0,1) (3,8) (3,5) (5,2) (3,6) (1,9) (8,1) (5,1) (9,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->8->3->5->2->1->9->4->7." - } - ] - }, - { - "id": "hamilton-easy-graph293", - "image": "data/hamilton/graph_visual/Base/easy/graph293.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,0) (2,5) (7,9) (9,6) (5,6) (4,8) (6,1) (0,3) (5,3) (8,7) (3,4) (4,0) (0,5) (8,1) (2,7) (3,9) (6,8) (7,3) (4,1) (1,7) (1,9) (0,6) (0,1) (0,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->9->6->1->8->4->3->5->2." - } - ] - }, - { - "id": "hamilton-easy-graph239", - "image": "data/hamilton/graph_visual/Base/easy/graph239.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,0) (0,5) (1,9) (4,2) (5,9) (0,2) (8,3) (2,5) (9,2) (0,3) (3,2) (7,6) (3,5) (6,8) (7,5) (4,3) (6,4) (5,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->7->6->8->3->4->2->9->1." - } - ] - }, - { - "id": "hamilton-easy-graph19", - "image": "data/hamilton/graph_visual/Base/easy/graph19.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (2,0) (0,1) (4,5) (4,3) (4,2) (5,3) (4,1) (2,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->5->3->4->1." - } - ] - }, - { - "id": "hamilton-easy-graph190", - "image": "data/hamilton/graph_visual/Base/easy/graph190.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,3) (4,5) (8,2) (4,2) (0,1) (4,6) (4,9) (5,2) (2,6) (2,7) (1,4) (8,3) (9,7) (5,8) (7,0) (4,7) (7,5) (5,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->4->6->2->5->8->3->7->9." - } - ] - }, - { - "id": "hamilton-easy-graph30", - "image": "data/hamilton/graph_visual/Base/easy/graph30.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,6) (1,6) (5,1) (2,6) (3,4) (4,6) (4,5) (4,0) (0,2) (5,3) (6,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->3->5->1->6->2." - } - ] - }, - { - "id": "hamilton-easy-graph69", - "image": "data/hamilton/graph_visual/Base/easy/graph69.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,6) (3,5) (5,0) (0,6) (2,1) (4,3) (6,5) (1,0) (2,6) (0,4) (7,6) (1,4) (3,2) (5,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->3->4->1->2->6->7." - } - ] - }, - { - "id": "hamilton-easy-graph111", - "image": "data/hamilton/graph_visual/Base/easy/graph111.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,0) (6,3) (1,5) (2,5) (5,7) (7,8) (1,8) (3,8) (8,5) (8,2) (7,4) (4,6) (1,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->5->2->8->7->4->6->3." - } - ] - }, - { - "id": "hamilton-easy-graph98", - "image": "data/hamilton/graph_visual/Base/easy/graph98.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (5,3) (1,5) (0,7) (7,1) (3,6) (5,7) (7,4) (4,6) (3,2) (6,7) (4,2) (0,4) (2,0) (1,0) (5,4) (3,4) (5,2) (2,1) (6,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->1->5->3->6->4->2." - } - ] - }, - { - "id": "hamilton-easy-graph37", - "image": "data/hamilton/graph_visual/Base/easy/graph37.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (3,5) (2,5) (3,1) (6,1) (0,1) (6,2) (6,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->5->2->6->4." - } - ] - }, - { - "id": "hamilton-easy-graph260", - "image": "data/hamilton/graph_visual/Base/easy/graph260.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,5) (4,2) (3,0) (4,1) (9,7) (6,8) (9,0) (7,1) (8,0) (4,9) (6,9) (3,1) (3,8) (6,2) (6,3) (1,2) (4,7) (6,4) (1,8) (3,9) (9,8) (4,3) (0,4) (3,5) (3,7) (0,1) (7,8) (5,8) (0,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->1->4->2->6->8->9->7->5." - } - ] - }, - { - "id": "hamilton-easy-graph41", - "image": "data/hamilton/graph_visual/Base/easy/graph41.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (3,4) (3,2) (6,4) (5,4) (4,0) (2,6) (1,0) (4,1) (1,3) (5,0) (0,2) (6,0) (0,3) (3,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->2->6->4->5." - } - ] - }, - { - "id": "hamilton-easy-graph131", - "image": "data/hamilton/graph_visual/Base/easy/graph131.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,0) (5,6) (5,4) (6,3) (1,4) (2,6) (3,8) (8,5) (8,6) (2,7) (6,1) (7,8) (0,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->6->2->7->8->5->4->1." - } - ] - }, - { - "id": "hamilton-easy-graph160", - "image": "data/hamilton/graph_visual/Base/easy/graph160.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,3) (8,5) (8,2) (2,5) (8,3) (5,1) (2,7) (6,0) (3,4) (7,6) (6,5) (3,7) (3,0) (6,2) (0,8) (4,8) (2,0) (0,1) (7,8) (4,0) (1,7) (0,7) (1,6) (1,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->7->2->3->4->8->5->1." - } - ] - }, - { - "id": "hamilton-easy-graph263", - "image": "data/hamilton/graph_visual/Base/easy/graph263.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,0) (2,8) (4,8) (0,8) (6,8) (7,0) (4,1) (4,6) (3,0) (3,9) (7,6) (0,6) (7,8) (8,5) (2,1) (4,0) (7,9) (1,9) (4,3) (0,1) (2,0) (2,7) (5,2) (3,6) (5,1) (2,9) (3,8) (2,6) (5,6) (5,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->8->2->1->4->6->7->9->3." - } - ] - }, - { - "id": "hamilton-easy-graph186", - "image": "data/hamilton/graph_visual/Base/easy/graph186.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,1) (3,6) (4,2) (4,7) (6,2) (7,8) (6,0) (3,5) (8,5) (1,3) (1,0) (7,3) (5,0) (5,1) (2,0) (1,6) (2,3) (0,8) (5,7) (4,3) (4,5) (6,4) (0,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->3->1->7->8->5->4->2." - } - ] - }, - { - "id": "hamilton-easy-graph71", - "image": "data/hamilton/graph_visual/Base/easy/graph71.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,3) (6,7) (1,6) (3,0) (3,1) (1,0) (7,5) (4,7) (2,6) (5,6) (0,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->4->7->5->6->2." - } - ] - }, - { - "id": "hamilton-easy-graph76", - "image": "data/hamilton/graph_visual/Base/easy/graph76.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,1) (5,2) (0,2) (3,4) (6,0) (2,3) (0,4) (7,3) (0,7) (6,5) (7,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->3->2->5->6->7->1." - } - ] - }, - { - "id": "hamilton-easy-graph200", - "image": "data/hamilton/graph_visual/Base/easy/graph200.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,8) (5,7) (6,7) (7,2) (3,1) (4,3) (1,0) (8,4) (2,0) (3,8) (4,1) (5,8) (7,1) (6,1) (9,0) (6,2) (5,3) (3,7) (6,0) (1,9) (4,2) (0,4) (8,0) (3,9) (3,2) (5,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->4->2->6->7->5->8->9." - } - ] - }, - { - "id": "hamilton-easy-graph117", - "image": "data/hamilton/graph_visual/Base/easy/graph117.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,0) (8,7) (5,1) (1,0) (6,0) (6,1) (3,4) (1,7) (0,7) (1,8) (4,5) (2,7) (2,4) (5,2) (5,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->3->4->2->7->8->1->6." - } - ] - }, - { - "id": "hamilton-easy-graph21", - "image": "data/hamilton/graph_visual/Base/easy/graph21.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (4,1) (3,2) (4,3) (0,3) (0,4) (4,2) (1,5) (5,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->5->4->3->2." - } - ] - }, - { - "id": "hamilton-easy-graph223", - "image": "data/hamilton/graph_visual/Base/easy/graph223.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,5) (3,9) (5,6) (5,8) (2,0) (7,4) (1,7) (6,9) (6,1) (4,5) (3,0) (0,5) (8,4) (9,8) (7,2) (4,1) (4,2) (6,7) (3,5) (1,0) (8,0) (2,9) (1,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->7->4->8->5->3->9->6->1." - } - ] - }, - { - "id": "hamilton-easy-graph234", - "image": "data/hamilton/graph_visual/Base/easy/graph234.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,0) (4,8) (2,1) (9,0) (3,9) (3,4) (6,7) (6,5) (8,0) (7,8) (1,4) (7,1) (4,0) (8,3) (5,9) (1,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->1->4->8->7->6->5->9->3." - } - ] - }, - { - "id": "hamilton-easy-graph242", - "image": "data/hamilton/graph_visual/Base/easy/graph242.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,1) (4,9) (4,2) (1,7) (6,9) (0,2) (7,8) (1,5) (5,3) (3,9) (2,3) (6,5) (7,4) (2,6) (5,2) (3,7) (2,7) (6,1) (4,0) (7,5) (9,7) (6,7) (0,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->5->3->9->4->2->6->7->8." - } - ] - }, - { - "id": "hamilton-easy-graph135", - "image": "data/hamilton/graph_visual/Base/easy/graph135.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,3) (1,8) (2,1) (8,6) (4,0) (0,6) (7,6) (6,4) (5,6) (3,7) (2,3) (3,8) (8,5) (0,3) (2,6) (2,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->6->7->3->2->1->8->5." - } - ] - }, - { - "id": "hamilton-easy-graph268", - "image": "data/hamilton/graph_visual/Base/easy/graph268.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,7) (7,3) (8,7) (9,3) (2,7) (2,1) (9,8) (3,5) (0,9) (8,1) (5,6) (5,2) (4,8) (9,2) (9,5) (7,4) (4,9) (8,3) (5,0) (0,7) (9,7) (0,2) (1,9) (3,1) (4,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->3->7->6->5->2->1->8->4." - } - ] - }, - { - "id": "hamilton-easy-graph197", - "image": "data/hamilton/graph_visual/Base/easy/graph197.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,1) (9,2) (6,4) (6,2) (6,1) (5,3) (7,8) (8,3) (1,8) (4,3) (3,1) (3,6) (4,1) (1,7) (2,0) (8,2) (0,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->2->6->4->3->5->1->8->7." - } - ] - }, - { - "id": "hamilton-easy-graph238", - "image": "data/hamilton/graph_visual/Base/easy/graph238.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,5) (6,4) (4,8) (1,7) (6,9) (1,6) (9,3) (2,8) (6,3) (2,4) (8,9) (6,7) (4,9) (7,3) (9,0) (1,5) (4,1) (5,3) (9,7) (8,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->5->1->7->3->6->4->8->2." - } - ] - }, - { - "id": "hamilton-easy-graph240", - "image": "data/hamilton/graph_visual/Base/easy/graph240.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,9) (2,8) (4,3) (3,0) (0,9) (5,1) (7,2) (9,8) (7,6) (4,7) (1,2) (3,9) (0,6) (6,1) (1,7) (7,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->7->4->3->9->8->2->1->5." - } - ] - }, - { - "id": "hamilton-easy-graph43", - "image": "data/hamilton/graph_visual/Base/easy/graph43.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (1,2) (5,1) (1,0) (0,2) (6,3) (2,5) (1,3) (3,2) (6,2) (4,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->5->2->6->3->4." - } - ] - }, - { - "id": "hamilton-easy-graph23", - "image": "data/hamilton/graph_visual/Base/easy/graph23.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,0) (1,3) (1,2) (0,2) (3,2) (2,4) (4,3) (5,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->1->2->4->5." - } - ] - }, - { - "id": "hamilton-easy-graph170", - "image": "data/hamilton/graph_visual/Base/easy/graph170.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,0) (5,7) (5,1) (3,8) (2,5) (0,1) (2,1) (0,5) (4,2) (5,8) (7,4) (3,1) (6,2) (2,3) (5,4) (0,8) (3,6) (3,4) (1,4) (2,0) (6,7) (8,6) (1,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->5->1->2->4->3->8->6." - } - ] - }, - { - "id": "hamilton-easy-graph193", - "image": "data/hamilton/graph_visual/Base/easy/graph193.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,2) (0,5) (1,4) (8,2) (8,5) (0,6) (9,3) (1,6) (0,9) (9,6) (5,1) (8,0) (3,6) (9,7) (9,1) (0,3) (2,3) (6,8) (3,8) (4,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->8->5->1->4->3->6->9->7." - } - ] - }, - { - "id": "hamilton-easy-graph177", - "image": "data/hamilton/graph_visual/Base/easy/graph177.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,5) (4,2) (1,0) (8,0) (1,3) (6,5) (8,4) (2,5) (7,8) (3,5) (6,8) (3,6) (8,5) (2,7) (7,1) (0,4) (1,8) (2,3) (2,0) (0,7) (4,1) (2,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->5->7->8->4->2->6." - } - ] - }, - { - "id": "hamilton-easy-graph152", - "image": "data/hamilton/graph_visual/Base/easy/graph152.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,4) (5,2) (4,6) (0,3) (8,6) (6,3) (5,3) (1,8) (2,0) (8,5) (2,6) (0,1) (0,8) (0,6) (8,2) (7,0) (8,7) (1,2) (1,4) (3,4) (4,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->6->4->1->2->5->8->7." - } - ] - }, - { - "id": "hamilton-easy-graph49", - "image": "data/hamilton/graph_visual/Base/easy/graph49.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,5) (1,6) (2,6) (2,3) (4,0) (2,1) (4,1) (5,3) (4,6) (3,1) (4,5) (5,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->1->6->2->5->3." - } - ] - }, - { - "id": "hamilton-easy-graph133", - "image": "data/hamilton/graph_visual/Base/easy/graph133.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,5) (7,4) (0,6) (0,5) (0,1) (1,7) (4,3) (2,7) (1,3) (2,4) (6,8) (5,1) (5,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->4->7->2->5->6->8." - } - ] - }, - { - "id": "hamilton-easy-graph142", - "image": "data/hamilton/graph_visual/Base/easy/graph142.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,8) (1,7) (5,7) (3,2) (5,1) (7,6) (7,4) (6,5) (2,8) (0,2) (4,1) (5,3) (0,5) (3,0) (2,7) (4,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->3->5->1->4->7->6->8." - } - ] - }, - { - "id": "hamilton-easy-graph269", - "image": "data/hamilton/graph_visual/Base/easy/graph269.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,4) (8,0) (3,1) (4,8) (7,9) (9,5) (3,8) (3,0) (7,3) (3,2) (9,8) (3,6) (8,2) (4,5) (9,6) (1,2) (4,9) (7,0) (3,4) (3,5) (0,1) (5,6) (9,2) (7,1) (5,8) (6,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->4->1->3->7->9->5->6->2." - } - ] - }, - { - "id": "hamilton-easy-graph2", - "image": "data/hamilton/graph_visual/Base/easy/graph2.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (4,3) (3,2) (2,0) (1,4) (4,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->3->4->1." - } - ] - }, - { - "id": "hamilton-easy-graph191", - "image": "data/hamilton/graph_visual/Base/easy/graph191.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,2) (3,8) (8,9) (5,7) (2,4) (4,7) (2,6) (4,0) (1,7) (5,3) (3,2) (6,3) (9,4) (5,4) (9,5) (0,8) (3,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->2->6->3->8->9->5->7->1." - } - ] - }, - { - "id": "hamilton-easy-graph1", - "image": "data/hamilton/graph_visual/Base/easy/graph1.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (2,1) (4,1) (1,3) (3,4) (0,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->1->4->3." - } - ] - }, - { - "id": "hamilton-easy-graph65", - "image": "data/hamilton/graph_visual/Base/easy/graph65.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (0,7) (3,6) (2,0) (7,1) (3,4) (1,0) (2,3) (0,6) (4,5) (2,7) (2,1) (6,7) (7,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->1->7->6->3->4->5." - } - ] - }, - { - "id": "hamilton-easy-graph209", - "image": "data/hamilton/graph_visual/Base/easy/graph209.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,9) (7,8) (7,3) (9,6) (8,5) (8,4) (9,2) (6,2) (0,5) (1,3) (0,9) (0,8) (1,7) (3,0) (4,6) (9,3) (0,2) (1,6) (6,5) (1,4) (1,2) (5,1) (0,6) (4,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->9->6->2->1->3->7->8->4." - } - ] - }, - { - "id": "hamilton-easy-graph12", - "image": "data/hamilton/graph_visual/Base/easy/graph12.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (4,3) (1,3) (4,5) (4,2) (4,0) (2,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->2->5->3->1." - } - ] - }, - { - "id": "hamilton-easy-graph148", - "image": "data/hamilton/graph_visual/Base/easy/graph148.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (0,6) (2,6) (1,5) (0,2) (0,7) (2,8) (0,4) (4,8) (4,1) (1,8) (3,1) (5,4) (4,6) (5,7) (7,4) (0,8) (3,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->2->8->4->1->5->7->3." - } - ] - }, - { - "id": "hamilton-easy-graph123", - "image": "data/hamilton/graph_visual/Base/easy/graph123.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,6) (0,8) (8,4) (0,2) (5,6) (7,3) (7,8) (2,4) (6,7) (5,1) (4,1) (8,1) (3,4) (7,4) (0,3) (3,6) (0,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->7->3->6->5->1->4->2." - } - ] - }, - { - "id": "hamilton-easy-graph13", - "image": "data/hamilton/graph_visual/Base/easy/graph13.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (2,5) (1,2) (4,3) (3,1) (0,1) (5,3) (1,5) (4,0) (4,5) (2,3) (4,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->2->5->3->4." - } - ] - }, - { - "id": "hamilton-easy-graph100", - "image": "data/hamilton/graph_visual/Base/easy/graph100.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,5) (5,6) (2,0) (4,3) (6,1) (6,7) (4,1) (2,4) (2,6) (1,0) (5,2) (4,5) (7,0) (2,3) (3,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->5->3->4->1->6->7." - } - ] - }, - { - "id": "hamilton-easy-graph40", - "image": "data/hamilton/graph_visual/Base/easy/graph40.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,6) (5,6) (3,4) (1,5) (4,6) (1,3) (6,2) (5,0) (0,3) (2,3) (4,5) (3,6) (1,4) (3,5) (1,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->5->1->4->3->2." - } - ] - }, - { - "id": "hamilton-easy-graph139", - "image": "data/hamilton/graph_visual/Base/easy/graph139.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,1) (7,1) (6,7) (8,0) (6,3) (8,5) (8,4) (0,5) (2,5) (7,5) (2,0) (0,4) (6,2) (3,1) (7,0) (7,2) (5,3) (5,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->1->7->6->3->5->8->4." - } - ] - }, - { - "id": "hamilton-easy-graph224", - "image": "data/hamilton/graph_visual/Base/easy/graph224.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,2) (5,4) (2,0) (8,3) (7,6) (3,5) (6,8) (5,6) (7,8) (1,6) (7,9) (1,8) (2,6) (5,7) (8,9) (2,7) (2,5) (3,4) (1,4) (2,9) (4,0) (9,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->4->5->3->8->1->6->7->9." - } - ] - }, - { - "id": "hamilton-easy-graph112", - "image": "data/hamilton/graph_visual/Base/easy/graph112.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,0) (8,5) (4,3) (0,8) (7,8) (0,1) (5,0) (4,6) (2,6) (1,5) (4,5) (2,5) (8,6) (3,8) (4,0) (7,6) (2,7) (8,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->8->3->4->6->2->5->1." - } - ] - }, - { - "id": "hamilton-easy-graph198", - "image": "data/hamilton/graph_visual/Base/easy/graph198.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,8) (3,9) (6,1) (9,5) (2,4) (4,9) (4,8) (6,3) (4,3) (5,7) (6,5) (0,2) (6,7) (2,5) (0,9) (8,7) (9,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->4->9->3->6->1->8->7->5." - } - ] - }, - { - "id": "hamilton-easy-graph143", - "image": "data/hamilton/graph_visual/Base/easy/graph143.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (3,7) (8,6) (8,2) (6,1) (1,4) (0,3) (6,3) (6,2) (5,1) (5,4) (6,0) (5,6) (2,7) (3,5) (7,6) (5,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->7->2->8->6->1->4->5." - } - ] - }, - { - "id": "hamilton-easy-graph265", - "image": "data/hamilton/graph_visual/Base/easy/graph265.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,4) (8,3) (5,6) (8,7) (1,2) (4,3) (4,8) (5,4) (6,0) (9,0) (1,7) (1,9) (6,3) (2,4) (8,0) (4,9) (8,1) (0,2) (6,7) (7,3) (9,3) (1,3) (3,5) (4,6) (0,1) (2,6) (3,0) (5,2) (9,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->5->4->1->2->9->3->8->7." - } - ] - }, - { - "id": "hamilton-easy-graph78", - "image": "data/hamilton/graph_visual/Base/easy/graph78.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (5,6) (3,0) (5,7) (7,0) (3,1) (0,2) (3,2) (4,2) (2,5) (4,1) (1,7) (2,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->1->4->2->6->5->7." - } - ] - }, - { - "id": "hamilton-easy-graph126", - "image": "data/hamilton/graph_visual/Base/easy/graph126.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,3) (8,7) (4,2) (5,8) (1,3) (5,0) (2,1) (7,4) (6,0) (6,7) (5,6) (4,6) (2,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->8->7->3->1->2->4->6." - } - ] - }, - { - "id": "hamilton-easy-graph106", - "image": "data/hamilton/graph_visual/Base/easy/graph106.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,0) (5,8) (8,3) (4,7) (3,2) (3,6) (3,5) (0,5) (2,4) (2,6) (8,2) (7,8) (0,2) (3,0) (6,5) (0,4) (4,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->8->5->3->6->2->4->1." - } - ] - }, - { - "id": "hamilton-easy-graph137", - "image": "data/hamilton/graph_visual/Base/easy/graph137.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,1) (7,6) (8,3) (2,1) (2,4) (3,1) (2,6) (1,5) (5,0) (7,2) (8,7) (4,5) (8,4) (0,3) (4,7) (6,0) (8,2) (7,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->1->6->7->2->4->8->3." - } - ] - }, - { - "id": "hamilton-easy-graph90", - "image": "data/hamilton/graph_visual/Base/easy/graph90.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,2) (3,6) (2,7) (2,6) (1,7) (1,0) (7,0) (1,6) (5,3) (0,6) (7,6) (4,6) (2,5) (5,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->7->2->3->6->4->5." - } - ] - }, - { - "id": "hamilton-easy-graph53", - "image": "data/hamilton/graph_visual/Base/easy/graph53.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (3,0) (6,2) (2,4) (6,4) (3,2) (1,0) (2,5) (3,5) (5,6) (1,5) (4,5) (0,4) (6,0) (5,0) (4,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->2->6->4->5->1." - } - ] - }, - { - "id": "hamilton-easy-graph228", - "image": "data/hamilton/graph_visual/Base/easy/graph228.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,6) (5,2) (0,2) (7,2) (1,2) (4,5) (1,0) (7,1) (6,8) (5,8) (5,0) (1,5) (9,8) (1,8) (6,3) (3,1) (6,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->7->1->3->6->4->5->8->9." - } - ] - }, - { - "id": "hamilton-easy-graph282", - "image": "data/hamilton/graph_visual/Base/easy/graph282.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,4) (0,2) (8,9) (3,9) (3,2) (7,8) (1,5) (3,4) (6,2) (7,6) (4,5) (7,9) (5,6) (9,6) (0,6) (1,8) (3,6) (4,7) (7,0) (1,6) (1,4) (5,8) (0,3) (4,6) (1,9) (4,2) (3,7) (9,0) (5,9) (1,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->3->9->4->5->1->8->7->6." - } - ] - }, - { - "id": "hamilton-easy-graph64", - "image": "data/hamilton/graph_visual/Base/easy/graph64.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (2,6) (5,6) (2,3) (7,5) (5,2) (7,0) (1,3) (4,7) (3,0) (1,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->2->6->5->7->4." - } - ] - }, - { - "id": "hamilton-easy-graph175", - "image": "data/hamilton/graph_visual/Base/easy/graph175.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,5) (3,5) (1,7) (3,8) (6,4) (7,4) (2,4) (7,0) (0,8) (0,4) (5,0) (6,8) (0,2) (7,6) (4,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->3->8->6->7->1->4->2." - } - ] - }, - { - "id": "hamilton-easy-graph61", - "image": "data/hamilton/graph_visual/Base/easy/graph61.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,1) (3,2) (7,6) (1,6) (3,6) (5,0) (2,0) (0,4) (4,5) (7,4) (3,1) (7,3) (7,1) (2,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->4->1->6->7->3->2." - } - ] - }, - { - "id": "hamilton-easy-graph174", - "image": "data/hamilton/graph_visual/Base/easy/graph174.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,1) (1,8) (4,8) (1,7) (7,8) (2,1) (7,6) (3,2) (3,0) (5,6) (6,2) (6,8) (0,7) (3,6) (8,5) (7,2) (3,8) (2,0) (5,3) (3,1) (7,5) (3,7) (0,6) (0,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->2->1->4->8->7->6->5." - } - ] - }, - { - "id": "hamilton-easy-graph44", - "image": "data/hamilton/graph_visual/Base/easy/graph44.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,6) (1,4) (3,6) (1,6) (3,0) (2,4) (3,5) (4,6) (5,4) (3,2) (1,3) (2,0) (0,4) (5,6) (1,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->6->2->4->1->5." - } - ] - }, - { - "id": "hamilton-easy-graph203", - "image": "data/hamilton/graph_visual/Base/easy/graph203.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,3) (4,2) (6,3) (7,1) (0,5) (5,4) (1,2) (9,3) (5,1) (4,6) (8,0) (2,9) (5,9) (3,8) (9,4) (4,3) (9,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->3->6->4->2->9->5->1->7." - } - ] - }, - { - "id": "hamilton-easy-graph188", - "image": "data/hamilton/graph_visual/Base/easy/graph188.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,8) (2,8) (3,5) (1,7) (7,8) (4,9) (0,3) (0,2) (9,7) (2,9) (6,8) (3,7) (6,9) (7,4) (2,1) (4,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->1->7->4->9->6->8->3->5." - } - ] - }, - { - "id": "hamilton-easy-graph214", - "image": "data/hamilton/graph_visual/Base/easy/graph214.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,1) (9,0) (1,8) (0,7) (2,9) (2,7) (6,9) (7,1) (5,4) (5,8) (7,8) (9,8) (5,7) (4,6) (9,4) (3,4) (2,3) (5,1) (0,4) (8,3) (0,3) (6,2) (3,5) (3,1) (9,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->2->7->1->8->5->3->4->6." - } - ] - }, - { - "id": "hamilton-easy-graph140", - "image": "data/hamilton/graph_visual/Base/easy/graph140.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,7) (5,0) (6,1) (1,4) (1,3) (1,5) (0,6) (7,4) (6,5) (7,0) (5,8) (4,5) (6,2) (5,3) (4,3) (8,7) (3,0) (8,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->7->8->4->3->1->6->2." - } - ] - }, - { - "id": "hamilton-easy-graph9", - "image": "data/hamilton/graph_visual/Base/easy/graph9.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,5) (5,2) (0,4) (2,0) (2,4) (1,3) (0,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->2->5->3->1." - } - ] - }, - { - "id": "hamilton-easy-graph248", - "image": "data/hamilton/graph_visual/Base/easy/graph248.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,2) (4,3) (0,3) (3,7) (4,1) (8,2) (9,8) (5,3) (6,2) (4,6) (9,5) (8,5) (6,3) (9,3) (9,4) (1,0) (2,9) (4,0) (9,7) (7,1) (7,4) (7,8) (8,3) (8,6) (5,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->2->8->9->5->7->1->4->6." - } - ] - }, - { - "id": "hamilton-easy-graph237", - "image": "data/hamilton/graph_visual/Base/easy/graph237.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,0) (7,1) (5,9) (2,9) (2,5) (7,5) (8,1) (6,7) (0,6) (4,8) (0,3) (7,4) (8,5) (2,8) (8,7) (5,3) (2,3) (4,0) (9,0) (0,5) (1,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->7->1->9->5->3->2->8->4." - } - ] - }, - { - "id": "hamilton-easy-graph218", - "image": "data/hamilton/graph_visual/Base/easy/graph218.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,4) (1,2) (7,1) (8,4) (9,5) (2,6) (0,2) (0,3) (9,7) (2,5) (0,9) (6,9) (4,9) (5,4) (8,7) (5,8) (3,6) (5,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->1->4->8->7->9->5->6->3." - } - ] - }, - { - "id": "hamilton-easy-graph192", - "image": "data/hamilton/graph_visual/Base/easy/graph192.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,4) (1,0) (8,4) (1,3) (5,7) (1,9) (5,9) (3,5) (3,7) (2,3) (3,8) (0,8) (9,2) (8,6) (4,2) (0,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->7->5->9->2->4->8->6." - } - ] - }, - { - "id": "hamilton-easy-graph207", - "image": "data/hamilton/graph_visual/Base/easy/graph207.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,9) (0,6) (7,8) (5,9) (6,2) (0,3) (9,6) (2,0) (2,3) (5,8) (3,7) (7,0) (7,4) (2,5) (7,2) (8,9) (7,9) (4,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->2->3->7->4->8->5->9->1." - } - ] - }, - { - "id": "hamilton-easy-graph51", - "image": "data/hamilton/graph_visual/Base/easy/graph51.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (2,3) (4,2) (4,3) (4,6) (6,1) (4,0) (2,0) (1,5) (2,5) (1,4) (0,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->3->2->5->1->6." - } - ] - }, - { - "id": "hamilton-hard-graph429", - "image": "data/hamilton/graph_visual/Base/hard/graph429.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,9) (6,16) (15,3) (3,14) (6,9) (5,15) (5,11) (14,16) (5,13) (4,11) (7,4) (9,16) (8,7) (9,15) (1,0) (12,15) (6,7) (6,1) (4,16) (10,14) (8,9) (6,4) (5,0) (2,15) (1,11) (9,11) (11,17) (13,9) (0,6) (11,12) (3,2) (7,13) (2,11) (6,3) (7,10) (2,9) (5,2) (8,6) (10,16) (16,2) (17,15) (14,12) (16,0) (11,13) (0,10) (4,17) (3,7) (13,8) (14,11) (10,8) (6,14) (8,16) (13,12) (6,13) (12,17)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->6->16->14->3->15->12->17->4->7->10->8->13->5->2->11->1." - } - ] - }, - { - "id": "hamilton-hard-graph555", - "image": "data/hamilton/graph_visual/Base/hard/graph555.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,1) (18,5) (5,9) (9,15) (8,19) (4,10) (14,7) (0,14) (14,8) (4,9) (11,15) (11,7) (9,0) (3,18) (10,12) (9,12) (5,16) (4,12) (15,3) (9,3) (8,10) (9,14) (5,14) (17,3) (0,1) (14,15) (13,3) (9,8) (19,14) (18,17) (2,13) (7,5) (16,18) (3,4) (16,6) (8,3) (2,10) (11,1) (0,17) (4,11) (3,0) (9,10) (14,17) (1,7) (13,18) (4,0) (16,9) (7,4) (6,10) (18,0) (11,17) (3,19) (0,10) (15,17) (1,14) (19,12) (7,8) (5,19) (12,2) (13,0) (18,1) (16,15) (17,12) (16,19) (14,13) (19,6) (14,10) (5,6) (2,0) (16,14) (3,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->14->7->11->15->9->5->16->6->19->8->10->1->18->17->3->13->2->12->4." - } - ] - }, - { - "id": "hamilton-hard-graph5", - "image": "data/hamilton/graph_visual/Base/hard/graph5.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,2) (9,6) (0,2) (7,3) (9,1) (8,2) (5,7) (0,3) (7,0) (3,10) (4,5) (9,10) (8,9) (7,2) (4,3) (2,4) (3,2) (1,10) (8,6) (9,4) (1,5) (6,0) (7,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->6->9->1->10->3->4->5->7->8." - } - ] - }, - { - "id": "hamilton-hard-graph345", - "image": "data/hamilton/graph_visual/Base/hard/graph345.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,12) (11,8) (0,2) (3,0) (6,11) (12,8) (4,6) (9,2) (10,1) (13,9) (5,0) (14,0) (2,13) (5,15) (4,7) (4,14) (6,10) (5,8) (8,7) (9,1) (3,6) (1,13) (1,15) (3,13) (14,11) (12,3) (13,14) (7,11) (11,1) (15,3) (10,12) (0,6) (6,2) (10,11) (8,1) (9,3) (11,13) (14,3) (10,9) (14,7) (1,2) (3,2) (5,2) (3,8) (9,8) (13,15) (11,4) (1,7) (9,5) (12,13) (7,10) (10,8) (0,8) (5,14) (3,4) (3,7) (11,12) (12,9) (10,14) (7,13) (1,0) (15,12) (2,14) (14,6) (14,15) (14,8) (1,3) (2,15) (0,13) (12,7) (8,13) (13,4) (7,9) (15,11) (10,3) (9,0) (0,15) (5,11) (6,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->9->13->1->10->6->11->8->12->14->4->7->3->15->5." - } - ] - }, - { - "id": "hamilton-hard-graph575", - "image": "data/hamilton/graph_visual/Base/hard/graph575.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (3,14) (18,13) (10,9) (11,1) (12,8) (16,17) (11,10) (1,9) (19,15) (0,2) (11,7) (17,12) (5,12) (12,6) (16,2) (12,14) (18,1) (7,4) (18,5) (2,6) (10,19) (2,12) (8,2) (11,3) (1,10) (5,19) (2,11) (17,15) (15,7) (4,11) (12,3) (3,15) (17,2) (14,8) (9,17) (1,2) (3,18) (18,12) (12,4) (5,14) (14,10) (0,13) (19,9) (10,16) (9,7) (9,2) (16,8) (3,7) (18,8) (11,8) (6,7) (0,15) (9,14) (0,9) (8,17) (1,3) (8,5) (16,18) (6,16) (10,12) (0,10) (19,3) (3,4) (1,6) (6,0) (11,16) (14,13) (1,17) (14,1) (18,19) (9,18) (7,16) (0,4) (16,19) (0,7) (18,0) (16,14) (10,3) (17,0) (16,9) (2,7) (6,3) (7,5) (12,15) (8,9) (8,4) (6,4) (7,18) (15,16) (15,14) (5,0) (8,6) (0,12) (5,3) (4,9) (7,8) (16,1) (12,11) (12,1) (19,13) (13,6) (2,13) (4,14) (8,10) (12,7) (14,17) (12,13) (10,18) (1,0) (4,13) (5,6) (17,5) (10,17) (16,3) (2,18)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->16->17->12->8->14->3->11->1->9->10->19->15->7->4->6->13->18->5." - } - ] - }, - { - "id": "hamilton-hard-graph72", - "image": "data/hamilton/graph_visual/Base/hard/graph72.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,4) (9,4) (10,9) (5,11) (3,1) (8,1) (7,9) (9,3) (1,0) (3,7) (3,10) (6,10) (9,6) (7,2) (5,8) (11,2) (8,4) (11,10) (5,0) (5,1) (10,0) (2,9) (7,0) (1,4) (3,2) (6,3) (4,5) (8,7) (1,6) (5,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->9->4->5->8->7->2->11->10->6." - } - ] - }, - { - "id": "hamilton-hard-graph186", - "image": "data/hamilton/graph_visual/Base/hard/graph186.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,5) (12,11) (6,2) (4,8) (7,8) (3,4) (8,12) (12,3) (11,7) (5,2) (8,0) (3,5) (3,13) (3,0) (4,0) (13,1) (9,2) (5,4) (5,9) (12,4) (6,4) (2,8) (6,9) (1,2) (6,8) (3,8) (5,13) (10,9) (13,4) (1,12) (3,2) (1,8) (3,11) (0,11) (7,12) (12,0) (5,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->4->3->13->5->10->9->6->2->1->12->11->7." - } - ] - }, - { - "id": "hamilton-hard-graph152", - "image": "data/hamilton/graph_visual/Base/hard/graph152.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,10) (3,9) (12,0) (12,6) (1,8) (12,3) (11,1) (1,2) (0,7) (6,0) (3,7) (4,0) (3,11) (0,3) (12,4) (5,1) (9,4) (2,0) (10,9) (9,6) (11,7) (2,8) (2,11) (4,1) (6,5) (2,3) (8,7) (7,4) (0,8) (2,4) (1,12) (2,7) (7,9) (5,4) (9,11) (0,11) (10,12) (9,0) (11,8) (11,10) (11,4) (9,12) (6,2) (6,1) (10,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->6->9->3->7->11->1->8->2->4->5->10." - } - ] - }, - { - "id": "hamilton-hard-graph494", - "image": "data/hamilton/graph_visual/Base/hard/graph494.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (10,17) (5,9) (13,0) (1,5) (12,16) (13,11) (1,8) (12,6) (17,4) (0,6) (12,13) (16,5) (0,12) (18,12) (11,14) (1,11) (4,1) (14,0) (12,14) (3,17) (9,4) (9,2) (18,4) (6,2) (12,11) (10,15) (15,5) (3,1) (6,13) (0,15) (14,17) (6,10) (10,14) (12,1) (15,11) (1,13) (10,11) (11,9) (12,2) (14,7) (6,15) (5,12) (0,18) (1,0) (6,11) (14,4) (7,12) (2,1) (8,9) (7,9) (18,8) (5,2) (0,4) (5,7) (7,0) (9,1) (3,13) (1,14) (17,16) (4,8) (0,17) (12,8) (2,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->11->14->12->16->5->15->10->6->2->1->3->17->4->18->8->9->7." - } - ] - }, - { - "id": "hamilton-hard-graph314", - "image": "data/hamilton/graph_visual/Base/hard/graph314.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,1) (1,2) (7,1) (4,8) (1,13) (0,3) (4,10) (13,4) (10,3) (15,13) (15,4) (10,5) (14,11) (11,15) (11,9) (10,1) (13,11) (15,2) (5,8) (12,10) (6,1) (8,15) (11,8) (9,15) (2,4) (8,9) (1,9) (11,0) (5,7) (2,0) (10,9) (9,6) (3,14) (12,1) (6,8) (6,3) (1,4) (9,3) (9,14) (12,9) (4,0) (5,1) (12,13) (1,15) (4,7) (7,11) (9,7) (3,8) (11,12) (2,9) (12,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->10->4->8->5->7->1->11->14->9->6->12->13->15->2." - } - ] - }, - { - "id": "hamilton-hard-graph394", - "image": "data/hamilton/graph_visual/Base/hard/graph394.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,3) (15,4) (16,4) (0,3) (15,16) (13,16) (13,11) (14,7) (8,1) (14,15) (1,5) (5,12) (16,0) (10,11) (3,1) (2,8) (8,0) (16,11) (3,6) (11,8) (1,12) (15,8) (0,5) (9,7) (9,10) (3,13) (14,1) (16,3) (7,12) (4,13) (6,12) (1,16) (10,13) (9,16) (14,0) (16,10) (16,8) (4,7) (7,8) (5,13) (15,7) (3,9) (13,0) (4,9) (2,5) (3,7) (2,14) (10,2) (8,14) (6,11) (6,2) (6,15) (3,8) (6,14) (2,0) (2,1) (4,8) (5,4) (12,10) (6,9) (10,0) (6,0) (12,14) (2,12) (11,0) (10,14) (5,3) (11,2) (14,5) (5,16) (0,9) (2,13) (15,10) (7,1) (2,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->12->5->1->8->2->14->7->9->10->11->13->16->4->15->6." - } - ] - }, - { - "id": "hamilton-hard-graph221", - "image": "data/hamilton/graph_visual/Base/hard/graph221.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (11,3) (6,1) (12,3) (5,1) (9,10) (6,9) (10,2) (8,4) (2,5) (9,5) (10,0) (5,12) (9,1) (4,2) (3,8) (13,5) (10,12) (12,2) (3,9) (3,13) (11,9) (7,2) (4,9) (3,2) (6,10) (13,8) (11,4) (8,6) (8,7) (10,1) (9,2) (4,0) (3,6) (0,9) (1,7) (5,3) (13,6) (8,0) (5,11) (12,4) (0,3) (9,13) (1,3) (11,10) (5,0) (13,11) (13,0) (7,12) (12,0) (13,10) (7,11) (1,13) (7,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->9->6->1->5->2->4->8->3->12->7->11->13." - } - ] - }, - { - "id": "hamilton-hard-graph59", - "image": "data/hamilton/graph_visual/Base/hard/graph59.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,6) (0,4) (0,2) (5,9) (8,0) (10,0) (5,7) (0,3) (4,5) (6,10) (0,1) (4,2) (8,9) (6,0) (5,1) (7,4) (2,5) (9,0) (3,8) (2,6) (8,2) (4,6) (2,9) (3,5) (6,9) (9,3) (2,1) (1,9) (10,8) (6,5) (3,4) (1,3) (10,7) (10,1) (8,1) (0,5) (10,2) (8,4) (9,10) (5,8) (10,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->5->9->8->3->1->6->2->10->7." - } - ] - }, - { - "id": "hamilton-hard-graph256", - "image": "data/hamilton/graph_visual/Base/hard/graph256.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,7) (8,10) (0,9) (1,9) (5,4) (9,8) (14,0) (4,9) (5,7) (12,1) (11,8) (12,6) (3,1) (4,10) (14,4) (7,11) (2,11) (9,5) (0,4) (6,8) (10,3) (6,13) (10,7) (11,0) (14,8) (3,4) (3,9) (3,11) (10,5) (8,1) (13,5) (7,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->1->12->6->13->5->4->14->8->10->3->7->11->2." - } - ] - }, - { - "id": "hamilton-hard-graph144", - "image": "data/hamilton/graph_visual/Base/hard/graph144.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (10,4) (9,6) (9,12) (4,5) (2,0) (2,12) (1,3) (5,11) (8,1) (2,7) (12,1) (5,0) (9,2) (9,10) (4,2) (6,3) (0,8) (12,8) (12,11) (8,3) (3,4) (3,2) (12,6) (12,4) (1,5) (9,11) (5,12) (4,1) (7,0) (6,4) (9,1) (2,10) (7,10) (12,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->12->9->11->5->1->8->3->6->4->10->7." - } - ] - }, - { - "id": "hamilton-hard-graph307", - "image": "data/hamilton/graph_visual/Base/hard/graph307.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,15) (6,7) (15,1) (6,0) (15,5) (3,15) (13,14) (8,12) (4,15) (0,15) (8,15) (9,5) (2,7) (9,11) (7,8) (7,13) (4,2) (11,10) (4,7) (10,14) (6,1) (3,12) (15,6) (6,11) (4,9) (3,13) (8,13) (4,12) (7,9) (12,5) (12,2) (4,6) (7,0) (14,4) (4,0) (12,13) (12,15) (5,13) (6,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->7->2->4->14->10->11->9->5->12->8->13->3->15->1." - } - ] - }, - { - "id": "hamilton-hard-graph497", - "image": "data/hamilton/graph_visual/Base/hard/graph497.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,3) (12,15) (11,8) (1,9) (18,13) (17,13) (6,0) (7,15) (15,9) (6,9) (14,5) (2,5) (7,17) (12,9) (2,6) (5,0) (5,12) (12,6) (8,18) (7,4) (6,18) (7,12) (9,10) (1,13) (3,12) (7,11) (3,11) (10,14) (6,3) (17,11) (6,16) (10,1) (0,1) (15,6) (15,0) (13,7) (2,12) (11,6) (15,14) (13,8) (7,18) (3,10) (9,5) (5,17) (14,6) (2,13) (8,0) (9,2) (1,5) (11,5) (6,7) (1,2) (9,7) (14,18) (2,16) (17,3) (17,9) (16,7) (1,11) (0,17) (2,8) (2,7) (16,4) (14,9) (8,14) (12,4) (4,14) (11,14) (14,13) (10,16) (4,13) (4,1) (7,8) (4,17) (3,2) (13,15) (1,18) (16,0) (15,18) (8,10) (18,16) (16,11) (0,13) (6,4) (0,3) (7,10) (16,13) (12,17)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->9->1->13->18->8->11->7->15->12->5->14->10->3->17->4->16->2." - } - ] - }, - { - "id": "hamilton-hard-graph197", - "image": "data/hamilton/graph_visual/Base/hard/graph197.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,6) (3,12) (4,3) (13,7) (1,7) (11,7) (5,11) (9,5) (10,11) (8,6) (7,8) (9,11) (4,0) (8,12) (11,6) (9,2) (0,2) (8,4) (8,0) (6,1) (1,4) (10,1) (13,0) (4,10) (11,4) (2,13) (12,7) (2,4) (13,4) (13,11) (13,1) (10,12) (3,8) (3,1) (12,9) (5,6) (2,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->3->6->8->7->1->10->12->9->5->11->13->2." - } - ] - }, - { - "id": "hamilton-hard-graph170", - "image": "data/hamilton/graph_visual/Base/hard/graph170.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,9) (2,8) (2,7) (6,2) (5,3) (10,9) (6,12) (6,8) (12,0) (8,11) (6,3) (11,10) (5,2) (7,4) (8,9) (3,9) (2,0) (12,9) (3,8) (4,12) (7,1) (7,9) (8,4) (12,7) (8,12) (11,1) (4,3) (11,2) (2,3) (4,10) (1,0) (5,10) (2,4) (7,5) (8,7) (0,5) (7,0) (7,11) (10,3) (3,7) (10,12) (12,3) (11,6) (3,11) (11,9) (5,12) (4,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->6->9->10->11->8->2->5->3->4->7->1." - } - ] - }, - { - "id": "hamilton-hard-graph581", - "image": "data/hamilton/graph_visual/Base/hard/graph581.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,11) (15,2) (15,5) (10,4) (16,19) (15,16) (14,12) (1,9) (8,5) (15,9) (14,8) (6,12) (5,2) (13,4) (0,4) (18,0) (3,17) (1,8) (12,4) (15,7) (14,2) (6,19) (18,7) (1,4) (1,17) (7,8) (0,6) (10,7) (18,1) (1,13) (7,19) (3,0) (0,11) (2,7) (18,6) (4,18) (9,14) (8,6) (15,10) (2,3) (7,13) (2,11) (9,11) (13,17) (19,14) (19,1) (6,11) (10,2) (15,4) (15,13) (4,3) (5,6) (16,10) (9,8) (3,18) (17,0) (12,16) (3,7) (17,10) (2,17) (19,3) (18,15) (3,11) (10,8) (18,5) (18,17) (17,12) (11,12) (2,16) (15,11) (18,2) (3,13) (4,7) (10,0) (9,0) (6,7) (16,8) (11,13) (8,11) (19,0) (9,4) (0,13) (13,10) (9,12) (19,17) (5,14) (17,11) (1,16) (13,14) (8,0) (4,17) (15,17) (1,10) (14,0) (11,4) (6,10) (6,17) (12,19) (19,13) (14,7) (7,12) (5,4) (5,17) (18,11) (3,9) (18,9) (8,13) (16,6) (16,11) (4,2) (15,19) (18,14) (19,10) (8,2) (16,14) (0,5) (3,1) (6,4) (3,5) (11,19) (14,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->10->7->15->2->5->8->14->12->6->19->16->1->11->9->3->18->17->13." - } - ] - }, - { - "id": "hamilton-hard-graph111", - "image": "data/hamilton/graph_visual/Base/hard/graph111.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,9) (11,10) (10,9) (6,10) (8,7) (1,2) (3,1) (5,10) (9,8) (5,4) (11,2) (8,10) (8,4) (8,2) (4,1) (9,5) (4,9) (0,6) (0,2) (1,5) (2,3) (7,4) (3,6) (4,2) (11,6) (1,10) (9,0) (10,3) (6,5) (9,1) (0,5) (11,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->10->11->2->1->3->9->8->7->4->5." - } - ] - }, - { - "id": "hamilton-hard-graph293", - "image": "data/hamilton/graph_visual/Base/hard/graph293.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,0) (0,2) (3,11) (12,3) (5,0) (0,8) (12,9) (11,9) (2,12) (7,3) (13,1) (5,10) (8,9) (5,11) (12,7) (9,0) (7,4) (11,8) (8,5) (6,14) (1,10) (8,14) (8,10) (6,1) (5,9) (7,13) (3,9) (8,4) (2,10) (10,0) (1,4) (4,2) (2,1) (9,10) (6,3) (6,2) (7,1) (8,12) (4,11) (0,1) (8,3) (10,3) (7,0) (6,4) (14,10) (11,14) (2,14) (2,13) (14,7) (1,12) (13,4) (9,6) (4,3) (10,4) (4,5) (9,13) (11,7) (12,13) (12,4) (14,0) (5,6) (1,11) (13,8) (11,6) (5,3) (2,7) (10,6) (6,12) (5,2) (13,11) (6,8) (0,11) (7,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->1->10->5->11->3->12->9->8->14->6->2->4->7." - } - ] - }, - { - "id": "hamilton-hard-graph569", - "image": "data/hamilton/graph_visual/Base/hard/graph569.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (6,18) (7,17) (4,5) (14,12) (0,7) (2,1) (19,5) (2,0) (18,11) (7,10) (12,18) (8,18) (12,17) (16,12) (9,14) (0,19) (17,15) (8,11) (0,8) (9,8) (7,1) (11,7) (4,11) (17,0) (18,7) (9,0) (6,9) (19,17) (11,13) (5,16) (7,9) (18,19) (8,16) (6,0) (12,6) (4,13) (8,10) (7,19) (15,4) (14,8) (4,19) (8,12) (4,1) (3,1) (2,13) (11,15) (6,2) (15,3) (0,13) (9,2) (6,17) (12,5) (5,17) (18,0) (0,1) (0,16) (13,15) (16,14) (1,9) (10,13) (5,10) (13,6) (8,3) (3,9) (4,9) (2,14) (12,2) (2,17) (10,11) (16,9) (0,5) (1,10) (13,1) (2,16) (17,4) (0,3) (14,0) (10,19) (12,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->17->12->14->9->8->18->6->2->1->3->15->4->11->13->10->19->5->16." - } - ] - }, - { - "id": "hamilton-hard-graph125", - "image": "data/hamilton/graph_visual/Base/hard/graph125.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,0) (9,3) (7,3) (0,10) (12,9) (2,7) (4,7) (2,0) (2,8) (10,8) (8,7) (6,5) (6,2) (4,8) (7,0) (6,8) (9,8) (1,2) (3,10) (7,5) (0,8) (4,6) (5,3) (10,4) (9,5) (3,4) (8,5) (0,11) (6,11) (6,1) (3,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->6->1->2->7->3->10->4->8->5->9->12." - } - ] - }, - { - "id": "hamilton-hard-graph189", - "image": "data/hamilton/graph_visual/Base/hard/graph189.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,13) (2,11) (4,9) (10,2) (11,12) (2,5) (13,1) (9,12) (6,11) (3,1) (6,13) (7,12) (8,5) (5,3) (9,11) (6,7) (3,13) (8,13) (11,1) (5,1) (6,5) (5,0) (5,4) (10,13) (8,10) (0,13) (10,9) (2,9) (10,0) (6,8) (3,12) (2,1) (9,6) (7,1) (0,2) (6,3) (7,13) (2,6) (12,10) (8,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->2->11->12->13->3->1->7->6->8->10->9->4." - } - ] - }, - { - "id": "hamilton-hard-graph426", - "image": "data/hamilton/graph_visual/Base/hard/graph426.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (13,4) (12,1) (14,13) (3,16) (12,0) (11,17) (14,1) (12,15) (0,3) (11,6) (13,6) (15,7) (17,12) (0,9) (9,14) (6,4) (12,14) (4,15) (2,14) (13,0) (1,16) (4,1) (5,9) (11,8) (4,9) (7,6) (17,4) (6,0) (2,13) (16,15) (5,0) (14,8) (9,15) (2,10) (2,3) (10,14) (8,2) (8,0) (6,8) (16,10) (5,13) (16,7) (17,15) (8,15) (13,7) (8,12) (6,1) (13,16) (15,2) (8,7) (11,2) (16,0) (11,9) (9,1) (11,5) (11,7) (5,8) (7,5) (13,15) (10,4) (11,4) (12,6) (6,5) (1,10) (9,6) (13,17) (11,16) (3,6) (9,2) (1,17)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->1->14->13->4->6->11->17->15->7->8->5->9->2->10->16->3." - } - ] - }, - { - "id": "hamilton-hard-graph132", - "image": "data/hamilton/graph_visual/Base/hard/graph132.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (4,10) (8,10) (2,9) (1,9) (6,3) (6,9) (8,0) (10,0) (12,9) (0,7) (2,7) (8,11) (2,8) (9,10) (4,12) (1,12) (2,3) (9,5) (2,5) (4,2) (9,11) (0,9) (12,8) (11,6) (12,10) (5,12) (4,11) (3,5) (6,12) (5,0) (3,4) (7,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->10->4->12->1->9->2->7->5->3->6->11." - } - ] - }, - { - "id": "hamilton-hard-graph162", - "image": "data/hamilton/graph_visual/Base/hard/graph162.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,11) (7,10) (5,10) (10,12) (5,3) (12,8) (9,1) (7,0) (1,8) (0,8) (10,0) (8,5) (11,9) (5,0) (2,0) (0,1) (11,7) (3,6) (10,9) (5,4) (3,2) (1,5) (10,11) (11,1) (4,12) (12,9) (5,7) (12,11) (1,2) (0,9) (3,11) (9,4) (2,4) (12,6) (10,3) (0,4) (0,11) (3,9) (7,9) (8,11) (5,9) (7,2) (3,4) (0,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->10->5->3->6->11->9->1->8->12->4->2." - } - ] - }, - { - "id": "hamilton-hard-graph286", - "image": "data/hamilton/graph_visual/Base/hard/graph286.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,8) (11,1) (9,11) (14,10) (8,14) (10,13) (8,0) (9,4) (7,0) (10,9) (3,0) (13,5) (8,1) (5,10) (8,7) (7,2) (11,2) (3,5) (14,1) (5,2) (3,2) (10,0) (1,4) (12,10) (3,1) (5,8) (12,6) (9,7) (9,12) (5,9) (6,0) (2,10) (12,11) (11,5) (4,7) (0,4) (10,1) (6,3) (12,1) (11,6) (11,3) (8,2) (10,8) (10,3) (3,7) (1,5) (13,8) (12,7) (4,8) (0,5) (12,13) (8,11) (6,8) (2,6) (1,13) (14,2) (4,6) (1,7) (8,12) (7,14) (3,9) (14,6) (4,3) (13,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->9->11->1->14->10->13->5->3->2->7->4->6->12." - } - ] - }, - { - "id": "hamilton-hard-graph281", - "image": "data/hamilton/graph_visual/Base/hard/graph281.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (13,1) (1,3) (7,10) (4,7) (10,0) (9,8) (12,14) (0,12) (5,10) (4,9) (2,0) (8,7) (2,5) (1,0) (4,10) (4,6) (1,2) (14,2) (13,4) (1,8) (0,14) (1,11) (0,4) (10,2) (2,11) (14,10) (8,2) (6,13) (9,12) (11,5) (12,2) (4,12) (5,7) (1,5) (5,9) (14,3) (9,3) (8,3) (2,7) (14,6) (13,0) (11,4) (13,11) (12,7) (5,12) (9,14) (11,7) (5,3) (0,9) (6,11) (4,1) (6,10) (2,6) (14,4) (10,11) (14,5) (11,3) (3,12) (11,12) (0,5) (5,6) (14,7) (8,5) (9,1) (8,13) (6,9) (4,3) (8,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->7->4->9->8->1->13->6->14->12->2->5->11->3." - } - ] - }, - { - "id": "hamilton-hard-graph395", - "image": "data/hamilton/graph_visual/Base/hard/graph395.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,5) (0,4) (12,4) (2,10) (8,1) (12,8) (16,0) (6,13) (8,10) (7,16) (9,6) (16,8) (14,6) (15,13) (14,12) (9,11) (2,14) (5,14) (2,8) (13,10) (0,11) (12,0) (15,5) (3,4) (15,11) (14,7) (3,2) (7,15) (12,7) (5,13) (6,11) (9,13) (16,9) (5,16) (13,0) (16,13) (6,1) (3,16) (4,10) (10,1) (9,10) (12,1) (3,6) (13,4) (0,10) (11,7) (15,2) (3,10) (8,4) (3,15) (14,1) (15,10) (14,13) (3,0) (1,2) (5,9) (0,1) (12,2) (7,9) (2,16) (12,15) (15,16) (14,8) (13,1) (13,7) (13,3) (6,12) (10,11) (2,4) (5,4) (4,6) (16,4) (6,0) (5,3) (14,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->12->8->1->6->13->15->5->11->9->16->7->14->2->10->3." - } - ] - }, - { - "id": "hamilton-hard-graph560", - "image": "data/hamilton/graph_visual/Base/hard/graph560.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (13,8) (1,3) (8,16) (16,12) (15,5) (0,6) (15,18) (8,14) (11,1) (2,15) (4,5) (13,19) (19,11) (15,3) (17,15) (12,15) (5,16) (18,19) (12,7) (5,8) (2,19) (8,3) (12,1) (6,17) (14,13) (19,4) (5,3) (6,1) (3,12) (10,3) (17,2) (2,6) (6,15) (13,5) (8,0) (18,12) (4,14) (5,2) (6,7) (1,9) (9,10) (16,11) (11,4) (6,8) (5,7) (9,18) (16,6) (2,7) (2,18) (12,5) (2,16) (9,11) (11,0) (7,15) (5,17) (9,13) (16,13) (10,15) (12,19) (13,10) (12,9) (12,14) (6,12) (11,18) (10,8) (19,10) (7,14) (16,1) (7,17) (0,12) (18,8) (18,7) (2,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->17->15->5->4->19->13->8->16->12->1->3->10->9->11->18->2->7->14." - } - ] - }, - { - "id": "hamilton-hard-graph18", - "image": "data/hamilton/graph_visual/Base/hard/graph18.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,5) (6,10) (0,6) (5,8) (5,2) (6,5) (1,3) (4,8) (4,0) (8,3) (1,8) (4,9) (2,3) (4,3) (3,0) (1,7) (10,3) (2,8) (9,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->10->5->9->4->8->2->3->1->7." - } - ] - }, - { - "id": "hamilton-hard-graph505", - "image": "data/hamilton/graph_visual/Base/hard/graph505.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (18,0) (8,9) (17,14) (5,4) (0,12) (6,14) (18,8) (14,15) (18,3) (17,16) (14,3) (7,4) (17,9) (15,11) (13,14) (10,1) (18,4) (12,14) (13,11) (18,2) (0,9) (10,0) (5,14) (4,8) (15,16) (7,2) (0,6) (12,5) (18,11) (9,11) (16,5) (7,18) (17,11) (13,5) (7,5) (13,15) (1,12) (13,18) (2,10) (8,13) (6,8) (15,5) (15,12) (6,16) (8,17) (14,1) (17,18) (13,16) (9,5) (4,0) (14,11) (2,6) (2,14) (2,15) (17,15) (0,7) (12,18) (4,15) (10,16) (10,6) (11,7) (12,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->18->8->9->17->16->15->11->13->5->4->7->2->10->1->12->6->14->3." - } - ] - }, - { - "id": "hamilton-hard-graph305", - "image": "data/hamilton/graph_visual/Base/hard/graph305.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (5,15) (10,11) (15,3) (1,15) (11,8) (12,9) (5,13) (11,5) (1,5) (3,10) (3,2) (11,4) (3,11) (7,8) (3,9) (7,1) (9,5) (4,1) (14,7) (13,4) (15,7) (9,7) (4,12) (11,13) (15,12) (9,6) (13,6) (11,9) (9,14) (6,5) (12,10) (8,14) (13,10) (9,10) (13,7) (12,2) (13,2) (4,7) (1,6) (1,0) (4,3) (13,14) (0,4) (2,7) (6,10) (11,6) (2,9) (15,2) (6,7) (11,7) (12,7) (0,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->15->5->13->4->11->10->3->2->12->9->6->7->8->14." - } - ] - }, - { - "id": "hamilton-hard-graph21", - "image": "data/hamilton/graph_visual/Base/hard/graph21.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,4) (0,10) (9,8) (3,5) (3,7) (1,4) (2,7) (1,0) (5,7) (4,9) (1,3) (9,0) (2,9) (0,6) (9,6) (4,8) (6,2) (2,1) (4,7) (8,5) (0,8) (8,7) (3,10) (10,9) (10,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->3->5->4->1->2->7->8->9->6." - } - ] - }, - { - "id": "hamilton-hard-graph190", - "image": "data/hamilton/graph_visual/Base/hard/graph190.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,6) (9,3) (9,7) (11,7) (3,7) (11,12) (5,4) (5,2) (9,8) (12,1) (0,12) (3,4) (9,6) (2,8) (2,4) (10,7) (9,4) (13,6) (5,6) (8,0) (1,4) (4,6) (0,10) (7,1) (4,13) (3,12) (13,2) (13,1) (8,10) (6,12) (11,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->11->7->9->3->4->5->6->1->13->2->8->10." - } - ] - }, - { - "id": "hamilton-hard-graph358", - "image": "data/hamilton/graph_visual/Base/hard/graph358.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,3) (8,10) (15,3) (11,2) (12,6) (10,2) (15,12) (12,8) (4,9) (7,8) (15,9) (13,14) (9,8) (0,6) (4,13) (13,3) (0,15) (6,3) (15,7) (8,0) (8,3) (0,1) (2,9) (0,7) (0,10) (8,13) (2,0) (14,7) (11,0) (1,7) (3,4) (13,2) (6,8) (9,6) (4,15) (14,4) (10,12) (5,7) (10,7) (8,11) (7,13) (7,3) (3,5) (1,11) (12,2) (8,4) (8,2) (4,1) (5,2) (9,7) (4,0) (1,10) (5,12) (11,9) (0,5) (1,9) (2,3) (2,15) (13,10) (14,15) (3,11) (6,2) (15,1) (14,1) (12,0) (2,7) (1,5) (13,9) (15,6) (8,14) (13,1) (12,14) (12,4) (3,10) (3,14) (5,9) (1,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->12->15->3->1->7->8->10->13->14->4->9->11->2->5." - } - ] - }, - { - "id": "hamilton-hard-graph508", - "image": "data/hamilton/graph_visual/Base/hard/graph508.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (9,18) (0,13) (5,9) (4,9) (2,17) (3,12) (7,6) (4,18) (1,18) (11,16) (13,8) (10,12) (9,12) (10,9) (18,5) (14,13) (9,14) (8,15) (14,3) (2,10) (1,10) (6,4) (16,6) (16,3) (17,18) (4,10) (3,6) (7,16) (5,13) (11,8) (12,18) (8,2) (16,9) (13,4) (7,5) (6,0) (13,3) (15,2) (9,3) (8,16) (16,2) (18,10) (5,2) (17,4) (12,14) (7,1) (14,5) (10,5) (13,17) (1,11) (13,16) (16,17) (18,11) (12,6) (14,8) (17,11) (1,14) (17,9) (15,12) (9,7) (12,7) (12,5) (1,9) (0,3) (8,12) (15,3) (7,8) (9,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->8->15->2->17->18->9->5->7->6->4->10->12->3->14->1->11->16." - } - ] - }, - { - "id": "hamilton-hard-graph355", - "image": "data/hamilton/graph_visual/Base/hard/graph355.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (6,5) (14,9) (4,0) (6,11) (4,14) (1,12) (15,5) (14,10) (1,7) (12,5) (6,4) (4,15) (9,7) (10,2) (8,7) (3,10) (8,14) (11,13) (7,15) (12,0) (2,1) (8,1) (6,7) (5,10) (9,8) (7,14) (2,13) (13,12) (10,0) (3,12) (15,10) (8,12) (15,8) (11,1) (15,12) (4,10) (6,13) (7,13) (3,7) (9,2) (2,5) (3,15) (14,3) (0,8) (4,7) (0,2) (10,1) (10,8) (15,9) (0,1) (9,4) (14,13) (0,13) (14,6) (12,2) (0,5) (2,7) (15,11) (7,10) (3,13) (0,6) (11,2) (0,15) (9,13) (14,2) (13,10) (11,10) (4,8) (2,15) (12,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->14->9->7->1->12->5->6->11->13->2->10->3->15->8." - } - ] - }, - { - "id": "hamilton-hard-graph434", - "image": "data/hamilton/graph_visual/Base/hard/graph434.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,16) (15,7) (8,16) (15,9) (2,7) (13,7) (13,17) (5,9) (3,17) (3,11) (0,12) (13,12) (12,8) (13,4) (13,5) (8,3) (8,7) (3,4) (4,10) (9,1) (16,13) (2,1) (3,13) (2,4) (10,15) (9,17) (6,12) (6,13) (15,6) (8,10) (9,14) (8,14) (8,2) (4,12) (11,4) (12,10) (8,15) (5,2) (12,9) (1,3) (10,13) (14,10) (14,5) (12,1) (16,9) (15,4) (4,0) (5,12) (16,11) (8,1) (9,2) (0,15) (7,11) (2,10) (9,6) (0,7) (7,6) (0,1) (0,14) (6,4) (1,11) (1,14) (17,6) (3,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->13->7->15->9->5->2->1->16->8->14->10->4->11->3->17->6." - } - ] - }, - { - "id": "hamilton-hard-graph51", - "image": "data/hamilton/graph_visual/Base/hard/graph51.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,10) (1,0) (6,2) (3,10) (10,6) (10,9) (9,7) (8,5) (5,4) (8,6) (0,9) (6,9) (4,2) (5,9) (3,0) (5,2) (8,4) (6,4) (2,0) (9,8) (0,6) (6,3) (2,8) (6,1) (3,1) (7,8) (9,4) (0,5) (0,8) (3,4) (7,10) (1,4) (0,7) (2,7) (2,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->6->2->4->5->8->9->7->10->3." - } - ] - }, - { - "id": "hamilton-hard-graph331", - "image": "data/hamilton/graph_visual/Base/hard/graph331.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,10) (3,12) (3,13) (12,2) (14,8) (0,8) (11,14) (9,2) (15,8) (15,2) (1,15) (7,9) (13,15) (4,9) (14,6) (2,10) (10,14) (10,7) (8,10) (12,6) (7,4) (4,2) (13,9) (4,11) (3,10) (11,6) (13,2) (11,2) (4,5) (8,3) (5,14) (2,7) (12,1) (1,9) (9,15) (1,6) (11,5) (6,8) (9,0) (2,3) (5,12) (10,0) (14,7) (9,14) (14,2) (11,3) (12,0) (12,15) (12,4) (8,12) (1,14) (15,7) (4,1) (2,8) (10,4) (14,12) (5,8) (4,13) (15,0) (6,7) (1,2) (8,4) (15,10) (5,0) (1,13) (4,3) (9,10) (13,8) (3,15) (13,14) (5,1) (5,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->14->11->4->9->2->12->3->13->15->10->7->6->1->5." - } - ] - }, - { - "id": "hamilton-hard-graph357", - "image": "data/hamilton/graph_visual/Base/hard/graph357.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,8) (5,0) (15,3) (10,4) (6,4) (0,1) (14,5) (14,4) (4,5) (14,13) (0,2) (11,6) (12,13) (14,3) (7,13) (10,5) (12,14) (12,8) (10,15) (10,8) (1,6) (11,1) (3,0) (8,13) (3,2) (9,2) (5,9) (5,3) (14,8) (5,2) (15,4) (4,12) (3,13) (9,8) (7,11) (4,13) (10,6) (9,15) (1,4) (7,10) (3,10) (5,1) (1,10) (9,13) (1,7) (2,4) (5,7) (0,14) (11,2) (13,11) (12,10) (15,11) (15,7) (8,7) (9,4) (3,12) (7,6) (8,4) (4,3) (0,8) (8,15) (0,10) (2,1) (15,0) (13,10) (15,6) (6,14) (2,15) (13,6) (10,11) (8,5) (12,15) (14,7) (0,11) (11,5) (4,0) (7,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->14->4->10->15->3->2->9->8->1->6->11->7->13->12." - } - ] - }, - { - "id": "hamilton-hard-graph450", - "image": "data/hamilton/graph_visual/Base/hard/graph450.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (13,3) (6,12) (4,9) (6,14) (10,13) (6,2) (9,3) (10,12) (8,14) (9,11) (16,3) (17,16) (1,16) (15,14) (1,15) (4,0) (15,5) (6,10) (2,17) (13,6) (17,4) (6,3) (1,3) (3,15) (7,9) (14,7) (0,12) (1,17) (11,6) (14,5) (3,8) (17,12) (7,11) (1,7) (0,1) (16,9) (4,8) (16,6) (12,16) (8,0) (13,5) (2,0) (0,14) (13,7) (14,12) (16,7) (5,2) (13,9) (0,9) (14,13) (1,8) (10,5) (10,1) (16,0) (9,12) (11,17) (9,6) (10,17) (2,4) (6,1) (4,10) (0,5) (7,10) (11,13) (5,6) (8,5) (1,13) (15,2) (7,17) (7,15) (15,4) (3,14) (4,5) (10,0) (3,11) (13,8) (15,8) (12,1) (4,6) (17,9) (12,15) (16,10) (8,2) (2,3) (11,14) (5,11) (0,6) (10,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->9->3->13->10->12->6->14->8->1->16->17->2->5->15->7->11." - } - ] - }, - { - "id": "hamilton-hard-graph86", - "image": "data/hamilton/graph_visual/Base/hard/graph86.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,6) (7,8) (0,3) (2,9) (1,4) (5,3) (5,4) (1,10) (0,7) (9,3) (2,7) (2,3) (0,2) (6,0) (6,10) (8,5) (4,2) (1,0) (0,8) (5,11) (1,6) (10,11) (11,0) (7,1) (3,7) (5,6) (4,10) (1,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->9->2->7->6->1->4->10->11->5->8." - } - ] - }, - { - "id": "hamilton-hard-graph409", - "image": "data/hamilton/graph_visual/Base/hard/graph409.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,16) (2,11) (14,16) (7,2) (6,12) (13,15) (9,15) (2,14) (15,2) (2,1) (4,5) (14,9) (11,3) (11,13) (15,14) (11,5) (1,15) (6,3) (5,16) (6,5) (6,15) (9,4) (8,0) (16,15) (1,6) (8,3) (10,1) (12,0) (15,5) (12,3) (15,12) (10,7) (10,13) (15,0) (13,5) (10,0) (7,0) (8,2) (16,7) (1,5) (13,9) (6,4) (13,7) (10,14) (8,11) (3,7) (1,14) (0,3) (11,16) (3,15) (16,3) (11,15) (2,16) (2,13) (8,9) (12,13) (11,4) (6,10) (4,2) (1,9) (4,10) (1,8) (7,12) (4,15) (1,12) (15,8) (14,5) (8,12) (4,13) (7,5) (13,3) (16,4) (2,10) (2,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->16->14->2->11->3->6->12->15->13->10->1->8->9->4->5->7." - } - ] - }, - { - "id": "hamilton-hard-graph140", - "image": "data/hamilton/graph_visual/Base/hard/graph140.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,8) (12,10) (0,1) (0,2) (10,5) (8,1) (2,12) (5,11) (11,8) (10,7) (9,12) (9,0) (6,2) (0,10) (3,7) (9,4) (6,4) (2,1) (0,12) (3,5) (9,6) (8,0) (2,3) (1,5) (4,3) (12,3) (6,0) (2,10) (9,3) (0,11) (2,4) (12,5) (3,6) (11,7) (8,5) (1,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->8->7->10->12->2->6->4->9->3->5->11." - } - ] - }, - { - "id": "hamilton-hard-graph157", - "image": "data/hamilton/graph_visual/Base/hard/graph157.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,4) (9,12) (10,9) (11,3) (9,2) (7,9) (7,0) (7,2) (11,9) (4,7) (6,5) (2,6) (7,8) (10,12) (11,0) (6,3) (10,4) (2,8) (4,1) (0,4) (6,0) (8,10) (3,9) (10,1) (9,8) (3,5) (1,6) (7,1) (2,10) (12,4) (8,12) (11,12) (8,1) (5,8) (9,0) (3,8) (7,11) (0,12) (7,3) (6,8) (5,7) (11,10) (3,12) (2,3) (0,5) (1,9) (6,4) (1,12) (2,5) (6,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->9->12->10->4->2->6->1->8->5->3->11." - } - ] - }, - { - "id": "hamilton-hard-graph270", - "image": "data/hamilton/graph_visual/Base/hard/graph270.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,7) (8,0) (2,8) (5,0) (4,3) (6,3) (10,8) (14,13) (11,2) (0,11) (7,5) (13,7) (5,3) (11,3) (0,2) (5,14) (13,8) (2,9) (5,4) (0,3) (2,4) (6,8) (10,14) (8,7) (12,4) (9,7) (3,13) (0,13) (13,5) (6,10) (9,5) (6,14) (12,13) (5,11) (4,11) (2,3) (12,6) (6,0) (7,4) (7,14) (6,13) (0,10) (10,3) (8,14) (7,1) (9,6) (12,10) (12,1) (0,7) (12,0) (9,11) (10,5) (1,2) (3,14) (10,4) (2,10) (1,8) (13,9) (10,11) (5,12) (1,5) (5,6) (9,12) (4,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->2->11->7->5->3->4->10->14->13->6->9->12->1." - } - ] - }, - { - "id": "hamilton-hard-graph371", - "image": "data/hamilton/graph_visual/Base/hard/graph371.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,13) (15,11) (7,1) (3,11) (1,2) (3,10) (6,11) (6,2) (10,8) (0,4) (9,8) (7,13) (15,1) (13,2) (4,3) (12,13) (4,5) (5,2) (13,5) (8,14) (15,3) (9,10) (14,13) (5,3) (4,12) (6,3) (10,2) (8,11) (14,10) (8,13) (7,14) (16,3) (4,7) (11,0) (2,11) (13,0) (7,15) (1,8) (3,14) (16,4) (6,0) (16,14) (1,3) (12,16) (16,13) (5,14) (8,15) (9,15) (12,2) (5,10) (12,10) (4,8) (1,12) (12,6) (16,6) (10,11) (1,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->3->11->13->7->1->2->6->12->16->14->8->15->9->10->5." - } - ] - }, - { - "id": "hamilton-hard-graph455", - "image": "data/hamilton/graph_visual/Base/hard/graph455.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,14) (1,13) (1,17) (4,13) (14,9) (11,12) (11,13) (7,17) (4,17) (8,16) (17,16) (0,1) (0,16) (15,11) (10,1) (17,3) (11,8) (9,11) (6,2) (11,17) (12,17) (15,2) (4,2) (15,10) (16,13) (1,3) (7,8) (2,8) (2,17) (0,15) (11,14) (17,9) (4,1) (7,6) (10,9) (4,11) (9,3) (0,17) (3,12) (2,1) (6,3) (16,11) (11,7) (1,5) (16,15) (1,9) (13,8) (5,14) (10,7) (6,12) (9,16) (12,8) (16,10) (2,9) (11,10) (3,4) (15,13) (13,5) (5,12) (2,0) (10,14) (7,2) (5,6) (12,16) (12,13) (10,4) (14,3) (4,16) (9,8) (11,3) (15,1) (10,6) (5,7) (11,6) (7,9) (6,17) (4,7) (10,13) (6,16) (2,14) (17,8) (1,7) (12,0) (3,8) (4,6) (2,3) (15,7) (4,8) (0,5) (7,12) (13,7) (9,15) (2,13) (9,5) (12,2) (0,13) (5,17) (4,14) (2,5) (4,0) (13,9) (14,0) (10,0) (12,14) (5,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->13->4->17->7->8->16->11->12->3->9->14->15->2->5->6->10." - } - ] - }, - { - "id": "hamilton-hard-graph67", - "image": "data/hamilton/graph_visual/Base/hard/graph67.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,6) (4,8) (9,10) (10,3) (1,9) (2,0) (11,10) (4,11) (2,1) (3,6) (8,5) (3,9) (7,9) (4,6) (9,8) (6,7) (10,7) (3,5) (1,4) (9,2) (1,10) (1,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->1->6->3->9->7->10->11->4->8->5." - } - ] - }, - { - "id": "hamilton-hard-graph374", - "image": "data/hamilton/graph_visual/Base/hard/graph374.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (8,2) (7,5) (14,1) (11,15) (4,7) (0,14) (0,5) (4,11) (6,4) (11,13) (12,1) (14,16) (5,11) (3,7) (8,15) (0,1) (0,6) (1,10) (16,4) (5,10) (7,9) (4,0) (5,4) (2,0) (2,13) (0,9) (7,2) (1,6) (3,14) (3,11) (10,4) (6,16) (12,16) (15,4) (10,8) (16,8) (6,10) (12,9) (13,3) (1,15) (13,10) (15,14) (3,0) (8,12) (8,11) (3,15) (3,5) (15,6) (9,1) (8,14) (16,10) (10,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->14->1->12->16->4->7->5->11->3->13->2->8->15->6->10->9." - } - ] - }, - { - "id": "hamilton-hard-graph406", - "image": "data/hamilton/graph_visual/Base/hard/graph406.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (15,1) (7,13) (1,13) (11,5) (7,15) (1,7) (9,0) (13,10) (4,1) (5,1) (2,1) (10,6) (10,1) (0,4) (6,7) (13,3) (2,15) (16,7) (8,14) (2,14) (2,3) (5,13) (13,11) (9,10) (14,1) (14,5) (6,15) (13,12) (6,14) (15,5) (6,13) (6,8) (16,9) (12,2) (16,5) (1,9) (8,2) (10,12) (3,1) (13,16) (5,6) (7,14) (11,2) (9,12) (8,4) (12,3) (8,11) (15,10) (0,6) (5,7) (15,4) (5,9) (13,4) (0,8) (11,15) (5,3) (7,8) (3,4) (13,14) (8,5) (8,10) (14,10) (2,13) (3,9) (4,6) (15,12) (2,9) (15,16) (6,9) (15,0) (11,3) (4,9) (2,0) (7,2) (11,16) (1,16)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->10->13->7->15->1->4->8->14->2->12->3->11->16->5->6." - } - ] - }, - { - "id": "hamilton-hard-graph218", - "image": "data/hamilton/graph_visual/Base/hard/graph218.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (10,11) (13,6) (3,6) (11,3) (9,5) (11,2) (8,7) (6,10) (1,2) (1,13) (13,8) (1,0) (5,3) (8,12) (9,3) (6,5) (2,5) (1,8) (4,5) (8,10) (2,13) (7,4) (1,11) (5,7) (9,12) (12,13) (2,3) (0,3) (4,1) (4,10) (4,2) (11,7) (4,0) (0,13) (12,2) (13,4) (1,6) (1,10) (3,12) (10,3) (12,7) (2,6) (1,7) (11,12) (3,8) (13,10) (8,5) (9,1) (12,10) (1,5) (0,10) (11,0) (9,0) (6,7) (11,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->2->11->10->6->13->8->7->4->5->9->3->12." - } - ] - }, - { - "id": "hamilton-hard-graph119", - "image": "data/hamilton/graph_visual/Base/hard/graph119.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,6) (8,2) (5,4) (6,5) (11,0) (0,6) (8,0) (9,6) (8,5) (9,8) (11,4) (1,6) (1,9) (9,3) (8,10) (4,10) (7,4) (7,9) (5,7) (8,6) (1,10) (3,6) (8,7) (11,8) (11,7) (2,5) (4,9) (3,8) (0,4) (0,3) (9,11) (7,1) (0,2) (11,5) (10,2) (5,0) (4,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->4->6->5->8->2->10->1->7->9->3." - } - ] - }, - { - "id": "hamilton-hard-graph425", - "image": "data/hamilton/graph_visual/Base/hard/graph425.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,17) (13,5) (12,5) (13,0) (4,10) (17,3) (0,15) (15,8) (9,2) (5,1) (8,17) (12,8) (6,3) (15,2) (11,15) (13,10) (0,1) (4,0) (11,2) (10,17) (14,6) (4,12) (14,5) (13,8) (3,7) (2,5) (10,5) (16,12) (11,4) (7,15) (3,5) (12,7) (6,2) (15,14) (14,1) (6,13) (3,16) (14,13) (6,7) (9,4) (11,9) (12,1) (5,8) (3,10) (8,11) (9,6) (6,10) (13,17) (3,11) (15,13) (7,16) (10,12) (4,1) (12,9) (13,16) (14,12) (16,0) (9,10) (2,0) (6,8) (17,2) (16,14) (17,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->5->12->8->15->2->9->4->10->17->11->3->6->7->16->14->1." - } - ] - }, - { - "id": "hamilton-hard-graph436", - "image": "data/hamilton/graph_visual/Base/hard/graph436.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (14,8) (6,14) (10,3) (7,11) (12,15) (11,15) (4,11) (6,9) (13,3) (16,11) (13,10) (2,1) (17,9) (17,7) (0,14) (2,17) (15,14) (14,5) (13,8) (12,6) (10,16) (7,4) (13,11) (0,11) (16,1) (2,4) (0,3) (6,2) (3,11) (14,13) (17,6) (14,11) (13,4) (12,10) (10,15) (10,1) (14,12) (3,9) (8,17) (16,6) (4,8) (15,3) (17,0) (14,3) (2,9) (17,14) (16,12) (16,9) (3,1) (2,12) (7,14) (12,4) (10,17) (2,0) (1,7) (17,5) (9,7) (0,13) (3,7) (13,1) (7,16) (2,5) (1,14) (4,14) (3,5) (12,17) (0,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->14->8->13->3->10->16->11->15->12->6->9->17->5->2->1->7->4." - } - ] - }, - { - "id": "hamilton-hard-graph329", - "image": "data/hamilton/graph_visual/Base/hard/graph329.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,10) (9,6) (15,4) (7,10) (13,0) (2,15) (8,11) (13,4) (0,14) (2,4) (14,2) (12,15) (14,3) (5,9) (0,2) (8,15) (4,1) (1,2) (11,1) (8,13) (12,5) (5,13) (13,9) (0,10) (2,7) (6,2) (15,1) (10,9) (8,7) (12,13) (3,13) (12,2) (4,9) (11,9) (8,10) (14,15) (15,10) (13,6) (3,8) (14,9) (12,4) (11,5) (0,1) (6,3) (11,14) (6,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->10->7->2->15->8->11->1->4->12->5->9->6->3->14." - } - ] - }, - { - "id": "hamilton-hard-graph489", - "image": "data/hamilton/graph_visual/Base/hard/graph489.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,15) (13,16) (13,15) (14,0) (4,8) (10,17) (5,9) (15,6) (6,17) (16,15) (9,7) (7,11) (18,15) (4,17) (5,0) (2,17) (16,11) (8,1) (16,4) (13,0) (10,1) (5,7) (1,4) (3,8) (0,8) (0,15) (5,12) (11,10) (11,14) (13,3) (5,18) (4,0) (7,16) (4,12) (3,6) (12,2) (7,17) (12,6) (11,9) (10,14) (12,7) (13,11) (8,11) (7,2) (11,17) (15,10) (6,18) (11,6) (6,13) (3,15) (18,17) (1,11) (17,9) (14,13) (10,13) (10,18) (15,7) (16,8) (1,16) (11,12) (3,9) (0,17) (13,5) (14,12) (9,6) (0,10) (4,10) (4,13) (8,18) (6,14) (8,5) (7,6) (12,15)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->14->15->13->16->11->7->9->5->12->4->1->8->3->6->18->10->17->2." - } - ] - }, - { - "id": "hamilton-hard-graph480", - "image": "data/hamilton/graph_visual/Base/hard/graph480.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (13,15) (17,13) (5,3) (13,9) (2,1) (2,15) (17,5) (3,9) (15,4) (16,10) (10,8) (5,14) (14,1) (15,3) (4,11) (15,16) (9,12) (11,3) (0,7) (8,14) (11,16) (7,1) (0,8) (10,12) (6,12) (17,12) (15,18) (8,9) (10,11) (5,4) (4,2) (2,9) (1,18) (14,16) (7,6) (4,17) (1,9) (0,13) (12,1) (15,7) (6,15) (12,2) (4,6) (8,16) (15,8) (3,1) (0,2) (6,17) (12,5) (3,8) (3,17) (12,16) (8,12) (5,1) (9,14) (17,1) (2,8) (16,0) (12,7) (2,16) (5,16) (6,11) (18,10) (2,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->1->2->15->13->17->5->3->9->12->6->4->11->16->14->8->10->18." - } - ] - }, - { - "id": "hamilton-hard-graph150", - "image": "data/hamilton/graph_visual/Base/hard/graph150.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,6) (11,0) (1,12) (12,4) (7,5) (5,0) (7,12) (2,12) (5,4) (9,3) (1,8) (2,6) (5,3) (1,9) (11,7) (11,6) (8,7) (5,9) (11,12) (10,12) (3,2) (7,6) (4,2) (3,11) (5,12) (2,1) (11,5) (11,9) (3,4) (5,2) (5,6) (1,3) (11,4) (1,11) (1,6) (4,0) (1,4) (8,12) (12,9) (4,9) (4,6) (8,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->7->5->4->9->3->2->6->1->8->12->10." - } - ] - }, - { - "id": "hamilton-hard-graph344", - "image": "data/hamilton/graph_visual/Base/hard/graph344.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,0) (7,0) (15,11) (0,15) (5,0) (13,2) (0,8) (15,12) (10,14) (12,3) (0,4) (9,15) (6,1) (15,5) (3,15) (2,15) (15,14) (13,10) (8,10) (14,3) (8,4) (8,6) (6,2) (14,9) (11,1) (9,1) (1,5) (7,9) (15,7) (9,6) (12,9) (8,11) (3,4) (0,1) (4,14) (1,12) (6,4) (3,8) (0,9) (11,5) (11,3) (6,10) (0,2) (4,11) (3,1) (1,13) (12,13) (0,3) (3,7) (8,9) (1,4) (11,14) (5,6) (7,11) (2,14) (13,3) (13,7) (15,1) (7,8) (9,2) (1,8) (13,8) (5,9) (15,13) (14,0) (5,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->15->11->1->6->8->10->14->4->3->7->13->2->9->5." - } - ] - }, - { - "id": "hamilton-hard-graph346", - "image": "data/hamilton/graph_visual/Base/hard/graph346.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,15) (15,6) (10,4) (10,9) (3,14) (3,9) (0,3) (15,14) (4,9) (12,11) (12,4) (5,13) (7,2) (2,15) (13,7) (14,11) (9,5) (4,1) (15,4) (2,13) (10,1) (4,0) (8,3) (1,6) (5,4) (13,11) (15,3) (5,12) (7,15) (4,8) (3,6) (11,3) (7,3) (9,11) (0,2) (2,9) (13,3) (0,5) (13,14) (5,7) (2,10) (13,0) (12,0) (1,9) (10,6) (4,3) (14,8) (9,8) (6,5) (8,11) (1,2) (4,2) (2,12) (4,14) (9,15) (3,5) (12,15) (8,5) (13,10) (8,2) (0,11) (1,5) (1,15) (6,13) (1,11) (13,15) (0,10) (2,3) (9,7) (10,12) (6,2) (12,3) (10,11) (6,14) (6,8) (14,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->14->15->10->4->9->5->13->7->2->1->6->8->11->12." - } - ] - }, - { - "id": "hamilton-hard-graph174", - "image": "data/hamilton/graph_visual/Base/hard/graph174.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,6) (2,0) (8,0) (4,0) (2,11) (1,12) (8,5) (12,6) (9,0) (9,6) (1,3) (0,11) (4,11) (7,2) (6,4) (12,11) (9,5) (2,12) (1,11) (0,5) (7,0) (6,0) (9,2) (8,10) (5,4) (3,11) (8,12) (10,12) (7,4) (10,2) (2,1) (9,11) (10,5) (3,4) (4,10) (2,3) (6,8) (10,7) (10,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->11->4->6->3->1->12->8->5->9->10->7." - } - ] - }, - { - "id": "hamilton-hard-graph335", - "image": "data/hamilton/graph_visual/Base/hard/graph335.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,9) (13,6) (8,1) (6,14) (0,9) (13,1) (11,10) (10,4) (13,10) (2,8) (7,5) (4,7) (2,10) (10,14) (8,15) (14,12) (3,0) (11,3) (10,6) (8,7) (15,5) (7,6) (14,8) (7,14) (1,7) (2,11) (6,2) (7,9) (0,1) (12,10) (5,6) (0,15) (7,0) (6,12) (11,6) (7,13) (5,2) (8,3) (5,3) (4,8) (1,3) (4,9) (8,11) (13,0) (9,10) (5,0) (9,5) (13,8) (13,5) (12,7) (8,5) (3,7) (4,2) (3,12) (0,2) (9,13) (12,2) (5,4) (8,6) (14,2) (14,13) (12,1) (15,11) (1,15) (3,14) (2,15) (11,1) (1,5) (13,2) (0,4) (12,4) (14,15) (6,3) (5,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->11->10->4->7->5->15->8->1->13->6->14->2->12->3." - } - ] - }, - { - "id": "hamilton-hard-graph78", - "image": "data/hamilton/graph_visual/Base/hard/graph78.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (8,6) (3,1) (1,10) (7,3) (2,0) (10,2) (6,10) (3,10) (5,10) (10,8) (9,6) (2,3) (1,2) (11,6) (10,0) (3,8) (4,9) (4,3) (0,1) (7,5) (8,11) (5,11) (7,10) (3,0) (7,4) (7,6) (8,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->10->1->3->7->5->11->8->6->9->4." - } - ] - }, - { - "id": "hamilton-hard-graph138", - "image": "data/hamilton/graph_visual/Base/hard/graph138.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,11) (7,11) (6,3) (2,9) (8,3) (2,1) (2,3) (2,12) (3,12) (0,1) (5,6) (8,10) (7,5) (10,0) (10,5) (2,4) (2,8) (6,1) (6,4) (5,11) (0,8) (6,9) (10,2) (4,12) (9,8) (11,8) (11,0) (2,0) (5,12) (9,10) (5,4) (5,2) (3,4) (10,7) (10,6) (6,0) (8,12) (2,7) (4,1) (9,12) (4,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->2->9->6->3->11->7->5->10->8->12->4." - } - ] - }, - { - "id": "hamilton-hard-graph183", - "image": "data/hamilton/graph_visual/Base/hard/graph183.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (10,0) (9,2) (11,0) (3,9) (10,4) (8,9) (11,13) (2,12) (11,6) (8,7) (13,1) (11,7) (6,2) (7,9) (4,2) (10,7) (2,10) (0,1) (6,5) (7,13) (13,3) (5,1) (3,7) (7,2) (3,10) (6,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->3->9->8->7->11->13->1->5->6->4->2->12." - } - ] - }, - { - "id": "hamilton-hard-graph55", - "image": "data/hamilton/graph_visual/Base/hard/graph55.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,3) (3,8) (4,6) (2,4) (5,3) (3,10) (0,6) (4,0) (0,5) (1,8) (7,5) (2,1) (4,5) (6,5) (6,1) (3,9) (5,10) (2,10) (8,4) (8,2) (6,9) (6,2) (1,7) (5,2) (2,0) (5,9) (1,3) (8,7) (9,4) (0,7) (10,1) (4,7) (8,5) (0,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->4->3->8->2->10->1->7->5->9." - } - ] - }, - { - "id": "hamilton-hard-graph3", - "image": "data/hamilton/graph_visual/Base/hard/graph3.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,5) (7,2) (6,4) (4,5) (3,6) (6,5) (4,0) (7,4) (1,5) (9,7) (0,9) (10,9) (0,2) (5,3) (6,7) (10,1) (4,8) (3,1) (1,7) (10,4) (6,1) (0,1) (2,6) (8,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->6->2->7->9->10->1->3->5->8." - } - ] - }, - { - "id": "hamilton-hard-graph441", - "image": "data/hamilton/graph_visual/Base/hard/graph441.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,12) (2,4) (4,16) (6,0) (8,17) (4,11) (2,10) (0,3) (14,12) (17,16) (10,9) (6,2) (5,15) (0,12) (12,13) (17,15) (1,0) (14,10) (1,13) (4,3) (5,10) (6,4) (9,15) (3,13) (4,12) (16,1) (17,9) (7,16) (7,14) (16,6) (16,3) (0,2) (1,4) (0,15) (13,6) (2,3) (8,2) (5,8) (15,6) (6,7) (16,2) (4,5) (12,7) (3,1) (7,17) (9,7) (2,15) (5,13) (15,7) (4,0) (1,2) (6,8) (9,8) (17,10) (4,13) (11,14) (13,15) (9,4) (7,1) (10,4) (14,1) (17,3) (5,16) (14,13) (5,0) (2,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->2->4->16->17->8->5->15->13->3->1->12->7->9->10->14->11." - } - ] - }, - { - "id": "hamilton-hard-graph324", - "image": "data/hamilton/graph_visual/Base/hard/graph324.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,3) (8,9) (5,4) (4,14) (5,15) (0,1) (1,14) (0,2) (11,1) (12,11) (9,10) (2,14) (2,8) (3,10) (10,8) (10,7) (11,6) (15,9) (8,13) (4,6) (15,0) (15,8) (6,8) (7,12) (7,14) (12,3) (7,13) (3,14) (4,12) (1,3) (4,11) (2,7) (13,14) (14,0) (1,13) (6,14) (11,15) (6,12) (7,9) (2,13) (1,8) (7,1) (8,11) (15,13) (15,1) (12,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->14->4->5->15->9->8->2->13->7->10->3->11->12->6." - } - ] - }, - { - "id": "hamilton-hard-graph217", - "image": "data/hamilton/graph_visual/Base/hard/graph217.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (10,1) (4,3) (7,3) (9,12) (0,12) (3,9) (9,6) (11,1) (10,12) (6,12) (0,7) (8,6) (4,9) (5,8) (4,12) (1,12) (7,12) (11,0) (6,7) (2,1) (5,4) (8,3) (2,0) (13,3) (2,12) (1,4) (8,13) (2,6) (9,7) (4,6) (7,11) (8,2) (1,8) (11,8) (12,5) (1,3) (7,8) (10,0) (0,6) (3,0) (3,6) (10,7) (3,5) (13,11) (11,4) (11,10) (1,9) (10,3) (7,1) (13,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->9->3->4->5->8->6->2->1->10->7->11->13." - } - ] - }, - { - "id": "hamilton-hard-graph6", - "image": "data/hamilton/graph_visual/Base/hard/graph6.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,5) (8,5) (6,0) (7,0) (3,9) (10,4) (6,1) (9,4) (10,1) (9,8) (6,4) (0,2) (5,2) (3,7) (3,4) (2,3) (8,2) (6,10) (9,1) (6,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->1->10->4->9->8->5->2->3->7." - } - ] - }, - { - "id": "hamilton-hard-graph504", - "image": "data/hamilton/graph_visual/Base/hard/graph504.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (10,14) (18,9) (13,4) (15,6) (13,1) (12,11) (0,15) (1,17) (7,17) (3,1) (7,18) (7,1) (9,0) (18,13) (4,7) (4,18) (4,16) (16,6) (5,10) (9,10) (5,4) (14,8) (11,15) (17,5) (0,8) (17,0) (14,7) (10,2) (6,9) (16,2) (6,18) (0,5) (18,11) (6,13) (13,2) (4,15) (12,10) (15,17) (13,14) (16,10) (6,5) (14,18) (2,8) (14,6) (2,18) (12,2) (10,15) (3,9) (3,10) (3,5) (12,16) (9,8) (17,13) (15,1) (16,8) (0,10) (4,12) (7,8) (17,8) (18,0) (9,1) (17,14) (6,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->15->6->16->4->13->1->17->7->18->9->3->5->10->14->8->2->12->11." - } - ] - }, - { - "id": "hamilton-hard-graph178", - "image": "data/hamilton/graph_visual/Base/hard/graph178.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,9) (7,8) (12,10) (4,6) (11,0) (2,3) (0,9) (6,5) (0,8) (0,12) (10,8) (5,11) (1,2) (10,1) (1,4) (5,9) (11,4) (2,7) (7,6) (1,3) (3,11) (11,8) (12,5) (2,10) (9,1) (5,1) (7,9) (11,7) (6,1) (8,1) (8,12) (10,4) (5,3) (7,4) (2,4) (4,8) (9,10) (4,3) (9,3) (0,4) (11,2) (10,0) (3,6) (7,0) (2,9) (12,1) (11,6) (8,2) (5,0) (8,6) (4,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->5->6->4->1->2->3->9->7->8->10->12." - } - ] - }, - { - "id": "hamilton-hard-graph215", - "image": "data/hamilton/graph_visual/Base/hard/graph215.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,10) (13,5) (2,9) (9,11) (11,13) (7,3) (13,3) (5,12) (2,6) (3,5) (7,2) (2,3) (10,11) (7,12) (3,9) (13,0) (8,9) (9,5) (3,4) (0,2) (8,3) (4,6) (0,4) (8,13) (10,9) (4,2) (5,6) (11,8) (2,8) (1,7) (11,0) (1,3) (1,8) (9,6) (3,0) (2,1) (12,11) (1,6) (0,9) (7,10) (12,1) (13,7) (7,11) (10,0) (11,5) (11,1) (6,12) (10,13) (5,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->5->12->7->3->2->9->11->10->8->1->6->4." - } - ] - }, - { - "id": "hamilton-hard-graph149", - "image": "data/hamilton/graph_visual/Base/hard/graph149.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,3) (7,3) (10,4) (0,9) (9,1) (11,10) (9,4) (5,4) (12,7) (5,1) (9,2) (1,4) (10,7) (0,6) (5,9) (2,8) (12,3) (8,7) (8,4) (7,11) (7,2) (12,1) (4,7) (10,0) (4,12) (10,1) (0,2) (5,2) (3,11) (9,11) (8,1) (4,0) (5,6) (5,12) (11,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->3->7->11->10->4->12->1->8->2->5->6." - } - ] - }, - { - "id": "hamilton-hard-graph580", - "image": "data/hamilton/graph_visual/Base/hard/graph580.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,0) (19,13) (6,12) (16,0) (19,3) (7,0) (10,8) (3,8) (18,7) (13,16) (15,11) (2,5) (17,4) (19,18) (19,12) (11,7) (5,7) (9,14) (2,17) (2,12) (14,4) (15,18) (10,5) (18,5) (0,17) (2,8) (13,15) (14,6) (5,4) (11,17) (0,19) (10,15) (4,7) (9,11) (18,0) (14,8) (14,16) (12,14) (3,17) (14,3) (2,4) (13,8) (18,8) (1,13) (17,15) (15,0) (7,19) (18,13) (13,6) (16,6) (0,6) (13,5) (1,2) (15,14) (12,9) (14,0) (5,17) (15,19) (1,10) (5,11) (6,8) (16,4) (4,1) (13,3) (11,3) (19,16) (8,17) (1,14) (8,9) (12,10) (9,2) (3,16) (3,9) (19,5) (15,9) (3,4) (12,0) (1,18) (17,16) (14,7) (10,13) (18,9) (6,4) (6,7) (13,14) (6,9) (17,12) (19,6) (5,12) (19,11) (11,12) (18,11) (15,2) (17,10) (0,2) (9,16) (6,3) (1,7) (9,19) (3,15) (3,10) (8,7) (13,2) (1,19) (17,13) (4,18) (10,7) (14,17) (17,7) (5,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->8->3->19->13->16->14->9->11->15->18->7->5->2->17->12->6->4->1." - } - ] - }, - { - "id": "hamilton-hard-graph222", - "image": "data/hamilton/graph_visual/Base/hard/graph222.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,9) (3,6) (6,12) (3,11) (3,7) (2,1) (5,8) (9,1) (0,3) (9,0) (4,7) (5,1) (2,5) (7,10) (5,3) (1,4) (9,8) (13,6) (13,8) (9,7) (7,5) (4,10) (0,11) (9,13) (3,2) (3,9) (12,0) (5,0) (13,12) (10,8) (1,13) (13,5) (3,4) (6,8) (0,2) (0,10) (13,2) (11,12) (12,4) (0,4) (11,7) (11,2) (11,5) (0,7) (3,1) (5,4) (7,12) (7,6) (6,10) (1,0) (9,2) (6,4) (11,10) (10,3) (13,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->6->9->1->2->5->8->13->12->11->7->4->10." - } - ] - }, - { - "id": "hamilton-hard-graph407", - "image": "data/hamilton/graph_visual/Base/hard/graph407.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,0) (6,15) (9,11) (8,14) (9,0) (1,10) (11,0) (11,4) (1,7) (0,15) (3,9) (3,2) (12,15) (15,3) (5,9) (15,8) (10,12) (16,11) (13,4) (15,9) (15,5) (1,3) (10,16) (11,8) (7,2) (14,6) (15,11) (7,0) (7,8) (16,7) (2,8) (12,1) (6,3) (14,9) (7,11) (0,5) (13,1) (14,5) (2,10) (3,5) (14,1) (12,3) (3,14) (0,14) (8,4) (16,3) (7,15) (4,5) (13,0) (5,11) (7,5) (12,4) (6,16) (12,14) (5,16) (9,6) (9,10) (14,15) (2,14) (14,13) (0,3) (10,5) (6,12) (9,2) (13,9) (9,12) (6,11) (13,6) (4,9) (4,6) (16,12) (11,13) (0,16) (6,10) (8,1) (12,11) (7,12) (3,7) (7,9) (4,15)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->15->6->14->8->11->9->3->2->7->1->10->16->5->4->13." - } - ] - }, - { - "id": "hamilton-hard-graph260", - "image": "data/hamilton/graph_visual/Base/hard/graph260.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,9) (1,3) (5,2) (0,10) (10,2) (14,11) (2,7) (5,0) (8,3) (9,1) (4,7) (11,6) (9,10) (2,6) (10,14) (2,3) (12,14) (6,13) (1,14) (11,10) (4,9) (9,12) (1,11) (13,1) (12,3) (5,8) (11,5) (10,3) (7,3) (14,6) (0,7) (8,13) (8,4) (9,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->2->5->8->9->1->13->6->11->14->12->3->7->4." - } - ] - }, - { - "id": "hamilton-hard-graph526", - "image": "data/hamilton/graph_visual/Base/hard/graph526.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (2,6) (6,7) (14,9) (4,6) (13,17) (6,9) (16,9) (17,2) (5,16) (2,16) (7,14) (8,18) (17,4) (18,10) (18,7) (10,2) (18,16) (6,1) (10,6) (9,15) (11,9) (15,18) (3,11) (8,5) (16,11) (12,5) (1,16) (9,1) (17,5) (4,18) (7,17) (14,10) (0,4) (1,11) (10,15) (10,3) (3,13) (9,3) (8,17) (13,16) (14,6) (5,11) (5,14) (18,5) (5,4) (6,11) (2,8) (13,11) (3,17) (7,12) (6,3) (3,15) (9,5) (10,9) (0,1) (7,10) (8,16) (0,5) (4,10) (16,4) (0,6) (10,8) (13,7) (16,15) (15,13) (8,7) (3,2) (14,0) (13,4) (17,11) (0,16) (16,12) (7,16) (18,14) (10,11) (5,15) (1,15) (12,11) (2,5) (0,3) (13,14) (4,8) (13,12) (11,14) (4,12) (10,5) (11,4) (3,4) (1,18) (11,7) (10,13) (18,2) (12,14) (15,4) (14,15) (18,11) (1,4) (9,0) (7,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->6->2->17->13->3->11->9->14->7->18->8->5->12->16->1->15->10." - } - ] - }, - { - "id": "hamilton-hard-graph259", - "image": "data/hamilton/graph_visual/Base/hard/graph259.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,10) (8,13) (2,12) (12,1) (5,1) (13,12) (14,7) (0,14) (12,5) (6,1) (10,0) (9,4) (8,2) (5,2) (14,10) (13,9) (0,13) (5,4) (7,3) (12,3) (0,3) (11,13) (4,11) (5,6) (3,14) (13,2) (3,13) (10,3) (10,6) (9,12) (5,3) (12,0) (11,6) (13,6) (9,2) (7,1) (7,5) (14,4) (4,13) (10,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->14->7->3->12->2->8->13->9->10->6->1->5->4->11." - } - ] - }, - { - "id": "hamilton-hard-graph435", - "image": "data/hamilton/graph_visual/Base/hard/graph435.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (13,11) (16,7) (2,7) (14,9) (9,10) (13,12) (17,0) (12,6) (0,7) (17,8) (0,15) (6,17) (4,1) (12,4) (2,12) (2,11) (9,5) (3,2) (11,16) (12,17) (10,6) (3,16) (3,11) (16,15) (5,3) (1,16) (15,12) (5,17) (2,10) (11,14) (4,0) (6,2) (12,0) (8,14) (2,4) (12,16) (3,17) (3,15) (10,8) (1,0) (9,15) (15,2) (13,6) (17,13) (15,6) (0,2) (1,7) (0,16) (3,7) (6,14) (9,7) (0,10) (14,3) (4,3) (9,0) (3,9) (14,2) (16,9) (10,13) (13,8) (14,0) (2,13) (6,16) (4,15) (16,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->17->8->14->9->10->6->12->13->11->2->7->16->1->4->15->3->5." - } - ] - }, - { - "id": "hamilton-hard-graph226", - "image": "data/hamilton/graph_visual/Base/hard/graph226.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,7) (7,9) (8,2) (11,2) (8,9) (13,2) (8,13) (13,5) (12,1) (12,9) (5,2) (2,0) (5,10) (0,1) (0,7) (8,3) (5,9) (6,3) (6,2) (13,6) (7,5) (8,12) (6,7) (9,10) (11,13) (6,1) (12,5) (12,7) (0,8) (13,12) (3,1) (1,13) (0,5) (9,0) (3,5) (3,7) (0,13) (6,12) (12,3) (5,8) (11,5) (1,9) (11,7) (4,13) (6,4) (7,10) (4,9) (8,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->8->9->7->12->1->3->6->4->13->11->5->10." - } - ] - }, - { - "id": "hamilton-hard-graph354", - "image": "data/hamilton/graph_visual/Base/hard/graph354.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,12) (10,8) (6,9) (8,14) (3,1) (10,14) (5,9) (8,6) (11,3) (13,0) (9,4) (8,0) (0,14) (15,10) (3,7) (1,13) (8,4) (1,11) (3,10) (13,9) (2,15) (9,11) (9,12) (14,11) (0,5) (13,5) (6,0) (5,11) (3,15) (6,11) (0,9) (9,1) (6,7) (10,11) (14,9) (2,11) (4,14) (4,2) (12,13) (15,1) (12,8) (2,12) (10,1) (2,8) (2,5) (4,5) (4,3) (0,4) (14,5) (6,5) (13,4) (10,7) (11,13) (5,3) (11,7) (1,5) (13,7) (15,0) (1,7) (8,1) (14,7) (0,10) (1,0) (12,3) (3,0) (10,5) (2,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->1->3->11->9->6->8->4->5->14->7->10->12->2->15." - } - ] - }, - { - "id": "hamilton-hard-graph593", - "image": "data/hamilton/graph_visual/Base/hard/graph593.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,19) (17,16) (18,15) (15,4) (8,5) (15,8) (4,3) (15,16) (16,1) (3,16) (0,5) (10,8) (4,19) (7,6) (18,17) (14,8) (10,7) (5,16) (6,18) (4,7) (0,2) (15,11) (9,1) (13,0) (17,0) (10,15) (10,13) (7,2) (0,19) (3,10) (14,4) (11,2) (6,1) (5,2) (11,19) (9,14) (19,10) (8,0) (2,6) (14,6) (1,12) (2,10) (1,11) (13,3) (18,19) (11,7) (16,14) (10,18) (16,19) (3,1) (2,4) (11,0) (8,13) (8,19) (13,19) (15,0) (12,8) (3,14) (0,12) (19,9) (11,13) (7,14) (16,12) (11,18) (15,14) (16,11) (9,0) (17,13) (11,9) (4,8) (8,2) (3,9) (12,17) (13,7) (12,18) (3,12) (11,3) (0,4) (16,2) (19,3) (14,10) (14,18) (4,17) (16,13) (1,13) (11,8) (3,8) (4,10) (15,9) (15,5) (18,13) (16,0) (5,14) (4,9) (12,14) (6,12) (6,0) (8,9) (6,3) (7,8) (13,6) (13,12) (15,13) (17,5) (16,9) (19,12) (10,9) (7,17) (5,18) (14,2) (16,8) (17,15) (3,0) (17,3) (11,5) (15,3) (8,18) (0,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->8->15->18->17->16->1->9->14->19->4->3->10->7->6->2->11->13->12." - } - ] - }, - { - "id": "hamilton-hard-graph104", - "image": "data/hamilton/graph_visual/Base/hard/graph104.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,8) (0,3) (8,3) (7,9) (7,1) (5,3) (3,6) (10,6) (1,2) (5,7) (1,5) (3,1) (11,0) (8,1) (0,1) (0,2) (5,6) (4,2) (1,9) (2,5) (10,4) (11,9) (9,10) (0,7) (9,3) (2,9) (0,6) (2,3) (5,11) (3,4) (7,8) (6,4) (5,0) (9,6) (6,7) (3,7) (10,11) (4,11) (2,11) (1,11) (6,11) (10,0) (5,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->8->11->9->7->1->2->4->10->6->5." - } - ] - }, - { - "id": "hamilton-hard-graph380", - "image": "data/hamilton/graph_visual/Base/hard/graph380.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (13,9) (4,14) (10,0) (2,1) (13,2) (12,3) (8,4) (9,2) (0,9) (5,3) (8,14) (8,7) (15,13) (16,0) (9,4) (4,6) (1,11) (10,12) (4,13) (3,10) (10,16) (2,6) (12,5) (10,7) (1,4) (4,16) (15,8) (6,3) (13,10) (3,11) (16,7) (10,15) (13,7) (7,9) (8,12) (8,2) (5,14) (16,11) (6,12) (12,4) (2,10) (10,1) (7,5) (8,5) (1,3) (12,13) (16,3) (14,2) (16,9) (9,10) (11,12) (10,11) (14,15)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->12->3->5->14->4->8->15->13->9->7->16->11->1->2->6." - } - ] - }, - { - "id": "hamilton-hard-graph263", - "image": "data/hamilton/graph_visual/Base/hard/graph263.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,0) (2,1) (5,2) (2,10) (11,8) (12,1) (13,12) (3,10) (14,1) (14,3) (11,13) (2,3) (5,0) (11,6) (4,5) (7,8) (9,1) (9,8) (9,6) (8,0) (10,7) (6,12) (12,9) (10,14) (12,11) (11,9) (14,13) (10,9) (4,2) (6,7) (4,1) (14,8) (8,1) (9,7) (1,11) (4,13) (3,13) (3,7) (13,10) (13,5) (4,0) (12,5) (10,0) (14,4) (11,5) (9,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->8->11->13->12->1->2->5->4->14->3->10->9->6." - } - ] - }, - { - "id": "hamilton-hard-graph584", - "image": "data/hamilton/graph_visual/Base/hard/graph584.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,2) (10,9) (18,12) (16,14) (2,6) (17,6) (16,4) (6,10) (5,3) (2,13) (18,14) (9,0) (4,2) (1,14) (16,9) (10,0) (19,17) (2,1) (10,8) (16,17) (0,16) (9,14) (3,13) (2,18) (18,5) (10,15) (16,11) (2,10) (2,12) (7,8) (1,19) (3,6) (14,10) (17,9) (10,12) (4,10) (2,19) (4,13) (11,18) (3,17) (6,18) (15,16) (4,12) (7,0) (5,9) (15,8) (9,18) (18,0) (17,0) (7,4) (4,0) (15,11) (3,9) (6,5) (0,15) (5,11) (9,4) (5,7) (8,16) (4,1) (7,6) (18,13) (0,14) (8,0) (9,7) (6,19) (4,6) (1,12) (0,2) (16,10) (9,1) (10,18) (12,8) (18,17) (8,11) (4,18) (12,15) (12,11) (1,0) (5,19) (17,12) (14,11) (3,16) (3,14) (19,15) (10,17) (13,19) (8,4) (12,13) (14,5) (3,10) (15,5) (3,12) (4,5) (11,1) (16,18) (18,3) (12,19) (4,3) (8,19) (12,9) (7,11) (6,13) (0,12) (13,5) (11,4) (15,18) (3,7) (4,15) (5,12) (19,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->10->6->2->15->16->14->18->12->4->13->3->5->7->8->11->1->19->17." - } - ] - }, - { - "id": "hamilton-hard-graph485", - "image": "data/hamilton/graph_visual/Base/hard/graph485.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,7) (16,2) (5,12) (9,10) (10,12) (7,15) (13,3) (2,6) (14,16) (9,12) (4,10) (3,0) (10,16) (15,9) (10,3) (12,2) (11,10) (8,13) (6,1) (13,15) (8,14) (18,10) (7,17) (1,3) (1,18) (1,7) (8,4) (0,18) (8,0) (11,2) (17,6) (4,9) (16,17) (2,7) (6,14) (16,1) (9,18) (18,14) (17,1) (6,0) (16,3) (14,3) (12,6) (18,6) (1,13) (1,2) (4,5) (17,14) (14,2) (5,10) (7,5) (15,4) (16,13) (17,5) (14,15) (3,17) (1,15) (18,5) (3,12) (12,0) (12,16) (17,4) (16,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->13->8->14->16->2->6->1->18->10->9->12->5->17->4->15->7->11." - } - ] - }, - { - "id": "hamilton-hard-graph123", - "image": "data/hamilton/graph_visual/Base/hard/graph123.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (10,9) (0,8) (5,12) (3,10) (12,11) (6,1) (9,12) (10,0) (4,8) (2,0) (5,7) (10,5) (7,1) (6,11) (3,2) (11,8) (11,1) (5,1) (11,5) (12,8) (7,0) (3,11) (8,10) (6,4) (12,7) (3,9) (6,12) (9,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->4->6->1->7->5->10->9->12->11->3->2." - } - ] - }, - { - "id": "hamilton-hard-graph518", - "image": "data/hamilton/graph_visual/Base/hard/graph518.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (3,14) (12,17) (12,16) (2,6) (14,11) (11,13) (2,7) (3,12) (12,13) (2,15) (15,4) (10,15) (10,14) (0,10) (15,16) (3,18) (15,13) (9,18) (8,3) (17,10) (9,4) (6,17) (3,4) (4,0) (1,17) (8,17) (7,9) (4,5) (15,11) (13,6) (3,10) (9,1) (5,18) (14,2) (12,15) (11,0) (16,1) (0,14) (5,13) (4,12) (18,10) (2,13) (5,17) (8,18) (4,13) (0,1) (2,17) (15,7) (1,13) (1,6) (14,15) (7,3) (1,5) (9,0) (16,13) (11,5) (14,17) (5,6) (0,2) (18,6) (1,10) (4,7) (18,16) (10,7) (12,9) (3,1) (18,0) (7,16) (12,1) (14,5) (15,3) (9,8) (16,17) (15,6) (7,17) (16,9) (10,16) (13,10) (8,7) (13,9) (7,1) (7,11) (4,6) (4,8) (7,0) (5,2) (18,2) (6,14) (15,5) (9,6) (5,10) (1,18) (12,0) (6,7) (8,11) (11,1) (14,18) (16,6) (11,12) (8,14) (17,18) (7,12) (4,14) (9,15)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->15->2->6->17->12->16->1->9->18->3->14->11->13->5->4->7->8." - } - ] - }, - { - "id": "hamilton-hard-graph9", - "image": "data/hamilton/graph_visual/Base/hard/graph9.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,0) (4,10) (10,3) (1,5) (6,3) (3,4) (10,7) (5,4) (1,2) (1,7) (3,7) (3,9) (0,9) (8,0) (3,8) (5,10) (6,7) (7,8) (4,6) (4,7) (1,3) (10,1) (9,4) (5,6) (7,0) (4,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->7->8->3->9->4->10->5->1->2." - } - ] - }, - { - "id": "hamilton-hard-graph10", - "image": "data/hamilton/graph_visual/Base/hard/graph10.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,8) (3,7) (4,8) (7,10) (9,8) (1,2) (2,10) (6,8) (10,4) (7,2) (4,0) (5,3) (0,5) (4,9) (9,0) (5,7) (9,10) (3,10) (2,6) (0,3) (5,6) (1,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->4->9->10->7->3->5->6->2->1." - } - ] - }, - { - "id": "hamilton-hard-graph509", - "image": "data/hamilton/graph_visual/Base/hard/graph509.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (6,12) (14,18) (7,8) (18,17) (14,4) (10,1) (18,11) (11,14) (12,4) (15,10) (7,10) (11,2) (9,16) (7,3) (12,7) (6,2) (2,10) (12,1) (9,6) (17,12) (8,11) (3,4) (14,5) (8,17) (17,16) (5,8) (5,11) (6,3) (0,4) (11,0) (14,12) (12,9) (18,6) (8,6) (15,16) (8,4) (8,3) (7,16) (9,13) (16,3) (9,1) (13,6) (18,12) (11,4) (14,3) (3,18) (16,6) (0,17) (9,7) (12,5) (15,0) (3,17) (1,11) (9,10) (3,12) (10,17) (15,6) (3,15) (7,13) (10,8) (0,9) (15,2) (5,13) (6,0) (7,4) (5,17) (6,1) (13,8) (0,14) (14,8) (14,13) (18,4) (16,8) (2,17)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->14->18->17->12->6->2->11->8->7->3->16->15->10->1->9->13->5." - } - ] - }, - { - "id": "hamilton-hard-graph75", - "image": "data/hamilton/graph_visual/Base/hard/graph75.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,0) (4,0) (0,9) (7,2) (10,6) (4,5) (9,1) (3,2) (7,4) (1,0) (9,3) (8,11) (0,6) (11,2) (10,7) (3,6) (8,1) (8,5) (7,3) (0,11) (10,8) (1,4) (10,0) (5,0) (2,8) (1,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->7->10->6->3->9->1->4->5->8->11." - } - ] - }, - { - "id": "hamilton-hard-graph486", - "image": "data/hamilton/graph_visual/Base/hard/graph486.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (6,10) (7,4) (5,16) (6,12) (5,8) (0,7) (9,1) (9,6) (13,15) (3,6) (17,10) (9,7) (6,14) (14,12) (5,15) (9,8) (16,18) (9,5) (7,6) (9,14) (0,2) (18,11) (5,12) (11,6) (12,4) (17,3) (5,18) (1,4) (11,1) (1,13) (3,15) (8,15) (4,0) (13,4) (0,14) (10,7) (4,18) (14,18) (16,0) (11,5) (6,2) (2,10) (9,3) (1,10) (1,6) (17,14) (0,10) (16,10) (3,16) (7,14) (0,1) (12,7) (1,14) (1,7) (16,15) (1,2) (5,13) (10,12) (3,5) (13,18) (2,9) (18,15) (18,17) (2,15) (0,3) (15,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->4->12->6->10->17->3->16->5->8->9->14->18->11->1->13->15->2." - } - ] - }, - { - "id": "hamilton-hard-graph188", - "image": "data/hamilton/graph_visual/Base/hard/graph188.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,4) (0,11) (13,2) (5,13) (2,6) (11,10) (4,10) (2,7) (7,1) (13,7) (10,7) (5,11) (10,6) (6,13) (12,3) (11,13) (11,2) (2,9) (12,9) (7,5) (3,13) (4,12) (12,7) (5,6) (12,8) (4,3) (7,9) (8,10) (9,4) (10,3) (8,3) (4,8) (1,9) (11,6) (1,5) (6,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->10->4->6->2->13->5->7->1->9->12->3->8." - } - ] - }, - { - "id": "hamilton-hard-graph474", - "image": "data/hamilton/graph_visual/Base/hard/graph474.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (7,16) (2,7) (0,1) (2,17) (13,12) (13,17) (14,5) (11,6) (10,1) (10,7) (12,17) (0,5) (7,0) (4,7) (13,5) (10,0) (12,2) (13,2) (14,15) (6,5) (0,6) (17,9) (0,17) (8,10) (3,16) (6,17) (4,12) (7,9) (14,16) (14,3) (12,11) (11,5) (3,5) (11,17) (2,0) (13,0) (15,16) (5,4) (3,11) (10,15) (9,16) (11,14) (4,6) (1,17) (9,4) (12,5) (14,8) (5,9) (4,17) (15,1) (13,10) (4,3) (15,9) (16,6) (6,12) (4,0) (7,5) (16,1) (1,12) (3,8) (1,2) (13,6) (15,12) (4,11) (16,10) (15,6) (9,0) (3,0) (15,4) (2,8) (16,0) (2,3) (14,9) (6,3) (2,9) (15,11) (10,14) (3,12) (1,3) (10,12) (15,8) (2,6) (4,10) (8,7) (1,4) (8,16) (9,8) (13,1) (8,17) (5,10) (15,17) (9,6) (9,3) (11,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->10->7->16->3->14->5->13->12->17->2->8->15->9->4->6->11." - } - ] - }, - { - "id": "hamilton-hard-graph444", - "image": "data/hamilton/graph_visual/Base/hard/graph444.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,14) (16,0) (14,5) (14,1) (5,10) (6,4) (17,0) (9,16) (1,8) (7,11) (3,1) (11,9) (7,17) (0,8) (5,13) (4,12) (9,14) (13,17) (5,4) (10,11) (16,4) (7,12) (16,5) (10,9) (7,0) (4,13) (8,2) (12,0) (7,14) (11,16) (9,3) (8,15) (16,3) (17,11) (0,2) (4,10) (7,15) (17,10) (15,12) (10,6) (4,1) (12,1) (7,3) (2,1) (14,12) (6,16) (12,17) (10,16) (12,8) (17,16) (1,16) (17,4) (5,2) (8,11) (6,1) (13,12) (4,15) (9,1) (6,12) (3,6) (6,15) (8,13) (4,3) (3,8) (11,13) (1,7) (5,17) (4,11) (11,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->16->9->11->7->17->13->5->14->15->8->2->1->3->6->10->4->12." - } - ] - }, - { - "id": "hamilton-hard-graph254", - "image": "data/hamilton/graph_visual/Base/hard/graph254.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,5) (6,13) (14,3) (14,7) (12,7) (8,4) (14,2) (4,9) (5,7) (10,1) (3,2) (0,5) (4,11) (9,12) (9,14) (10,4) (6,10) (1,12) (13,10) (7,8) (4,3) (5,3) (9,1) (11,8) (14,0) (10,8) (0,7) (5,11) (14,10) (3,8) (11,13) (6,14) (5,12) (2,8) (4,2) (13,12) (9,2) (5,9) (1,11) (13,9) (12,11) (0,4) (2,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->8->4->9->1->10->6->13->11->12->7->14->3->2." - } - ] - }, - { - "id": "hamilton-hard-graph438", - "image": "data/hamilton/graph_visual/Base/hard/graph438.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,6) (16,9) (8,3) (0,7) (5,15) (3,7) (4,14) (11,6) (5,3) (9,17) (4,17) (3,12) (3,16) (4,8) (9,2) (13,6) (7,14) (2,11) (15,7) (3,15) (11,4) (16,14) (15,12) (15,17) (0,3) (12,0) (17,16) (1,4) (14,3) (4,15) (4,7) (5,0) (16,2) (5,16) (10,11) (3,11) (4,2) (9,0) (10,12) (8,17) (7,13) (17,14) (14,0) (0,17) (15,2) (10,2) (9,10) (17,5) (13,17) (4,10) (5,6) (12,13) (2,17) (5,8) (1,14) (7,8) (11,0) (16,10) (11,9) (1,0) (2,14) (1,15) (11,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->11->2->9->16->3->8->4->17->5->15->1->14->7->13->12->10." - } - ] - }, - { - "id": "hamilton-hard-graph235", - "image": "data/hamilton/graph_visual/Base/hard/graph235.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (5,8) (1,6) (7,10) (9,2) (6,11) (3,11) (4,1) (8,10) (0,1) (13,12) (1,12) (0,2) (9,0) (9,5) (11,10) (11,5) (0,8) (5,2) (1,9) (3,9) (12,9) (4,10) (8,3) (5,1) (11,1) (3,10) (6,2) (13,2) (0,7) (2,7) (4,12) (3,0) (9,4) (5,13) (5,0) (5,6) (11,8) (5,7) (0,12) (2,3) (8,9) (11,13) (4,5) (13,1) (6,3) (3,13) (7,11) (8,2) (9,6) (6,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->6->11->3->9->2->13->12->4->10->7->5->8." - } - ] - }, - { - "id": "hamilton-hard-graph467", - "image": "data/hamilton/graph_visual/Base/hard/graph467.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,8) (14,17) (6,3) (10,14) (9,5) (6,5) (10,11) (17,2) (7,17) (14,13) (9,15) (0,6) (0,17) (0,3) (17,6) (13,2) (7,12) (15,13) (11,15) (5,12) (15,6) (13,17) (16,11) (13,7) (1,16) (4,7) (9,14) (15,16) (2,8) (11,14) (13,4) (15,5) (7,11) (16,8) (13,6) (7,5) (8,15) (4,3) (4,2) (10,2) (0,14) (1,5) (7,9) (10,17) (16,14) (14,1) (6,11) (14,6) (16,7) (8,14) (2,12) (2,14) (4,8) (13,9) (13,5) (5,8) (5,14) (11,0) (13,3) (1,3) (14,3) (11,9) (3,11) (9,10) (11,5) (7,0) (5,4) (10,8) (6,9) (12,3) (17,15) (8,3) (2,16) (3,9) (9,0) (15,0) (10,12) (4,6) (1,11) (8,11) (9,17) (0,12) (2,9) (14,15) (3,17) (11,17) (11,4) (9,4) (12,16) (13,8) (0,5) (2,11) (2,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->3->4->7->17->14->10->11->15->9->5->12->2->13->8->1->16." - } - ] - }, - { - "id": "hamilton-hard-graph512", - "image": "data/hamilton/graph_visual/Base/hard/graph512.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,12) (5,18) (16,14) (7,9) (1,10) (5,8) (2,11) (0,6) (16,6) (16,9) (2,7) (0,12) (1,4) (18,10) (9,18) (17,8) (18,13) (3,18) (2,8) (14,17) (8,3) (17,7) (10,4) (12,7) (16,15) (14,2) (1,12) (15,14) (3,7) (5,16) (1,3) (12,5) (13,12) (6,13) (11,4) (6,11) (0,9) (15,4) (7,1) (3,2) (10,11) (9,17) (16,13) (13,5) (2,17) (5,4) (2,5) (18,12) (1,16) (13,3) (0,3) (8,0) (1,15) (6,5) (0,16) (5,7) (11,18) (5,0) (15,12) (18,15) (16,18) (11,16) (1,17) (14,7) (10,7) (16,17) (11,3) (10,16) (8,14) (3,9) (7,8) (7,13) (18,2) (14,3) (7,18) (8,11) (6,10) (12,14) (2,13) (2,0) (14,9) (8,9) (5,14) (17,15) (10,2) (11,7) (8,16) (2,4) (10,17) (3,12) (15,11) (10,9) (18,0) (3,17) (6,9) (9,13) (7,15) (8,12) (17,0) (13,8) (11,12) (0,1) (17,13) (0,10) (0,7) (4,16) (1,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->16->14->17->12->7->9->18->5->8->2->11->10->4->15->1->3->13." - } - ] - }, - { - "id": "hamilton-hard-graph302", - "image": "data/hamilton/graph_visual/Base/hard/graph302.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,9) (2,13) (4,0) (3,12) (12,7) (15,10) (10,7) (12,15) (1,9) (15,5) (7,5) (11,4) (1,7) (8,9) (2,15) (1,11) (8,7) (13,6) (8,4) (3,0) (8,5) (12,1) (5,13) (10,0) (14,15) (5,12) (2,5) (11,10) (6,12) (9,14) (3,8) (3,14) (13,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->11->1->9->12->3->14->15->10->7->8->5->2->13->6." - } - ] - }, - { - "id": "hamilton-hard-graph396", - "image": "data/hamilton/graph_visual/Base/hard/graph396.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,7) (0,6) (13,8) (15,6) (6,9) (16,2) (4,3) (10,6) (10,11) (12,9) (3,1) (9,4) (14,0) (12,11) (8,16) (7,1) (5,15) (5,3) (4,2) (16,4) (7,13) (1,12) (13,12) (3,2) (11,4) (12,4) (2,7) (15,0) (14,8) (8,6) (10,12) (11,8) (4,1) (11,5) (16,3) (14,10) (6,5) (1,15) (6,14) (7,10) (12,14) (0,8) (6,2) (13,11) (13,9) (4,7) (0,9) (12,5) (1,10) (14,16) (7,11) (4,13) (16,9) (0,1) (12,7) (2,11) (5,9) (12,3) (3,9) (9,2) (12,0) (2,13) (1,8) (15,4) (0,7) (15,10) (12,15) (5,8) (16,5) (12,8) (16,0) (5,10) (13,10) (11,1) (13,15) (3,0) (14,4) (10,9) (1,9) (10,3) (9,7) (3,13) (8,15) (16,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->15->5->3->4->9->12->11->10->14->7->1->8->13->2->16." - } - ] - }, - { - "id": "hamilton-hard-graph154", - "image": "data/hamilton/graph_visual/Base/hard/graph154.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,5) (6,11) (12,4) (7,10) (2,7) (2,1) (7,1) (7,11) (5,10) (8,4) (11,9) (3,9) (8,11) (0,3) (3,11) (2,3) (0,12) (2,6) (10,9) (0,7) (10,3) (11,10) (5,12) (1,8) (3,6) (4,1) (10,8) (0,10) (1,5) (6,1) (4,0) (10,1) (8,9) (0,11) (2,4) (6,10) (6,12) (3,7) (9,7) (2,10) (11,2) (6,5) (10,12) (3,5) (4,10) (6,4) (9,2) (7,4) (5,2) (1,9) (7,12) (8,0) (5,9) (8,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->9->11->6->2->7->5->10->8->1->4->12." - } - ] - }, - { - "id": "hamilton-hard-graph139", - "image": "data/hamilton/graph_visual/Base/hard/graph139.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,4) (3,5) (0,2) (7,9) (10,4) (3,9) (12,8) (7,6) (1,11) (10,8) (4,7) (12,1) (2,3) (2,9) (11,8) (7,3) (11,12) (11,9) (8,6) (0,7) (4,8) (5,2) (1,7) (3,12) (5,12) (6,4) (9,1) (1,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->3->5->12->4->10->8->11->1->9->7->6." - } - ] - }, - { - "id": "hamilton-hard-graph261", - "image": "data/hamilton/graph_visual/Base/hard/graph261.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,1) (14,9) (2,0) (7,3) (14,8) (2,5) (9,2) (6,0) (2,11) (3,0) (6,14) (12,1) (4,1) (13,14) (9,8) (8,5) (13,4) (13,8) (2,14) (13,11) (3,10) (0,5) (0,11) (4,10) (3,2) (5,13) (1,5) (6,7) (13,0) (10,12) (4,5) (7,12) (11,7) (13,12) (9,6) (2,8) (6,8) (12,11) (14,10) (14,4) (8,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->5->8->14->9->6->7->3->1->12->10->4->13->11." - } - ] - }, - { - "id": "hamilton-hard-graph338", - "image": "data/hamilton/graph_visual/Base/hard/graph338.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,8) (8,5) (3,5) (6,7) (12,11) (2,7) (10,2) (2,4) (11,2) (14,7) (5,2) (6,1) (15,8) (2,3) (0,15) (15,13) (14,9) (4,8) (0,1) (11,1) (9,11) (0,8) (15,14) (10,12) (10,6) (10,7) (3,0) (0,4) (14,0) (4,3) (14,12) (10,9) (12,8) (8,1) (2,0) (14,5) (11,4) (4,13) (3,1) (15,12) (9,15) (9,3) (3,13) (15,6) (1,10) (0,10) (5,1) (6,13) (13,10) (3,14) (12,6) (10,8) (7,13) (7,4) (9,0) (2,6) (5,7) (9,7) (4,15) (5,12) (13,12) (15,7) (13,2) (10,4) (2,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->15->8->3->5->2->7->6->1->11->12->14->9->10->13->4." - } - ] - }, - { - "id": "hamilton-hard-graph404", - "image": "data/hamilton/graph_visual/Base/hard/graph404.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,11) (11,10) (8,5) (1,8) (7,13) (2,5) (9,11) (11,16) (9,5) (13,14) (7,2) (13,1) (13,3) (11,14) (9,14) (12,14) (0,13) (0,14) (15,1) (9,8) (15,0) (13,6) (8,6) (14,5) (16,3) (11,12) (12,16) (9,16) (1,6) (4,1) (7,14) (11,15) (0,16) (12,4) (4,9) (8,7) (15,13) (2,14) (2,6) (4,8) (10,5) (2,3) (1,5) (11,6) (10,0) (3,5) (9,12) (8,14) (16,7) (8,15) (10,1) (5,15) (3,7) (6,14) (8,13) (4,3) (15,10) (5,6) (5,11) (1,16) (11,1) (10,4) (2,16) (3,10) (2,9) (1,3) (6,15) (1,2) (7,15) (10,2) (1,7) (2,4) (12,2) (9,13) (11,8) (0,3) (1,9) (16,5) (12,6) (1,14) (14,15) (13,10) (8,16) (11,3) (3,14) (10,14) (13,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->7->11->10->5->8->1->15->6->2->14->9->16->3->4->12." - } - ] - }, - { - "id": "hamilton-hard-graph367", - "image": "data/hamilton/graph_visual/Base/hard/graph367.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (9,10) (3,9) (14,1) (1,5) (3,5) (9,13) (5,0) (11,1) (8,4) (2,8) (8,10) (9,14) (12,4) (8,12) (14,13) (6,15) (9,2) (13,4) (15,13) (4,14) (3,6) (12,7) (14,7) (15,5) (0,15) (3,16) (7,10) (9,7) (15,3) (3,8) (11,2) (15,4) (6,7) (1,6) (7,16) (10,16) (13,5) (0,1) (10,4) (9,8) (11,6) (14,16) (13,3) (6,0) (16,1) (15,9) (8,1) (10,11) (12,16) (10,6) (11,15) (8,7) (9,16) (0,9) (10,0) (5,11) (10,13) (6,2) (11,13) (1,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->1->14->9->10->8->4->12->7->6->2->11->15->13->3->16." - } - ] - }, - { - "id": "hamilton-hard-graph92", - "image": "data/hamilton/graph_visual/Base/hard/graph92.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,1) (1,5) (3,4) (0,8) (1,11) (10,9) (11,3) (10,0) (10,8) (8,2) (4,11) (1,10) (3,2) (1,7) (2,9) (3,10) (8,7) (1,9) (6,4) (8,11) (8,5) (8,4) (0,4) (11,6) (7,10) (4,5) (2,4) (7,11) (8,1) (6,8) (10,2) (5,6) (6,7) (3,5) (6,2) (9,0) (4,7) (11,0) (10,6) (9,4) (2,5) (6,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->10->9->2->3->1->5->4->11->6->7." - } - ] - }, - { - "id": "hamilton-hard-graph572", - "image": "data/hamilton/graph_visual/Base/hard/graph572.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,16) (19,11) (15,19) (8,19) (9,12) (10,9) (8,12) (12,0) (7,0) (10,14) (5,1) (1,8) (19,18) (1,11) (15,9) (11,9) (11,4) (1,3) (8,0) (16,7) (1,4) (8,4) (19,17) (7,15) (6,2) (10,5) (1,14) (3,18) (2,15) (3,5) (7,14) (11,6) (16,3) (6,5) (4,19) (15,18) (11,17) (15,6) (10,11) (7,3) (19,13) (2,9) (4,9) (11,12) (19,9) (3,17) (6,3) (12,3) (3,14) (18,4) (12,15) (2,11) (5,2) (10,12) (0,9) (14,18) (17,4) (12,13) (15,4) (12,14) (8,15) (10,7) (6,13) (12,17) (14,16) (1,9) (10,13) (19,2) (1,19) (14,4) (13,11) (17,8) (1,2) (13,0) (15,1) (6,9) (16,4) (12,7) (3,0) (0,6) (14,5) (16,5) (17,18) (7,19) (7,6) (14,8) (3,2) (16,12) (15,5) (18,7) (13,16) (7,1) (16,1) (6,18) (9,16) (19,3) (8,3) (2,8) (11,0) (19,0) (9,18) (15,17) (10,4) (9,17) (8,13) (19,6) (0,2) (6,12) (14,6) (8,16) (5,12) (10,2) (16,10) (5,18) (15,13) (10,18) (13,2) (17,16) (0,1) (2,18) (7,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->16->7->15->19->11->1->5->10->9->12->8->4->18->14->6->13->2->3->17." - } - ] - }, - { - "id": "hamilton-hard-graph245", - "image": "data/hamilton/graph_visual/Base/hard/graph245.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,4) (11,6) (2,11) (4,14) (0,9) (14,6) (0,2) (0,6) (13,1) (1,0) (12,14) (0,3) (12,0) (3,2) (9,8) (6,2) (8,11) (13,8) (12,6) (3,14) (7,10) (12,5) (1,5) (2,1) (4,5) (3,6) (1,14) (13,10) (1,9) (8,2) (2,12) (12,8) (0,14) (6,1) (2,13) (14,2) (7,2) (10,9) (8,0) (11,7) (6,13) (11,3) (11,4) (13,7) (9,12) (5,8) (9,13) (13,11) (5,10) (11,1) (6,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->8->11->6->14->4->1->13->7->10->5->12->2->3." - } - ] - }, - { - "id": "hamilton-hard-graph68", - "image": "data/hamilton/graph_visual/Base/hard/graph68.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,9) (8,5) (10,11) (0,6) (6,10) (10,0) (1,9) (7,10) (9,8) (10,4) (3,8) (1,5) (10,9) (5,7) (11,3) (5,9) (9,4) (7,6) (6,4) (1,2) (3,2) (7,9) (0,1) (7,1) (8,11) (3,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->10->11->9->8->5->7->1->2->3->4." - } - ] - }, - { - "id": "hamilton-hard-graph363", - "image": "data/hamilton/graph_visual/Base/hard/graph363.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,6) (1,16) (14,7) (1,6) (15,4) (1,13) (4,16) (15,11) (13,14) (2,4) (16,12) (16,13) (11,4) (4,7) (8,7) (5,11) (14,16) (6,15) (10,7) (15,3) (15,9) (16,9) (5,16) (10,1) (13,12) (2,8) (5,9) (7,15) (3,12) (14,8) (1,12) (5,6) (11,10) (9,14) (2,15) (12,2) (0,8) (1,5) (9,10) (10,3) (3,6) (1,7) (6,4) (13,10) (7,12) (13,3) (15,0) (16,2) (15,16) (12,11) (11,14) (9,1) (3,11) (11,0) (8,12) (4,8) (14,12) (6,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->7->14->13->1->16->4->15->11->5->9->10->3->6->12->2." - } - ] - }, - { - "id": "hamilton-hard-graph303", - "image": "data/hamilton/graph_visual/Base/hard/graph303.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,2) (7,0) (0,4) (0,2) (2,3) (5,3) (8,0) (13,4) (7,6) (10,11) (13,9) (2,14) (0,5) (4,9) (1,4) (11,3) (14,7) (11,5) (6,15) (12,3) (15,2) (7,4) (15,7) (4,3) (0,12) (0,1) (3,10) (12,14) (8,15) (5,7) (4,2) (1,11) (8,9) (9,3) (5,12) (3,6) (8,11) (15,12) (3,13) (9,15) (11,4) (14,10) (10,9) (11,6) (0,10) (6,9) (10,4) (9,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->6->15->2->11->1->4->13->3->5->12->14->10->9->8." - } - ] - }, - { - "id": "hamilton-hard-graph530", - "image": "data/hamilton/graph_visual/Base/hard/graph530.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,7) (3,4) (2,17) (15,16) (3,9) (5,17) (8,15) (12,5) (11,17) (16,9) (10,4) (15,0) (1,14) (4,9) (18,6) (17,4) (5,4) (12,0) (12,2) (10,2) (3,1) (18,4) (9,7) (14,2) (3,11) (18,15) (6,7) (7,12) (8,2) (2,16) (5,7) (15,11) (15,14) (13,4) (10,16) (18,0) (13,6) (8,0) (4,16) (11,18) (3,15) (6,12) (14,12) (3,6) (0,9) (17,12) (14,10) (4,12) (9,8) (5,8) (7,11) (1,13) (6,4) (17,10) (10,5) (3,0) (15,1) (12,11) (11,1) (15,17) (7,15) (1,2) (18,13) (18,16) (1,18) (2,7) (8,3) (6,5) (5,2) (3,7) (3,16) (10,11) (7,14) (14,6) (2,18) (11,4) (10,8) (5,14) (5,13) (5,15) (4,1) (0,16) (6,11) (5,0) (16,17) (8,1) (2,6) (7,1) (1,16) (0,1) (5,9) (12,8) (1,9) (18,14) (11,9) (13,3) (18,9) (10,13) (13,17) (8,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->15->16->9->3->4->10->2->17->5->12->7->8->1->14->6->13->18->11." - } - ] - }, - { - "id": "hamilton-hard-graph582", - "image": "data/hamilton/graph_visual/Base/hard/graph582.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (6,15) (8,2) (5,2) (11,18) (7,9) (12,17) (2,16) (10,15) (9,11) (7,1) (10,2) (0,19) (19,5) (2,7) (17,14) (9,14) (11,6) (2,3) (5,15) (18,3) (18,2) (12,0) (14,4) (18,14) (7,5) (7,14) (6,14) (18,19) (7,19) (3,4) (10,9) (0,17) (18,16) (2,17) (11,5) (13,6) (9,18) (13,16) (16,15) (15,3) (9,12) (3,8) (3,6) (10,12) (6,16) (6,17) (10,19) (10,17) (3,5) (19,9) (4,17) (11,1) (5,10) (13,9) (4,9) (19,16) (0,16) (19,4) (16,17) (16,8) (9,8) (19,15) (4,12) (13,0) (3,13) (17,5) (18,5) (1,8) (0,6) (13,7) (10,11) (12,7) (12,14) (18,1) (13,5) (18,4) (11,19) (19,12) (2,13) (8,12) (10,8) (2,9) (7,4) (8,5) (7,16) (11,8) (12,1) (15,0) (11,14) (7,0) (6,19) (17,8) (11,16) (16,4) (1,17) (17,15) (16,1) (8,6) (2,4) (1,3) (11,13) (6,2) (14,16)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->19->5->2->8->3->18->11->9->7->1->12->17->14->4->16->13->6->15->10." - } - ] - }, - { - "id": "hamilton-hard-graph567", - "image": "data/hamilton/graph_visual/Base/hard/graph567.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,17) (4,5) (7,3) (6,1) (8,1) (6,0) (2,10) (12,11) (2,3) (16,9) (15,7) (14,9) (13,16) (13,17) (10,15) (6,13) (4,14) (6,4) (18,12) (3,13) (10,11) (1,13) (9,6) (18,19) (5,7) (19,4) (6,10) (12,15) (14,17) (18,2) (1,16) (18,4) (1,7) (4,7) (10,19) (17,8) (17,7) (10,0) (6,18) (3,10) (15,2) (6,2) (3,4) (8,10) (8,2) (13,5) (1,12) (18,16) (0,18) (9,4) (5,6) (4,12) (0,12) (6,19) (10,18) (16,7) (14,3) (11,5) (17,3) (19,2) (16,19) (11,9) (17,0) (0,4) (18,9) (18,15) (13,19) (1,3) (19,7) (4,17) (2,13) (13,7) (19,12) (3,9) (5,9) (14,13) (0,16) (4,13) (10,4) (14,2) (10,7) (14,5) (5,16) (11,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->1->8->17->2->10->15->7->3->13->16->9->14->4->5->11->12->18->19." - } - ] - }, - { - "id": "hamilton-hard-graph225", - "image": "data/hamilton/graph_visual/Base/hard/graph225.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,6) (10,9) (12,8) (3,0) (11,10) (8,0) (0,9) (7,9) (7,2) (8,7) (3,1) (13,11) (6,5) (2,12) (12,9) (2,0) (0,13) (6,11) (11,3) (9,11) (4,6) (4,10) (2,13) (1,4) (4,11) (2,4) (13,7) (4,0) (10,12) (3,7) (11,8) (3,9) (3,5) (11,7) (5,11) (4,12) (11,0) (0,5) (9,1) (10,5) (13,9) (13,10) (7,0) (1,13) (8,13) (0,1) (3,10) (12,11) (1,6) (13,3) (12,0) (8,9) (4,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->1->4->6->7->9->10->12->2->13->8->11->5." - } - ] - }, - { - "id": "hamilton-hard-graph488", - "image": "data/hamilton/graph_visual/Base/hard/graph488.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (10,4) (16,6) (6,0) (5,13) (17,2) (9,10) (3,6) (14,3) (15,8) (5,0) (12,13) (0,9) (11,10) (3,2) (13,17) (10,12) (12,5) (9,14) (6,17) (5,16) (3,9) (18,12) (16,17) (7,5) (14,17) (11,9) (13,16) (17,9) (8,2) (10,5) (18,7) (4,2) (15,3) (13,14) (17,1) (13,15) (3,13) (6,14) (7,8) (17,10) (11,0) (0,14) (15,6) (6,10) (12,9) (18,16) (9,16) (18,17) (4,0) (6,11) (18,6) (4,17) (11,14) (18,3) (17,8) (13,8) (4,5) (8,0) (4,9) (1,10) (7,10) (2,10) (2,12) (15,10) (9,8) (8,18) (12,0) (0,10) (7,0) (3,16) (15,4) (5,8) (15,7) (5,17) (9,18) (4,18)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->16->5->13->12->10->4->2->3->14->11->9->8->15->7->18->17->1." - } - ] - }, - { - "id": "hamilton-hard-graph146", - "image": "data/hamilton/graph_visual/Base/hard/graph146.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (10,12) (7,4) (6,1) (5,3) (8,6) (7,8) (5,9) (10,8) (4,2) (0,3) (12,11) (0,5) (2,9) (0,2) (3,10) (11,1) (2,10) (1,10) (10,9) (7,2) (1,0) (3,7) (4,1) (8,0) (7,9) (0,4) (12,0) (12,7) (5,8) (3,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->5->9->2->4->7->8->6->1->11->12->10." - } - ] - }, - { - "id": "hamilton-hard-graph93", - "image": "data/hamilton/graph_visual/Base/hard/graph93.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,6) (11,0) (10,4) (11,10) (7,5) (11,9) (5,0) (3,1) (11,8) (3,8) (4,9) (10,5) (3,4) (6,9) (4,2) (7,6) (11,7) (8,6) (5,4) (7,9) (0,2) (5,1) (8,4) (9,1) (0,6) (8,0) (2,5) (0,10) (2,11) (11,4) (0,4) (1,7) (6,10) (8,1) (8,9) (2,7) (8,10) (7,8) (10,3) (4,7) (7,0) (5,8) (5,6) (1,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->10->4->9->6->2->5->7->1->3->8." - } - ] - }, - { - "id": "hamilton-hard-graph80", - "image": "data/hamilton/graph_visual/Base/hard/graph80.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (8,9) (0,11) (1,4) (0,7) (9,1) (9,3) (1,11) (5,4) (1,10) (10,2) (0,4) (7,3) (11,2) (5,9) (4,3) (7,1) (4,8) (5,11) (2,8) (4,6) (2,5) (9,6) (6,2) (9,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->5->4->3->7->1->10->2->8->9->6." - } - ] - }, - { - "id": "hamilton-hard-graph196", - "image": "data/hamilton/graph_visual/Base/hard/graph196.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,2) (9,0) (1,0) (10,5) (5,13) (12,9) (3,10) (12,13) (8,3) (6,11) (8,2) (9,13) (4,2) (1,5) (13,4) (13,10) (5,0) (13,0) (11,5) (8,0) (12,2) (6,5) (2,3) (4,12) (6,13) (9,2) (9,10) (1,4) (9,5) (7,10) (11,10) (10,6) (2,11) (10,12) (12,7) (7,6) (4,3) (1,3) (4,8) (1,13) (5,8) (2,13) (11,13) (6,4) (0,10) (10,1) (1,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->12->13->5->10->3->8->1->4->2->11->6->7." - } - ] - }, - { - "id": "hamilton-hard-graph60", - "image": "data/hamilton/graph_visual/Base/hard/graph60.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,0) (1,2) (4,3) (5,1) (6,9) (6,1) (2,8) (9,11) (10,3) (8,4) (7,11) (4,11) (4,2) (5,0) (1,4) (10,4) (3,7) (4,9) (4,6) (10,11) (5,8) (0,8) (10,7) (11,6) (4,7) (0,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->11->9->6->1->5->8->2->4->3->10." - } - ] - }, - { - "id": "hamilton-hard-graph207", - "image": "data/hamilton/graph_visual/Base/hard/graph207.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (2,12) (3,7) (4,5) (11,12) (0,4) (13,10) (10,0) (7,12) (2,11) (5,7) (9,7) (1,7) (13,11) (0,6) (2,13) (8,4) (1,10) (1,5) (3,2) (12,5) (2,8) (10,9) (13,6) (9,0) (4,11) (10,8) (2,1) (8,9) (9,3) (12,6) (5,6) (11,0) (5,8) (12,10) (6,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->5->7->3->9->8->2->12->11->6->13->10->1." - } - ] - }, - { - "id": "hamilton-hard-graph96", - "image": "data/hamilton/graph_visual/Base/hard/graph96.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,10) (3,5) (9,0) (1,0) (11,1) (8,11) (3,10) (11,3) (2,8) (7,3) (5,2) (9,2) (2,6) (4,7) (7,5) (1,10) (9,7) (9,3) (9,6) (5,9) (4,10) (4,3) (11,4) (2,3) (7,2) (1,2) (8,7) (4,0) (3,1) (1,5) (8,1) (11,5) (8,3) (5,10) (9,8) (6,11) (0,2) (11,2) (10,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->2->8->7->10->1->5->3->4->11->6." - } - ] - }, - { - "id": "hamilton-hard-graph252", - "image": "data/hamilton/graph_visual/Base/hard/graph252.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,7) (12,14) (2,10) (4,1) (4,13) (5,3) (4,11) (4,8) (8,10) (7,1) (4,3) (2,12) (14,7) (6,11) (8,3) (7,10) (2,1) (10,13) (9,6) (4,10) (5,13) (9,14) (12,3) (1,3) (12,13) (12,6) (5,2) (10,14) (13,1) (5,9) (8,2) (5,1) (9,2) (11,14) (9,13) (12,8) (6,4) (5,0) (0,12) (11,3) (12,5) (10,1) (3,2) (2,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->3->4->1->7->9->6->11->14->12->2->8->10->13." - } - ] - }, - { - "id": "hamilton-hard-graph416", - "image": "data/hamilton/graph_visual/Base/hard/graph416.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,13) (11,15) (4,11) (1,0) (5,6) (11,16) (4,7) (7,3) (9,10) (3,2) (13,2) (7,11) (4,2) (16,10) (8,2) (16,12) (12,9) (4,3) (4,6) (6,3) (2,0) (1,10) (6,2) (4,16) (15,2) (6,16) (1,16) (16,7) (12,10) (15,5) (7,0) (5,1) (4,10) (12,4) (11,9) (13,3) (2,1) (5,3) (5,8) (3,10) (8,3) (9,3) (0,5) (13,8) (7,6) (13,1) (9,13) (2,16) (6,13) (9,2) (8,0) (10,15) (14,1) (15,9) (7,1) (3,16) (0,4) (15,14) (14,2) (13,16) (10,5) (0,9) (3,1) (6,9) (1,15) (10,2) (5,9) (12,7) (13,11) (12,15)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->10->9->12->16->11->15->5->6->4->7->3->13->8->2->14." - } - ] - }, - { - "id": "hamilton-hard-graph91", - "image": "data/hamilton/graph_visual/Base/hard/graph91.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,1) (11,4) (6,11) (2,0) (5,11) (2,9) (2,4) (8,3) (6,8) (3,9) (0,3) (8,5) (1,8) (4,8) (1,9) (6,1) (4,10) (11,2) (11,3) (6,2) (1,0) (9,5) (9,8) (9,11) (2,7) (7,5) (4,9) (3,1) (11,8) (0,11) (10,3) (9,7) (0,4) (7,3) (3,4) (2,8) (9,0) (2,1) (7,4) (6,10) (8,7) (8,0) (11,7) (3,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->9->3->8->6->1->5->11->7->4->10." - } - ] - }, - { - "id": "hamilton-hard-graph366", - "image": "data/hamilton/graph_visual/Base/hard/graph366.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (6,8) (15,0) (1,8) (5,10) (9,4) (7,6) (13,16) (13,6) (0,4) (3,1) (5,6) (13,0) (5,12) (4,15) (14,16) (10,2) (12,9) (15,7) (14,13) (8,13) (8,4) (9,16) (11,6) (2,15) (13,10) (7,14) (8,2) (11,12) (1,2) (5,11) (0,11) (1,6) (10,9) (2,0) (15,3) (0,16) (13,12) (13,2) (6,2) (12,1) (14,2) (9,6) (0,14) (16,8) (2,12) (11,1) (13,9) (16,3) (6,16) (5,0) (9,1) (1,4) (4,14) (5,2) (16,1) (9,15) (9,0) (6,14) (7,5) (11,15)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->15->4->9->12->5->10->2->8->6->7->14->13->16->3->1->11." - } - ] - }, - { - "id": "hamilton-hard-graph242", - "image": "data/hamilton/graph_visual/Base/hard/graph242.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,5) (6,8) (14,8) (3,8) (0,3) (6,9) (13,8) (11,3) (13,6) (8,5) (3,7) (14,5) (12,9) (14,13) (10,14) (14,1) (5,3) (10,4) (4,7) (2,3) (4,8) (6,10) (2,9) (14,7) (7,12) (3,14) (11,6) (12,3) (12,14) (9,7) (13,4) (2,6) (9,8) (0,11) (0,5) (2,7) (4,9) (8,7) (1,3) (9,1) (5,2) (10,7) (11,13) (13,7) (4,2) (4,14) (5,9) (13,5) (0,4) (10,9) (6,0) (1,8) (8,0) (0,12) (6,7) (4,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->8->6->9->1->14->10->4->2->7->12->5->13->11." - } - ] - }, - { - "id": "hamilton-hard-graph289", - "image": "data/hamilton/graph_visual/Base/hard/graph289.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,8) (1,6) (13,7) (11,4) (10,4) (5,3) (8,7) (1,13) (0,13) (9,14) (5,1) (5,4) (6,13) (14,10) (7,9) (4,0) (14,2) (2,6) (11,8) (5,2) (8,1) (12,3) (2,3) (1,10) (7,5) (8,4) (1,7) (13,4) (9,12) (2,8) (6,0) (2,9) (5,10) (6,5) (12,6) (3,8) (12,13) (1,2) (0,7) (7,6) (6,9) (11,3) (9,10) (13,10) (14,8) (14,11) (10,6) (7,2) (4,7) (0,2) (12,1) (9,1) (13,14) (3,7) (11,10) (4,9) (0,10) (11,0) (11,12) (8,0) (14,4) (4,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->7->8->9->14->10->4->11->3->5->1->2->6->12." - } - ] - }, - { - "id": "hamilton-hard-graph136", - "image": "data/hamilton/graph_visual/Base/hard/graph136.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,7) (3,10) (0,12) (11,2) (3,8) (11,5) (0,1) (1,7) (2,4) (6,10) (1,11) (7,10) (12,3) (6,5) (8,10) (6,9) (2,12) (9,0) (9,5) (11,3) (10,4) (5,2) (4,9) (7,9) (1,4) (3,9) (0,2) (4,11) (0,7) (5,7) (3,5) (2,10) (10,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->3->8->10->6->5->11->2->4->9->7->1." - } - ] - }, - { - "id": "hamilton-hard-graph66", - "image": "data/hamilton/graph_visual/Base/hard/graph66.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,8) (5,2) (1,9) (11,10) (5,6) (9,10) (1,11) (8,3) (5,4) (10,7) (10,1) (4,9) (11,4) (11,3) (10,2) (2,4) (8,7) (2,9) (3,7) (6,8) (1,6) (8,2) (11,2) (3,9) (9,11) (5,11) (4,0) (0,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->3->11->1->6->5->2->4->9->10->7." - } - ] - }, - { - "id": "hamilton-hard-graph478", - "image": "data/hamilton/graph_visual/Base/hard/graph478.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (7,5) (0,4) (0,14) (5,6) (0,15) (10,4) (2,16) (3,17) (14,4) (11,1) (16,12) (14,5) (8,17) (10,15) (11,14) (3,16) (12,4) (10,5) (2,3) (17,9) (15,11) (12,11) (4,13) (16,15) (9,6) (9,8) (8,2) (11,13) (12,13) (14,16) (9,1) (10,12) (9,12) (5,0) (6,1) (13,6) (1,10) (5,8) (13,10) (11,9) (14,2) (16,1) (11,2) (4,2) (3,1) (6,11) (13,3) (6,8) (5,16) (7,8) (9,16) (9,15) (5,11) (15,1) (3,0) (14,1) (4,3) (16,10) (10,8) (0,10) (12,8) (7,15) (10,7) (10,9) (4,17) (1,13) (2,1) (17,1) (16,0) (2,12) (15,3) (7,1) (5,2) (13,16) (14,6) (12,3) (1,8) (17,13) (3,7) (10,3) (15,12) (9,5) (9,7) (10,11) (7,0) (4,1) (11,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->10->15->11->1->9->17->3->16->2->8->7->5->14->6->13->12." - } - ] - }, - { - "id": "hamilton-hard-graph405", - "image": "data/hamilton/graph_visual/Base/hard/graph405.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,5) (4,15) (9,11) (0,1) (14,6) (2,1) (12,15) (2,7) (8,14) (12,2) (9,0) (3,5) (11,10) (15,0) (13,12) (9,16) (13,0) (10,2) (1,4) (4,8) (8,11) (14,10) (4,10) (6,15) (14,15) (9,14) (5,13) (5,15) (6,10) (13,11) (2,5) (8,15) (9,5) (3,8) (8,12) (1,14) (14,3) (10,0) (10,7) (1,12) (15,7) (6,8) (3,6) (5,8) (0,16) (11,4) (5,1) (5,11) (4,13) (4,0) (3,1) (9,10) (16,14) (6,16) (13,3) (3,11) (15,13) (9,6) (6,4) (0,5) (3,4) (6,12) (2,11) (9,15) (8,16) (7,9) (4,9) (14,11) (16,5) (16,7) (15,10) (1,8) (8,2) (12,14) (7,12) (13,6) (3,0) (7,8) (16,4) (2,6) (2,14) (1,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->2->7->5->3->8->14->6->15->4->16->9->10->11->13->12." - } - ] - }, - { - "id": "hamilton-hard-graph47", - "image": "data/hamilton/graph_visual/Base/hard/graph47.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,9) (5,0) (0,3) (2,7) (3,10) (5,1) (10,9) (1,4) (7,3) (3,2) (9,3) (4,7) (0,1) (10,6) (5,7) (10,2) (8,3) (8,1) (1,7) (4,5) (8,4) (0,4) (2,8) (6,8) (0,6) (8,10) (4,6) (1,6) (0,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->1->4->7->2->3->10->9->6->8." - } - ] - }, - { - "id": "hamilton-hard-graph38", - "image": "data/hamilton/graph_visual/Base/hard/graph38.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,1) (7,8) (0,9) (5,7) (10,9) (6,5) (4,8) (1,5) (9,3) (6,1) (3,4) (9,7) (8,9) (2,3) (9,1) (4,6) (8,1) (9,2) (4,0) (7,6) (10,2) (6,0) (10,1) (3,6) (5,4) (2,8) (8,6) (2,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->5->7->8->4->6->3->9->10->2." - } - ] - }, - { - "id": "hamilton-hard-graph483", - "image": "data/hamilton/graph_visual/Base/hard/graph483.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,15) (6,10) (1,11) (15,2) (17,16) (15,0) (0,1) (13,10) (17,14) (16,1) (6,15) (7,6) (7,11) (5,15) (4,16) (1,5) (0,3) (1,12) (15,4) (9,17) (13,17) (18,15) (12,8) (17,8) (16,10) (1,9) (3,7) (3,10) (3,8) (16,13) (6,0) (15,16) (12,3) (11,3) (5,3) (2,7) (6,9) (18,16) (8,6) (18,13) (15,9) (0,10) (7,14) (5,7) (16,3) (18,7) (0,7) (8,15) (0,9) (7,9) (11,5) (3,2) (17,6) (17,0) (13,0) (11,2) (6,1) (12,2) (12,15) (18,10) (4,10) (10,14) (8,0) (17,1) (2,1) (18,0) (18,17) (10,2) (15,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->15->11->1->16->4->10->13->18->7->14->17->9->6->8->12->2->3->5." - } - ] - }, - { - "id": "hamilton-hard-graph522", - "image": "data/hamilton/graph_visual/Base/hard/graph522.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (16,6) (2,16) (9,17) (0,2) (10,8) (15,18) (17,10) (3,11) (6,1) (0,3) (8,13) (4,16) (15,10) (16,15) (18,11) (11,2) (16,17) (14,16) (17,7) (17,14) (16,11) (7,0) (10,0) (13,12) (8,1) (13,10) (14,0) (5,10) (9,2) (8,6) (6,11) (6,17) (3,7) (8,17) (1,4) (0,9) (8,0) (7,13) (9,12) (13,17) (2,15) (12,18) (12,10) (3,17) (9,1) (16,1) (7,16) (10,4) (10,11) (13,4) (12,15) (3,9) (12,8) (6,2) (7,9) (8,16) (16,12) (4,11) (18,0) (2,3) (7,11) (14,12) (12,0) (0,17) (1,17) (16,9) (14,9) (18,9) (3,13) (1,14) (7,14) (18,3) (15,13) (6,18) (2,4) (4,7) (15,9) (10,2) (4,3) (4,17) (13,11) (7,1) (9,11) (7,10) (6,12) (9,8) (13,5) (1,11) (0,1) (17,5) (8,3) (9,10) (4,0) (17,12) (14,10) (14,2) (8,4) (0,16) (16,10) (3,16) (14,13) (13,16) (4,14) (16,18) (0,13) (9,6) (0,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->16->6->1->8->10->17->9->12->15->18->11->3->7->14->4->13->5." - } - ] - }, - { - "id": "hamilton-hard-graph446", - "image": "data/hamilton/graph_visual/Base/hard/graph446.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,12) (14,2) (2,9) (2,3) (8,0) (10,6) (14,6) (7,3) (2,7) (14,7) (1,10) (4,10) (13,10) (1,8) (1,11) (11,15) (16,14) (17,11) (5,14) (12,0) (4,14) (3,8) (3,17) (13,14) (12,17) (15,7) (9,3) (4,16) (11,5) (2,6) (5,6) (16,1) (3,5) (14,9) (10,2) (15,17) (0,10) (8,14) (16,6) (7,0) (11,7) (12,5) (7,8) (12,15) (13,6) (16,3) (8,10) (5,7) (5,17) (11,16) (2,5) (7,1) (3,12) (17,0) (10,7) (4,15) (13,16) (12,14) (0,9) (9,1) (7,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->1->10->6->14->2->9->3->7->11->17->5->12->15->4->16->13." - } - ] - }, - { - "id": "hamilton-hard-graph214", - "image": "data/hamilton/graph_visual/Base/hard/graph214.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,8) (10,7) (9,8) (6,1) (7,2) (10,5) (4,11) (11,12) (8,5) (0,11) (6,10) (11,7) (13,8) (11,9) (8,11) (12,0) (8,2) (12,4) (2,3) (0,6) (4,2) (4,8) (0,2) (9,1) (13,6) (7,0) (13,11) (4,3) (10,2) (2,5) (4,6) (8,7) (5,9) (9,4) (3,9) (10,13) (3,7) (6,2) (1,0) (8,12) (11,5) (13,1) (12,9) (12,7) (8,1) (10,12) (12,6) (0,10) (3,12) (9,0) (9,7) (3,10) (12,5) (6,5) (7,13) (10,8) (13,2) (11,1) (1,7) (6,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->4->12->8->3->2->7->10->5->9->1->6->13." - } - ] - }, - { - "id": "hamilton-hard-graph184", - "image": "data/hamilton/graph_visual/Base/hard/graph184.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (10,0) (5,3) (8,13) (8,0) (6,2) (3,10) (3,9) (9,5) (12,4) (0,13) (1,6) (3,8) (6,12) (5,0) (9,6) (0,12) (1,2) (1,5) (2,13) (3,13) (0,11) (1,8) (6,3) (13,7) (6,5) (4,11) (6,13) (13,11) (6,11) (10,11) (7,10) (11,2) (6,0) (10,5) (8,2) (10,4) (4,6) (9,12) (11,8) (1,0) (11,9) (12,1) (12,7) (3,0) (9,13) (4,7) (10,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->3->5->9->6->2->1->8->13->7->12->4->11." - } - ] - }, - { - "id": "hamilton-hard-graph99", - "image": "data/hamilton/graph_visual/Base/hard/graph99.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,2) (9,7) (1,9) (7,6) (10,1) (0,1) (2,3) (6,1) (4,7) (2,6) (3,10) (10,4) (7,10) (11,9) (5,3) (8,7) (2,0) (2,4) (9,5) (2,1) (5,8) (1,5) (11,3) (11,2) (11,6) (11,10) (1,8) (11,1) (11,8) (0,10) (10,2) (4,8) (6,5) (0,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->9->7->2->3->10->4->8->5->6->11." - } - ] - }, - { - "id": "hamilton-hard-graph48", - "image": "data/hamilton/graph_visual/Base/hard/graph48.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,8) (1,3) (3,8) (2,3) (10,1) (7,3) (7,9) (9,1) (6,9) (6,2) (5,7) (7,6) (8,5) (2,1) (9,10) (9,5) (0,5) (8,1) (4,6) (0,10) (2,9) (0,6) (5,1) (3,0) (3,10) (10,6) (7,0) (10,7) (1,7) (5,6) (5,4) (3,4) (9,8) (4,0) (7,2) (4,2) (4,8) (10,5) (4,7) (5,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->7->3->1->10->9->6->8->4->2." - } - ] - }, - { - "id": "hamilton-hard-graph288", - "image": "data/hamilton/graph_visual/Base/hard/graph288.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,13) (9,2) (9,7) (10,0) (14,12) (3,14) (13,10) (11,7) (11,12) (8,2) (5,10) (4,13) (3,9) (8,6) (3,4) (5,12) (4,0) (11,10) (5,3) (2,3) (9,0) (14,6) (9,8) (3,12) (9,13) (14,9) (1,8) (2,6) (10,8) (1,9) (10,1) (2,14) (6,4) (10,4) (9,10) (6,12) (10,14) (10,7) (8,11) (8,7) (1,4) (10,3) (8,12) (0,13) (2,0) (0,8) (7,0) (1,14) (0,6) (7,1) (13,3) (13,12) (14,4) (2,10) (5,7) (11,4) (9,6) (5,8) (7,6) (13,2) (3,6) (14,7) (0,5) (1,12) (12,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->13->11->7->9->2->8->6->14->12->5->3->4->1." - } - ] - }, - { - "id": "hamilton-hard-graph327", - "image": "data/hamilton/graph_visual/Base/hard/graph327.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,7) (6,1) (8,10) (1,15) (4,2) (9,12) (14,10) (2,9) (5,8) (10,6) (10,0) (14,0) (3,1) (3,8) (12,10) (2,0) (3,13) (3,5) (6,8) (0,6) (8,13) (2,3) (8,14) (4,14) (13,1) (1,8) (11,9) (6,7) (3,6) (12,8) (13,10) (1,0) (6,5) (8,9) (14,9) (0,13) (9,4) (1,11) (0,9) (5,13) (12,3) (10,11) (2,12) (4,10) (5,11) (8,11) (3,15) (0,7) (7,4) (2,5) (3,0) (5,9) (6,2) (10,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->8->5->6->7->14->4->2->12->9->11->1->15->3->13." - } - ] - }, - { - "id": "hamilton-hard-graph411", - "image": "data/hamilton/graph_visual/Base/hard/graph411.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (9,2) (3,7) (16,14) (1,5) (0,3) (16,11) (10,1) (9,6) (16,4) (15,13) (11,12) (2,13) (2,16) (12,13) (14,0) (6,5) (10,0) (13,1) (0,2) (6,12) (13,3) (11,13) (8,11) (0,6) (2,7) (5,14) (1,9) (8,14) (3,4) (10,4) (12,5) (3,9) (10,15) (9,4) (7,5) (1,8) (10,8) (15,4) (16,7) (0,16) (14,10) (13,0) (15,3) (12,1) (0,5) (14,13) (3,6) (8,6) (3,8) (1,3) (10,3) (2,6) (12,0) (4,12) (10,5) (8,15) (7,13) (4,8) (0,11) (13,5) (5,15) (4,2) (0,15) (14,3) (16,5) (8,12) (3,2) (16,12) (15,16) (2,14) (12,3) (4,0) (4,6) (8,7) (7,12) (4,14) (12,2) (11,4) (14,15) (1,15) (1,11) (14,11) (12,14) (2,11) (9,0) (1,0) (15,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->7->2->9->6->5->1->10->4->16->14->8->11->12->13->15." - } - ] - }, - { - "id": "hamilton-hard-graph589", - "image": "data/hamilton/graph_visual/Base/hard/graph589.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,5) (14,9) (14,13) (4,5) (16,1) (11,6) (8,1) (3,14) (4,6) (6,18) (9,17) (8,2) (12,6) (3,12) (18,16) (9,10) (13,3) (13,16) (6,7) (5,17) (17,4) (2,7) (2,11) (2,13) (8,9) (1,9) (2,10) (9,4) (5,11) (8,12) (0,10) (11,3) (10,4) (9,5) (2,19) (1,11) (2,12) (13,0) (3,15) (0,18) (5,10) (18,2) (14,2) (9,6) (13,15) (10,19) (19,1) (9,16) (17,19) (2,3) (16,12) (0,4) (2,15) (1,13) (0,15) (17,12) (16,17) (15,1) (15,18) (5,14) (5,8) (15,10) (15,9) (0,9) (5,7) (13,4) (19,16) (4,8) (15,12) (16,2) (16,14) (1,7) (4,3) (19,9) (9,13) (14,11) (7,4) (13,12) (13,18) (13,10) (14,15) (7,12) (15,17) (10,6) (9,12) (12,18) (7,10) (4,15) (3,5) (2,5) (1,2) (13,11) (19,5) (6,0) (11,0) (7,3) (3,0) (6,3) (18,3) (8,13) (6,16) (16,7) (19,14) (11,18) (1,14) (3,19) (8,16) (18,1) (16,5) (7,17) (0,17) (7,19) (16,11) (17,2) (8,0) (6,14) (13,6) (7,18) (15,19) (14,7) (2,0) (3,9) (10,16) (6,2) (1,6) (1,5) (1,3) (12,11) (12,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->9->14->13->3->12->6->11->2->8->1->16->18->15->5->4->17->19->7." - } - ] - }, - { - "id": "hamilton-hard-graph594", - "image": "data/hamilton/graph_visual/Base/hard/graph594.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,16) (3,10) (17,2) (6,0) (16,9) (5,0) (10,5) (1,5) (2,14) (12,15) (18,13) (3,11) (2,18) (8,13) (7,16) (17,0) (11,6) (7,18) (13,15) (12,13) (17,6) (0,12) (0,16) (19,2) (12,1) (17,8) (3,6) (16,6) (8,11) (1,10) (9,14) (19,14) (3,13) (5,7) (4,17) (11,18) (3,19) (12,16) (9,0) (12,5) (5,3) (17,14) (1,15) (4,13) (13,14) (4,18) (11,15) (18,14) (13,5) (17,10) (7,12) (19,12) (5,11) (10,9) (8,18) (16,11) (11,4) (0,2) (1,18) (15,16) (5,15) (10,18) (1,3) (11,7) (9,3) (7,15) (19,4) (1,0) (0,14) (10,8) (2,9) (7,8) (5,17) (4,0) (17,3) (10,15) (3,15) (18,12) (9,11) (9,1) (1,6) (12,9) (4,15) (5,16) (10,19) (14,3) (16,8) (19,16) (6,14) (17,12) (13,16) (16,3) (17,16) (9,4) (9,6) (9,18) (14,7) (12,3) (13,1) (7,13) (6,12) (8,14) (13,2) (11,19) (1,14) (11,10) (15,9) (16,14) (14,15) (19,1) (15,0) (14,12) (14,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->11->3->10->5->1->12->15->13->18->2->16->9->14->19->4->17->8->7." - } - ] - }, - { - "id": "hamilton-hard-graph200", - "image": "data/hamilton/graph_visual/Base/hard/graph200.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (5,10) (7,2) (8,9) (1,7) (6,0) (1,2) (11,8) (9,5) (2,11) (3,5) (0,5) (11,12) (7,0) (10,13) (4,12) (1,13) (11,9) (10,12) (1,10) (0,13) (3,8) (7,12) (9,7) (5,7) (1,6) (9,10) (11,0) (3,2) (4,5) (6,13) (6,10) (3,7) (1,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->1->7->2->11->12->4->5->3->8->9->10->13." - } - ] - }, - { - "id": "hamilton-hard-graph515", - "image": "data/hamilton/graph_visual/Base/hard/graph515.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,4) (4,5) (7,17) (8,2) (13,18) (8,0) (14,17) (5,6) (6,13) (14,11) (2,0) (1,0) (15,4) (15,5) (16,4) (3,4) (8,12) (18,5) (13,5) (6,12) (16,11) (11,1) (12,1) (18,9) (8,18) (5,16) (3,0) (16,9) (8,7) (3,13) (14,3) (10,17) (11,10) (15,11) (17,6) (9,10) (0,16) (9,7) (12,7) (12,18) (1,2) (0,10) (11,2) (9,2) (3,2) (8,13) (16,2) (15,9) (13,2) (17,0) (7,1) (16,18) (6,10) (15,16) (7,5) (13,1) (13,14) (1,14) (1,16) (17,13) (1,18) (1,5) (4,7) (5,0) (16,10) (6,8) (12,11) (6,4) (6,16) (11,17) (9,4) (10,5) (14,12) (14,9) (1,10) (14,15) (2,7) (0,9) (16,13) (8,15) (13,11) (12,15) (10,14) (15,10) (12,13) (12,4) (5,17) (6,1) (0,14) (8,10) (3,16) (9,6) (9,11) (1,15) (7,14) (3,7) (0,7) (3,15) (14,5) (17,15) (7,6) (2,5) (3,18) (18,6) (18,2) (11,0) (17,1) (12,10) (5,9) (2,4) (4,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->2->1->11->4->5->6->13->18->9->16->15->14->17->10->12->7->3." - } - ] - }, - { - "id": "hamilton-hard-graph296", - "image": "data/hamilton/graph_visual/Base/hard/graph296.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,6) (14,11) (14,5) (3,11) (2,6) (4,12) (14,8) (5,3) (9,8) (2,5) (0,13) (9,3) (12,8) (4,9) (14,6) (2,10) (1,13) (2,3) (10,3) (12,7) (14,1) (1,11) (12,2) (11,0) (7,4) (7,2) (11,9) (2,11) (11,13) (8,10) (10,13) (6,8) (7,10) (10,11) (12,5) (2,4) (5,11) (13,4) (9,2) (2,0) (10,0) (9,6) (7,9) (8,13) (14,2) (2,8) (5,10) (5,1) (8,7) (9,1) (13,9) (12,13) (5,9) (8,1) (1,12) (7,13) (7,3) (4,1) (0,4) (10,1) (6,7) (5,8) (7,5) (3,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->1->6->2->5->14->11->3->9->8->12->4->7->10." - } - ] - }, - { - "id": "hamilton-hard-graph586", - "image": "data/hamilton/graph_visual/Base/hard/graph586.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (19,15) (11,18) (14,0) (2,3) (7,19) (18,3) (19,2) (18,1) (1,6) (5,12) (16,12) (19,5) (14,8) (2,6) (17,15) (12,11) (4,11) (0,8) (1,5) (4,2) (1,7) (16,5) (19,9) (7,9) (12,0) (10,8) (17,8) (9,0) (13,7) (4,15) (4,14) (18,0) (19,8) (18,15) (12,2) (16,15) (3,11) (11,6) (16,18) (11,17) (6,15) (17,18) (1,4) (15,12) (10,11) (18,5) (17,9) (14,15) (3,19) (13,12) (8,12) (8,3) (4,17) (7,14) (10,15) (4,3) (6,3) (18,6) (17,14) (11,15) (9,10) (10,5) (19,1) (10,18) (12,10) (19,14) (2,10) (11,5) (13,18) (7,6) (16,6) (0,5) (13,6) (14,18) (17,19) (3,0) (0,6) (8,5) (13,15) (16,10) (17,7) (2,16) (5,17) (1,14) (4,0) (10,17) (9,16) (7,11) (10,14) (19,13) (5,7) (12,19) (0,15) (0,16) (7,4) (14,5) (0,2) (14,11) (1,2) (12,18) (5,15) (6,8) (16,13) (9,11) (9,2) (16,8) (6,19) (1,17) (11,13) (10,19) (11,16) (16,14) (7,16)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->14->8->10->11->18->3->2->19->15->17->9->7->13->12->5->16->6->1->4." - } - ] - }, - { - "id": "hamilton-hard-graph249", - "image": "data/hamilton/graph_visual/Base/hard/graph249.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,10) (2,5) (12,9) (0,8) (10,0) (12,11) (13,10) (1,12) (14,1) (3,1) (13,1) (4,5) (0,7) (8,6) (6,0) (0,4) (5,7) (12,3) (5,3) (1,0) (9,8) (8,5) (2,4) (0,13) (14,10) (7,3) (9,7) (11,0) (10,8) (12,7) (10,12) (9,4) (7,6) (8,1) (5,14) (5,13) (6,4) (8,11) (2,14) (7,8) (9,3) (11,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->6->7->10->13->1->12->11->9->4->2->14->5->3." - } - ] - }, - { - "id": "hamilton-hard-graph454", - "image": "data/hamilton/graph_visual/Base/hard/graph454.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,0) (4,16) (7,9) (16,7) (1,16) (10,0) (8,14) (5,14) (0,15) (17,9) (17,7) (15,9) (13,1) (17,14) (3,8) (13,8) (5,0) (1,0) (17,0) (5,4) (17,10) (7,5) (16,9) (14,3) (9,3) (0,14) (13,7) (4,3) (13,5) (11,14) (17,3) (12,15) (7,3) (16,5) (10,11) (2,9) (6,8) (6,15) (11,4) (15,13) (15,7) (5,15) (9,4) (16,12) (13,16) (6,16) (2,13) (16,10) (6,13) (0,12) (15,16) (6,4) (0,2) (10,3) (4,8) (0,11) (15,14) (16,0) (1,6) (10,1) (5,6) (16,17) (13,17) (17,11) (17,5) (12,4) (14,9) (12,10) (17,4) (11,13) (1,7) (11,6) (9,12) (12,14) (13,4) (11,3) (1,11) (12,6) (5,3) (4,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->8->14->5->4->16->7->9->17->3->11->1->10->12->15->13->2." - } - ] - }, - { - "id": "hamilton-hard-graph124", - "image": "data/hamilton/graph_visual/Base/hard/graph124.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (12,10) (8,7) (11,0) (6,3) (7,9) (8,12) (7,2) (4,0) (12,1) (9,11) (1,0) (5,1) (5,10) (7,11) (9,10) (8,9) (0,5) (4,9) (1,10) (6,12) (9,12) (5,2) (10,11) (2,4) (8,3) (6,2) (12,7) (6,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->9->7->8->3->6->12->10->1->5->2->4." - } - ] - }, - { - "id": "hamilton-hard-graph135", - "image": "data/hamilton/graph_visual/Base/hard/graph135.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,3) (11,2) (6,1) (11,9) (0,6) (7,9) (1,10) (0,2) (5,6) (6,2) (3,11) (1,8) (12,8) (2,9) (2,5) (8,2) (10,12) (4,0) (3,0) (11,6) (12,2) (12,1) (7,1) (2,4) (9,6) (0,5) (6,4) (8,4) (7,5) (11,10) (10,9) (6,3) (9,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->1->10->12->8->4->2->9->11->3->7->5." - } - ] - }, - { - "id": "hamilton-hard-graph469", - "image": "data/hamilton/graph_visual/Base/hard/graph469.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,0) (15,9) (3,16) (9,6) (4,5) (17,6) (13,11) (13,7) (3,7) (7,1) (14,5) (7,5) (4,17) (12,10) (10,7) (14,9) (10,3) (4,10) (4,3) (16,7) (5,15) (2,1) (0,15) (3,1) (9,16) (0,17) (2,8) (15,10) (11,15) (10,13) (17,12) (17,2) (14,3) (14,16) (6,4) (5,9) (17,5) (15,4) (1,12) (4,1) (13,3) (6,10) (2,7) (5,6) (12,0) (8,0) (14,1) (7,11) (10,14) (7,4) (2,5) (14,4) (17,10) (7,14) (1,11) (1,13) (13,17) (12,6) (13,6) (4,12) (8,15) (2,0) (17,7) (17,11) (2,12) (3,12) (12,16) (3,11) (15,2) (1,8) (12,5) (17,15) (16,5) (11,6) (9,12) (16,8) (10,8) (9,8) (12,13) (2,9) (2,4) (11,0) (16,10) (3,5) (3,9) (0,7) (16,11) (3,8) (17,14) (15,3) (11,12) (0,5) (2,14) (10,2) (4,0) (0,16)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->7->13->11->15->9->6->17->4->5->14->3->16->12->10->8->2." - } - ] - }, - { - "id": "hamilton-hard-graph384", - "image": "data/hamilton/graph_visual/Base/hard/graph384.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,4) (11,0) (3,1) (2,0) (0,1) (9,8) (14,3) (12,9) (2,6) (2,3) (13,14) (16,0) (16,1) (10,4) (0,8) (7,8) (2,11) (9,16) (16,11) (14,0) (4,9) (4,2) (9,7) (13,2) (11,5) (6,0) (16,6) (8,4) (3,6) (5,6) (15,11) (11,13) (3,7) (14,1) (16,14) (8,6) (13,8) (0,12) (0,13) (14,8) (15,7) (5,9) (3,5) (5,0) (1,8) (9,3) (16,7) (0,3) (15,9) (13,12) (15,16) (5,4) (10,0) (12,1) (10,14) (7,0) (3,12) (1,5) (15,0) (5,12) (14,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->4->10->14->3->1->16->9->12->5->6->2->13->8->7->15." - } - ] - }, - { - "id": "hamilton-hard-graph262", - "image": "data/hamilton/graph_visual/Base/hard/graph262.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,13) (4,11) (13,7) (9,7) (8,6) (11,0) (9,14) (14,0) (11,8) (7,5) (6,9) (9,8) (4,5) (9,10) (3,13) (10,1) (4,9) (7,1) (12,14) (5,6) (5,2) (3,8) (1,14) (4,6) (12,1) (10,3) (2,6) (14,6) (0,3) (14,7) (7,6) (12,9) (3,2) (10,14) (7,8) (8,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->4->5->7->13->2->6->8->9->14->12->1->10->3." - } - ] - }, - { - "id": "hamilton-hard-graph11", - "image": "data/hamilton/graph_visual/Base/hard/graph11.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,4) (9,5) (10,1) (8,5) (7,8) (5,3) (1,9) (1,2) (10,7) (6,7) (5,4) (7,0) (9,4) (1,8) (0,6) (3,8) (5,7) (6,5) (4,6) (1,0) (6,2) (8,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->9->5->3->8->7->10->1->2->6." - } - ] - }, - { - "id": "hamilton-hard-graph7", - "image": "data/hamilton/graph_visual/Base/hard/graph7.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,7) (4,8) (8,2) (10,7) (8,9) (7,3) (2,3) (9,7) (8,5) (1,4) (3,6) (1,5) (0,10) (10,8) (10,9) (6,8) (2,5) (0,3) (1,3) (1,8) (5,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->7->9->8->4->1->5->2->3->6." - } - ] - }, - { - "id": "hamilton-hard-graph348", - "image": "data/hamilton/graph_visual/Base/hard/graph348.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,2) (2,4) (9,15) (9,2) (14,5) (2,12) (11,3) (4,1) (3,0) (11,8) (7,10) (15,2) (6,7) (13,2) (9,14) (10,1) (13,0) (12,4) (4,9) (11,2) (12,6) (13,9) (13,11) (0,8) (10,14) (6,5) (3,4) (3,14) (2,7) (4,11) (8,5) (2,0) (5,15) (3,9) (8,4) (14,13) (8,3) (1,12) (5,11) (11,12) (1,8) (6,10) (7,3) (10,11) (0,5) (6,8) (13,4) (4,6) (0,11) (5,13) (8,9) (7,12) (6,9) (14,4) (1,11) (15,10) (14,8) (5,12) (4,10) (9,12) (12,14) (3,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->2->4->1->10->7->6->12->11->8->5->14->13->9->15." - } - ] - }, - { - "id": "hamilton-hard-graph565", - "image": "data/hamilton/graph_visual/Base/hard/graph565.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,5) (7,11) (17,15) (5,10) (6,16) (14,0) (4,12) (7,0) (2,11) (4,2) (19,5) (13,14) (19,4) (17,8) (8,13) (13,3) (1,13) (2,10) (10,3) (16,0) (1,8) (19,13) (19,15) (0,6) (19,10) (2,18) (7,6) (9,8) (16,17) (8,11) (2,12) (5,17) (7,16) (16,5) (3,0) (4,16) (7,10) (10,0) (2,19) (16,15) (16,1) (1,18) (0,15) (10,11) (12,9) (15,6) (16,12) (15,12) (2,5) (2,8) (7,19) (1,5) (11,14) (7,1) (8,5) (0,5) (1,12) (6,4) (2,16) (8,15) (0,17) (5,13) (13,6) (9,11) (10,4) (1,19) (12,19) (14,2) (10,6) (7,4) (14,16) (18,14) (4,11) (7,14) (13,16) (8,3) (16,8) (13,17) (19,14) (0,13) (11,5) (3,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->14->13->8->17->15->19->5->9->12->4->2->11->3->10->7->6->16->1->18." - } - ] - }, - { - "id": "hamilton-hard-graph337", - "image": "data/hamilton/graph_visual/Base/hard/graph337.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (13,14) (7,6) (15,1) (2,1) (11,9) (13,1) (2,8) (12,8) (13,15) (15,4) (2,9) (14,8) (15,14) (11,6) (5,12) (5,11) (1,9) (8,9) (10,13) (0,15) (8,13) (1,3) (2,11) (3,10) (14,6) (2,15) (11,0) (9,0) (12,2) (15,11) (1,12) (6,10) (0,4) (2,7) (10,12) (0,10) (13,0) (2,6) (7,3) (5,14) (6,3) (14,11) (11,7) (4,6) (8,4) (8,10) (2,5) (8,11) (13,7) (13,6) (4,5) (0,2) (6,0) (1,6) (1,7) (9,7) (15,8) (7,5) (5,3) (3,12) (7,15) (7,4) (7,8) (5,0) (1,5) (10,2) (11,3) (12,15) (5,10) (1,0) (8,0) (5,8) (6,15) (9,3) (1,8) (10,7) (13,2) (9,12) (6,5) (11,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->15->1->2->8->12->5->11->9->7->3->10->13->14->6->4." - } - ] - }, - { - "id": "hamilton-hard-graph451", - "image": "data/hamilton/graph_visual/Base/hard/graph451.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,1) (1,2) (7,11) (17,6) (12,13) (9,4) (1,13) (10,2) (3,13) (15,9) (0,8) (11,16) (9,11) (0,6) (5,6) (14,5) (17,13) (1,15) (8,1) (3,7) (8,9) (5,11) (16,10) (6,2) (0,12) (14,1) (8,6) (8,17) (11,14) (7,12) (2,13) (9,0) (10,3) (9,13) (8,12) (9,16) (4,11) (3,6) (14,2) (11,0) (16,17) (7,5) (3,0) (4,5) (10,1) (15,11) (5,16) (5,10) (15,14) (5,13) (6,16) (8,14) (14,6) (11,2) (17,15) (13,4) (4,3) (11,3) (14,3) (17,1) (14,9) (7,17) (12,15) (10,9) (16,1) (7,16) (10,14) (6,13) (4,8) (17,10) (5,12) (0,15) (13,10) (7,10) (14,17) (13,0) (15,13) (12,9) (11,8) (12,2) (7,14) (2,15) (8,16) (15,8) (1,12) (7,8) (5,17) (0,7) (6,10) (13,16)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->1->6->17->13->12->7->11->16->10->2->15->9->4->5->14->3." - } - ] - }, - { - "id": "hamilton-hard-graph573", - "image": "data/hamilton/graph_visual/Base/hard/graph573.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,14) (4,16) (2,13) (6,7) (13,15) (14,8) (6,1) (12,1) (8,12) (14,12) (15,1) (5,18) (16,12) (15,8) (7,8) (12,18) (11,2) (16,5) (1,10) (14,15) (17,18) (7,11) (7,14) (3,19) (16,18) (19,13) (9,4) (11,0) (0,9) (13,14) (19,9) (0,4) (6,18) (11,13) (18,3) (7,0) (17,13) (12,6) (18,10) (17,8) (6,0) (16,7) (16,10) (14,9) (3,10) (11,4) (3,5) (9,10) (10,15) (8,1) (13,1) (12,9) (3,4) (15,2) (10,6) (2,5) (8,2) (5,15) (11,8) (2,18) (18,7) (1,16) (5,4) (4,12) (18,1) (13,0) (1,11) (7,10) (7,4) (16,9) (13,8) (16,6) (19,17) (4,19) (8,6) (17,16) (7,12) (9,6) (14,16) (3,9) (19,1) (10,14) (13,10) (8,10) (1,17) (13,18) (4,14) (12,5) (3,17) (16,3) (6,5) (14,19) (19,2) (5,0) (6,19) (18,4) (1,9) (9,5) (6,11) (12,10) (17,4) (0,1) (19,15) (15,16) (18,0) (2,9) (0,10) (13,9) (3,0) (17,14) (15,6) (4,2) (1,5) (3,2) (8,0) (11,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->2->13->15->1->14->8->12->16->4->9->19->3->10->7->6->5->18->17." - } - ] - }, - { - "id": "hamilton-hard-graph328", - "image": "data/hamilton/graph_visual/Base/hard/graph328.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (8,5) (13,6) (14,12) (1,8) (0,1) (9,14) (13,14) (15,6) (15,2) (6,5) (15,0) (1,13) (3,1) (0,2) (11,4) (13,7) (14,2) (13,2) (12,15) (13,15) (3,11) (4,10) (15,9) (7,4) (9,5) (11,8) (15,7) (2,11) (11,6) (8,7) (1,7) (15,10) (7,12) (10,3) (5,4) (10,12) (15,4) (0,13) (13,12) (5,7) (11,15) (12,9) (6,4) (14,15) (14,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->8->5->6->13->14->12->7->4->10->3->11->2->15->9." - } - ] - }, - { - "id": "hamilton-hard-graph556", - "image": "data/hamilton/graph_visual/Base/hard/graph556.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,4) (9,12) (11,12) (19,17) (15,9) (11,14) (5,13) (3,10) (15,2) (9,13) (9,2) (1,18) (8,19) (5,19) (13,17) (18,15) (14,9) (18,8) (4,0) (14,3) (8,6) (2,12) (15,4) (19,4) (19,9) (2,19) (13,2) (6,15) (5,16) (1,4) (5,12) (14,18) (11,2) (3,13) (18,9) (19,6) (9,4) (1,3) (7,10) (8,14) (19,3) (10,4) (7,16) (2,16) (1,16) (17,2) (7,5) (8,1) (9,8) (7,2) (17,5) (11,6) (18,2) (19,18) (7,3) (7,18) (13,12) (10,19) (0,9) (0,3) (4,14) (17,6) (11,8) (11,1) (15,11) (11,18) (6,18) (19,12) (11,4) (11,17) (0,8) (13,4) (1,10) (13,1) (13,16) (0,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->5->13->9->12->11->14->3->10->7->16->2->15->18->1->8->19->17->6." - } - ] - }, - { - "id": "hamilton-hard-graph63", - "image": "data/hamilton/graph_visual/Base/hard/graph63.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,6) (0,9) (3,11) (4,6) (2,7) (8,6) (7,0) (4,2) (2,5) (8,2) (9,6) (3,2) (10,11) (3,1) (7,10) (1,5) (5,0) (0,1) (2,0) (2,11) (4,3) (5,6) (5,4) (4,11) (0,6) (6,7) (10,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->6->3->1->5->4->11->10->7->2->8." - } - ] - }, - { - "id": "hamilton-hard-graph427", - "image": "data/hamilton/graph_visual/Base/hard/graph427.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,6) (3,2) (10,0) (13,14) (6,7) (5,9) (13,4) (5,6) (11,0) (1,9) (11,16) (14,3) (10,11) (6,11) (13,9) (12,11) (8,13) (3,7) (2,1) (0,1) (16,10) (5,0) (9,14) (13,16) (5,10) (7,4) (9,11) (0,15) (14,10) (2,14) (16,9) (14,15) (9,4) (12,17) (12,7) (14,12) (2,4) (3,5) (9,17) (16,15) (2,12) (6,3) (10,3) (16,17) (2,9) (7,9) (8,5) (1,10) (8,7) (1,5) (10,7) (8,9) (7,15) (16,1) (8,2) (0,12) (6,14) (16,12) (14,17) (0,2) (10,15) (6,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->11->16->13->14->3->6->12->17->9->1->5->8->2->4->7->15." - } - ] - }, - { - "id": "hamilton-hard-graph503", - "image": "data/hamilton/graph_visual/Base/hard/graph503.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (15,2) (2,12) (5,1) (9,13) (11,15) (17,18) (2,8) (3,5) (15,8) (5,15) (1,9) (11,7) (16,3) (17,14) (9,17) (7,17) (5,7) (15,17) (0,18) (6,1) (7,2) (16,10) (4,8) (6,17) (18,14) (1,7) (7,16) (17,11) (10,18) (14,11) (14,3) (9,12) (12,8) (7,3) (16,18) (5,8) (18,1) (11,13) (9,5) (4,11) (8,1) (2,13) (6,18) (15,16) (17,2) (14,10) (4,2) (12,1) (6,0) (6,7) (6,12) (5,11) (14,8) (3,9) (11,12) (16,6) (6,14) (2,5) (0,16) (18,15) (3,1) (15,4) (3,10) (5,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->18->17->14->11->15->2->13->9->1->5->3->10->16->7->6->12->8->4." - } - ] - }, - { - "id": "hamilton-hard-graph490", - "image": "data/hamilton/graph_visual/Base/hard/graph490.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,16) (13,17) (5,10) (12,8) (17,15) (17,18) (15,1) (6,2) (13,18) (3,16) (14,9) (14,4) (3,4) (15,0) (5,12) (4,7) (4,18) (12,11) (12,0) (3,10) (8,6) (2,18) (7,16) (14,7) (11,10) (7,18) (12,9) (7,15) (3,12) (3,17) (1,5) (6,3) (14,10) (3,5) (10,15) (3,8) (4,2) (14,16) (8,15) (15,18) (6,10) (18,14) (6,13) (5,4) (5,2) (8,2) (2,16) (4,17) (17,6) (0,4) (15,12) (8,1) (11,15) (8,17) (17,10) (14,17) (14,1) (18,8) (5,13) (5,11) (11,18) (17,5) (0,3) (18,12) (11,16) (12,16) (8,4) (10,1) (1,11) (9,0) (2,17) (1,18) (13,3) (7,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->15->17->16->3->4->14->9->12->8->2->6->10->11->1->5->13->18->7." - } - ] - }, - { - "id": "hamilton-hard-graph107", - "image": "data/hamilton/graph_visual/Base/hard/graph107.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,0) (9,8) (2,0) (8,1) (2,7) (0,5) (3,9) (9,4) (6,9) (8,3) (6,10) (7,8) (0,1) (11,0) (3,6) (4,6) (9,1) (7,1) (6,1) (3,0) (4,2) (2,9) (10,5) (1,10) (9,0) (5,2) (11,2) (11,10) (7,4) (1,2) (0,6) (7,9) (10,3) (6,8) (4,5) (2,6) (9,10) (11,5) (8,5) (1,4) (5,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->9->8->1->7->2->5->11->10->6->3." - } - ] - }, - { - "id": "hamilton-hard-graph216", - "image": "data/hamilton/graph_visual/Base/hard/graph216.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (8,7) (8,3) (0,9) (9,1) (2,3) (3,1) (3,13) (1,6) (13,11) (6,3) (12,6) (11,9) (9,6) (6,5) (7,11) (10,5) (10,0) (1,4) (7,13) (0,5) (1,13) (9,3) (4,6) (8,4) (11,0) (2,1) (12,13) (12,0) (11,1) (5,4) (13,2) (7,2) (5,11) (3,7) (2,8) (7,1) (9,2) (2,6) (7,5) (13,5) (10,13) (4,13) (8,0) (7,6) (8,13) (3,5) (1,0) (12,11) (5,8) (10,12) (10,7) (2,5) (3,12) (10,6) (12,1) (9,10) (2,11) (12,8) (0,3) (11,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->1->3->8->7->11->13->12->10->5->4->6->2." - } - ] - }, - { - "id": "hamilton-hard-graph547", - "image": "data/hamilton/graph_visual/Base/hard/graph547.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,1) (8,13) (6,5) (7,12) (13,19) (9,11) (3,2) (6,19) (3,4) (16,6) (11,3) (12,3) (6,2) (15,3) (13,16) (10,17) (13,17) (17,15) (14,12) (3,13) (5,15) (14,19) (18,15) (7,1) (6,0) (4,2) (5,12) (13,14) (1,17) (17,12) (5,16) (12,4) (18,4) (14,3) (15,11) (0,4) (17,6) (12,2) (15,16) (5,18) (5,4) (5,3) (19,5) (6,13) (14,10) (1,14) (8,9) (2,16) (17,19) (7,6) (6,4) (1,11) (2,19) (14,0) (9,7) (9,3) (8,1) (1,4) (16,12) (2,5) (15,9) (3,16) (19,3) (18,14) (11,6) (3,0) (3,8) (7,4) (11,12) (19,8) (4,14) (17,3) (0,19) (9,0) (17,14) (16,0) (15,14) (5,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->5->15->1->7->12->3->4->18->14->10->17->13->16->2->19->8->9->11." - } - ] - }, - { - "id": "hamilton-hard-graph431", - "image": "data/hamilton/graph_visual/Base/hard/graph431.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (11,2) (17,8) (12,8) (3,15) (2,13) (11,15) (1,13) (9,12) (2,5) (15,6) (4,8) (16,13) (14,17) (15,17) (6,16) (1,15) (8,13) (5,14) (14,12) (16,15) (5,17) (14,2) (3,6) (14,16) (13,12) (1,3) (6,2) (7,12) (1,2) (10,12) (3,5) (3,10) (4,1) (9,8) (8,14) (8,5) (9,15) (17,16) (3,11) (17,2) (0,17) (17,4) (10,14) (8,1) (5,11) (17,1) (1,9) (2,3) (4,7) (13,9) (10,13) (11,13) (16,3) (7,6) (17,10) (12,3) (1,12) (3,7) (2,15) (9,11) (3,4) (5,13) (2,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->17->8->12->9->15->3->6->16->13->10->14->5->11->2->1->4->7." - } - ] - }, - { - "id": "hamilton-hard-graph177", - "image": "data/hamilton/graph_visual/Base/hard/graph177.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,8) (1,4) (5,12) (6,1) (7,5) (12,0) (6,3) (1,12) (4,12) (10,11) (6,7) (7,9) (7,0) (5,8) (3,0) (9,10) (6,11) (5,10) (0,11) (9,8) (7,11) (6,0) (9,1) (12,6) (2,11) (8,10) (5,4) (9,5) (4,3) (10,7) (7,8) (2,0) (9,0) (9,4) (10,2) (11,12) (7,3) (5,11) (0,1) (4,2) (1,2) (0,4) (6,4) (8,12) (8,0) (12,3) (8,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->5->7->6->8->9->10->11->2->1->4->3." - } - ] - }, - { - "id": "hamilton-hard-graph43", - "image": "data/hamilton/graph_visual/Base/hard/graph43.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,8) (10,1) (10,0) (3,7) (1,3) (10,7) (0,9) (6,7) (9,7) (6,4) (2,1) (6,8) (10,6) (10,2) (8,3) (10,3) (8,5) (3,9) (7,4) (8,1) (3,5) (1,7) (1,0) (9,2) (3,4) (10,4) (2,8) (10,9) (2,4) (6,2) (0,7) (10,5) (5,7) (2,0) (3,2) (10,8) (6,5) (5,2) (5,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->6->7->3->1->10->4->5->2->9." - } - ] - }, - { - "id": "hamilton-hard-graph414", - "image": "data/hamilton/graph_visual/Base/hard/graph414.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,11) (2,9) (13,8) (3,12) (4,1) (5,15) (9,10) (13,3) (14,11) (9,6) (9,4) (2,12) (14,8) (6,15) (16,0) (3,0) (5,2) (5,13) (10,6) (8,10) (13,14) (11,12) (15,2) (7,5) (13,1) (4,7) (12,6) (3,9) (8,11) (4,15) (11,7) (5,9) (14,9) (8,4) (10,14) (3,16) (4,11) (0,10) (15,3) (14,5) (5,3) (4,5) (0,8) (12,0) (10,13) (15,8) (6,13) (14,7) (7,0) (8,2) (3,14) (11,16) (16,15) (7,13) (2,16) (3,10) (11,6) (5,16) (11,2) (10,12) (10,15) (14,12) (2,10) (4,12) (16,8) (7,6) (7,16) (1,5) (10,7) (14,6) (14,1) (13,12) (14,0) (14,15)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->16->3->12->2->9->10->6->15->5->11->14->8->13->1->4->7." - } - ] - }, - { - "id": "hamilton-hard-graph251", - "image": "data/hamilton/graph_visual/Base/hard/graph251.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,1) (8,4) (2,14) (6,10) (2,12) (14,8) (3,12) (3,0) (3,5) (3,7) (6,4) (11,14) (5,14) (2,1) (3,1) (0,5) (3,9) (7,2) (1,6) (6,12) (12,4) (6,13) (7,1) (0,14) (2,6) (10,2) (1,0) (13,4) (10,14) (0,7) (10,5) (13,3) (11,13) (9,13) (13,12) (9,11) (10,7) (7,13) (3,10) (3,8) (10,9) (4,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->12->2->14->8->4->6->1->9->11->13->7->10->5." - } - ] - }, - { - "id": "hamilton-hard-graph294", - "image": "data/hamilton/graph_visual/Base/hard/graph294.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (5,14) (5,2) (13,2) (1,10) (7,13) (9,6) (6,10) (1,7) (1,13) (9,12) (12,13) (13,5) (8,11) (10,12) (8,14) (12,5) (4,1) (0,4) (2,14) (12,4) (12,14) (9,13) (6,14) (4,9) (9,1) (10,8) (10,13) (8,1) (14,11) (14,1) (0,2) (8,13) (7,8) (0,9) (5,10) (6,5) (10,9) (7,10) (11,9) (6,2) (2,4) (6,4) (0,6) (13,0) (11,2) (6,3) (8,6) (0,5) (3,4) (14,7) (2,9) (7,12) (11,6) (9,8) (0,1) (2,12) (2,1) (11,7) (0,12) (11,4) (10,4) (9,3) (11,12) (8,3) (14,10) (8,4) (3,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->1->10->6->9->12->13->2->5->14->11->7->8->3." - } - ] - }, - { - "id": "hamilton-hard-graph243", - "image": "data/hamilton/graph_visual/Base/hard/graph243.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,8) (3,0) (11,12) (10,2) (5,4) (7,4) (1,10) (14,10) (7,6) (8,14) (5,6) (5,12) (11,5) (1,14) (0,7) (14,4) (2,13) (14,12) (10,5) (6,2) (4,0) (2,4) (14,11) (11,13) (6,13) (9,14) (13,0) (1,9) (13,8) (8,10) (7,13) (7,11) (5,3) (13,1) (5,13) (11,3) (0,2) (14,0) (12,3) (13,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->5->4->7->6->2->10->1->14->8->9->13->11->12." - } - ] - }, - { - "id": "hamilton-hard-graph108", - "image": "data/hamilton/graph_visual/Base/hard/graph108.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,4) (9,0) (9,1) (4,3) (0,10) (3,10) (6,0) (7,0) (5,1) (5,10) (7,1) (6,9) (0,2) (11,0) (3,0) (9,7) (1,11) (2,3) (5,8) (8,11) (10,9) (2,1) (6,7) (5,11) (4,7) (11,3) (5,2) (6,8) (5,3) (1,6) (4,6) (11,6) (0,1) (11,9) (1,3) (10,11) (4,10) (1,8) (2,6) (8,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->1->5->4->7->6->8->11->10->3->2." - } - ] - }, - { - "id": "hamilton-hard-graph551", - "image": "data/hamilton/graph_visual/Base/hard/graph551.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (13,3) (9,1) (5,14) (5,2) (3,2) (15,12) (8,10) (3,18) (16,6) (10,1) (16,9) (5,15) (8,15) (10,16) (15,4) (1,8) (9,11) (4,8) (14,11) (12,11) (9,15) (19,1) (11,5) (6,17) (2,4) (11,15) (8,6) (18,11) (13,0) (15,7) (14,3) (8,2) (12,19) (19,11) (0,17) (13,2) (0,5) (6,18) (11,3) (8,17) (17,16) (11,10) (5,7) (19,0) (18,14) (14,1) (8,5) (11,17) (2,17) (13,15) (14,4) (13,1) (17,7) (12,3) (9,0) (3,16) (11,4) (3,1) (7,16) (9,5) (2,18) (16,2) (11,7) (0,15) (18,0) (2,7) (10,12) (6,4) (7,0) (5,18) (10,7) (9,14) (14,16) (7,14) (8,11) (7,6) (14,6) (8,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->3->2->5->14->11->9->1->19->12->15->4->8->10->16->17->7->6->18." - } - ] - }, - { - "id": "hamilton-hard-graph116", - "image": "data/hamilton/graph_visual/Base/hard/graph116.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,2) (0,7) (3,4) (6,8) (3,7) (8,9) (7,9) (5,4) (7,1) (2,4) (8,10) (9,1) (2,0) (10,3) (6,4) (4,11) (11,9) (2,10) (0,4) (1,6) (8,4) (2,3) (0,5) (3,6) (1,10) (10,5) (3,11) (5,8) (6,10) (4,10) (1,2) (7,11) (3,0) (4,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->2->4->3->10->5->8->6->1->9->11." - } - ] - }, - { - "id": "hamilton-hard-graph352", - "image": "data/hamilton/graph_visual/Base/hard/graph352.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,4) (5,10) (9,5) (2,9) (12,11) (12,4) (11,3) (13,7) (4,13) (11,10) (7,11) (3,8) (10,0) (7,9) (12,10) (3,9) (13,2) (15,14) (4,3) (6,0) (6,1) (15,0) (12,7) (11,5) (3,1) (2,14) (15,8) (0,3) (8,4) (11,8) (0,5) (8,2) (7,10) (12,15) (4,5) (11,9) (14,5) (3,6) (11,1) (5,3) (11,4) (12,1) (2,12) (15,2) (4,14) (0,13) (14,10) (10,15) (4,15) (15,6) (4,10) (4,2) (0,11) (6,14) (10,13) (15,9) (4,7) (8,7) (8,6) (5,12) (0,8) (2,3) (2,7) (0,12) (1,10) (13,9) (2,11) (11,14) (7,0) (3,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->5->9->4->12->11->3->8->7->13->2->14->15->6->1." - } - ] - }, - { - "id": "hamilton-hard-graph498", - "image": "data/hamilton/graph_visual/Base/hard/graph498.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,14) (16,3) (8,0) (18,15) (13,3) (1,11) (12,4) (15,2) (10,5) (17,8) (11,6) (7,11) (14,0) (2,8) (4,5) (13,5) (13,14) (12,7) (11,13) (12,17) (8,1) (2,0) (12,8) (6,10) (3,11) (4,14) (6,9) (11,10) (13,6) (17,1) (7,2) (14,5) (18,9) (18,17) (0,4) (16,7) (4,10) (4,2) (2,13) (12,5) (15,5) (4,7) (15,1) (6,16) (9,13) (6,14) (10,9) (4,9) (9,11) (2,11) (18,5) (8,9) (8,11) (18,4) (2,12) (6,2) (7,10) (17,5) (4,16) (7,9) (6,4) (14,10) (8,4) (0,9) (14,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->17->12->4->5->10->6->11->1->14->13->3->16->7->2->15->18->9." - } - ] - }, - { - "id": "hamilton-hard-graph65", - "image": "data/hamilton/graph_visual/Base/hard/graph65.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (1,3) (10,3) (6,9) (9,4) (1,9) (1,2) (10,6) (10,5) (11,0) (11,10) (8,7) (3,6) (5,6) (6,0) (1,10) (1,7) (8,9) (3,11) (5,0) (5,11) (11,2) (0,4) (9,5) (11,4) (7,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->3->10->5->11->2->1->7->8->9->4." - } - ] - }, - { - "id": "hamilton-hard-graph223", - "image": "data/hamilton/graph_visual/Base/hard/graph223.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,1) (2,12) (8,12) (0,8) (0,4) (8,10) (4,8) (12,10) (6,10) (9,2) (7,6) (3,6) (13,11) (9,4) (5,11) (5,8) (7,11) (11,12) (5,10) (8,11) (4,3) (13,4) (7,8) (11,3) (2,1) (1,11) (7,1) (12,6) (9,13) (9,1) (5,9) (6,9) (0,3) (1,10) (0,5) (10,0) (7,5) (4,5) (2,7) (3,7) (5,2) (10,3) (0,13) (13,6) (10,7) (11,10) (5,6) (6,1) (11,0) (11,6) (9,7) (8,2) (5,13) (12,4) (8,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->12->2->9->4->1->11->13->6->10->5->7->3." - } - ] - }, - { - "id": "hamilton-hard-graph57", - "image": "data/hamilton/graph_visual/Base/hard/graph57.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,6) (2,9) (2,4) (10,0) (5,9) (3,5) (4,6) (9,8) (0,6) (8,5) (10,8) (0,5) (7,2) (10,2) (10,1) (6,3) (4,3) (3,0) (0,2) (8,0) (10,7) (1,6) (8,7) (5,1) (9,0) (9,10) (7,0) (9,3) (9,6) (1,8) (5,7) (1,4) (6,10) (1,7) (6,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->8->9->2->4->6->7->1->5->3." - } - ] - }, - { - "id": "hamilton-hard-graph315", - "image": "data/hamilton/graph_visual/Base/hard/graph315.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,14) (12,2) (1,0) (11,15) (9,14) (13,2) (6,1) (2,8) (2,10) (11,2) (3,7) (5,0) (1,10) (4,9) (9,11) (0,2) (5,2) (0,7) (4,10) (14,2) (6,10) (14,8) (4,12) (10,0) (5,15) (15,7) (6,13) (3,5) (13,4) (13,15) (15,14) (3,10) (1,11) (7,6) (15,2) (4,7) (4,5) (9,0) (3,14) (6,12) (0,3) (8,0) (12,9) (7,10) (12,3) (7,11) (0,14) (2,4) (14,11) (10,5) (9,6) (6,3) (12,15) (4,1) (14,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->6->10->2->12->4->13->15->5->3->7->11->9->14->8." - } - ] - }, - { - "id": "hamilton-hard-graph423", - "image": "data/hamilton/graph_visual/Base/hard/graph423.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,8) (15,2) (17,1) (9,12) (16,7) (11,6) (17,10) (12,0) (0,5) (7,13) (13,6) (11,17) (3,16) (17,16) (11,3) (15,17) (4,2) (0,13) (14,5) (17,3) (3,12) (13,8) (6,9) (13,15) (7,2) (1,0) (8,17) (8,5) (13,1) (16,4) (1,6) (8,10) (9,1) (2,11) (17,0) (6,15) (10,0) (6,12) (6,14) (1,16) (5,13) (10,14) (5,4) (12,10) (7,14) (2,5) (13,11) (2,9) (13,3) (4,3) (15,10) (2,6) (17,12) (1,7) (10,6) (5,17) (8,7) (15,5) (11,5) (10,2) (9,17) (12,4) (15,3) (0,14) (1,15) (16,8) (13,10) (5,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->9->8->13->7->16->3->11->6->1->17->10->14->5->4->2->15." - } - ] - }, - { - "id": "hamilton-hard-graph321", - "image": "data/hamilton/graph_visual/Base/hard/graph321.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (5,4) (2,11) (5,12) (1,5) (15,7) (9,0) (7,1) (8,11) (1,13) (3,6) (7,9) (4,8) (14,7) (1,2) (6,12) (4,12) (0,7) (15,13) (12,13) (3,11) (12,8) (0,13) (8,13) (5,14) (2,4) (14,1) (2,5) (4,0) (8,6) (9,15) (10,5) (15,6) (0,15) (13,10) (10,3) (13,3) (8,3) (15,11) (12,11) (7,2) (2,9) (12,9) (6,1) (6,10) (15,2) (0,5) (7,11) (3,2) (14,3) (3,1) (3,7) (14,2) (11,9) (13,11) (5,7) (12,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->7->15->13->1->5->4->8->11->2->14->3->10->6->12." - } - ] - }, - { - "id": "hamilton-hard-graph424", - "image": "data/hamilton/graph_visual/Base/hard/graph424.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (12,6) (11,12) (7,6) (16,3) (2,9) (13,9) (16,1) (17,6) (13,11) (11,5) (1,3) (0,7) (16,11) (2,12) (15,2) (7,3) (10,1) (14,2) (6,0) (5,17) (15,10) (2,4) (5,4) (0,9) (17,7) (5,8) (5,0) (11,2) (0,8) (15,7) (0,17) (8,11) (5,1) (7,1) (16,9) (4,16) (0,11) (5,16) (15,5) (3,12) (13,6) (7,9) (5,7) (1,13) (1,12) (5,10) (11,9) (3,17) (10,2) (0,14) (0,12) (0,15) (8,14) (17,2) (10,11) (1,14) (16,7) (14,7) (8,4) (0,10) (15,6) (12,14) (14,15) (4,7) (16,8) (1,11) (9,12) (9,10) (11,15) (6,2) (3,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->6->12->11->13->9->2->15->10->1->16->3->17->5->4->8->14." - } - ] - }, - { - "id": "hamilton-hard-graph230", - "image": "data/hamilton/graph_visual/Base/hard/graph230.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,0) (9,4) (3,5) (6,0) (1,6) (6,5) (5,10) (7,0) (6,12) (12,5) (5,2) (9,6) (3,8) (7,12) (9,13) (0,5) (2,10) (7,6) (1,3) (11,8) (11,5) (11,3) (3,10) (10,4) (2,11) (7,5) (12,2) (6,3) (2,9) (2,0) (12,4) (11,4) (0,8) (7,1) (1,10) (1,9) (8,4) (13,11) (11,0) (8,5) (5,1) (10,11) (6,11) (7,11) (1,2) (2,4) (13,6) (7,8) (2,3) (12,3) (8,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->6->1->3->5->10->2->11->13->9->4->8->7." - } - ] - }, - { - "id": "hamilton-hard-graph391", - "image": "data/hamilton/graph_visual/Base/hard/graph391.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,2) (10,8) (4,7) (5,1) (1,10) (2,14) (9,12) (4,9) (9,16) (3,16) (14,6) (12,3) (10,13) (16,10) (12,6) (2,13) (11,8) (9,8) (14,8) (14,1) (10,4) (16,7) (3,6) (9,13) (15,13) (5,4) (12,7) (4,8) (9,1) (5,7) (6,7) (12,14) (11,13) (2,8) (6,15) (2,4) (0,2) (5,3) (1,15) (10,11) (12,16) (5,6) (0,6) (12,0) (15,8) (16,13) (1,16) (3,11) (0,11) (10,6) (2,9) (16,0) (13,4) (1,11) (10,7) (12,5) (0,9) (12,15) (0,1) (13,7) (6,2) (5,8) (4,11) (13,6) (15,10) (15,5) (10,14) (12,8) (14,7) (1,3) (12,11) (9,15) (0,8) (7,3) (6,16) (9,14) (7,8) (10,2) (8,3) (0,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->16->9->12->3->6->14->8->10->1->5->7->4->11->13->15." - } - ] - }, - { - "id": "hamilton-hard-graph285", - "image": "data/hamilton/graph_visual/Base/hard/graph285.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,4) (10,14) (0,12) (13,12) (5,8) (12,8) (8,0) (10,3) (6,1) (3,13) (8,6) (11,7) (0,11) (1,8) (6,14) (14,5) (13,2) (0,4) (10,11) (9,12) (13,0) (13,10) (11,3) (3,1) (4,1) (2,6) (5,11) (1,14) (13,8) (9,10) (9,8) (1,13) (10,1) (5,1) (7,0) (0,9) (12,2) (2,5) (4,14) (9,4) (8,4) (2,1) (3,6) (14,7) (5,7) (4,3) (7,12) (7,8) (2,8) (11,8) (9,7) (5,4) (7,13) (3,14) (13,5) (7,1) (5,10) (0,6) (13,14) (0,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->4->1->6->8->5->14->10->9->7->11->3->13->2." - } - ] - }, - { - "id": "hamilton-hard-graph579", - "image": "data/hamilton/graph_visual/Base/hard/graph579.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,7) (13,19) (16,18) (5,17) (11,0) (15,4) (9,16) (11,17) (7,16) (0,6) (8,6) (3,1) (11,14) (18,12) (18,6) (5,13) (16,6) (19,9) (12,5) (5,2) (9,11) (14,18) (8,19) (1,4) (7,1) (16,15) (17,19) (13,2) (18,5) (18,10) (7,9) (8,0) (10,12) (17,18) (14,3) (8,15) (17,8) (2,8) (16,14) (2,1) (5,0) (1,16) (11,4) (5,6) (5,9) (8,3) (1,19) (17,13) (11,2) (10,2) (5,15) (15,2) (8,14) (17,10) (8,4) (2,6) (15,9) (7,2) (2,17) (5,8) (3,11) (15,13) (8,12) (3,17) (5,7) (1,18) (3,2) (11,7) (7,8) (14,17) (13,10) (7,18) (5,19) (9,1) (14,5) (5,10) (15,14) (19,4) (6,14) (4,12) (4,3) (1,14) (0,16) (5,16) (0,19) (3,5) (3,9) (10,9) (2,12) (17,16) (18,15) (13,3) (15,11) (4,14) (3,10) (18,3) (18,8) (12,19) (0,15) (10,14) (13,6) (1,17) (15,6) (6,1) (10,16) (13,18) (5,4) (14,0) (17,0) (13,1) (13,4) (8,10) (18,2) (17,7) (14,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->17->5->13->19->9->16->18->12->10->7->1->3->14->8->6->2->15->4." - } - ] - }, - { - "id": "hamilton-hard-graph540", - "image": "data/hamilton/graph_visual/Base/hard/graph540.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (17,5) (12,13) (5,13) (8,13) (5,19) (6,2) (10,18) (9,4) (2,11) (8,16) (0,9) (9,11) (6,8) (10,0) (19,13) (10,17) (5,7) (3,10) (18,9) (0,3) (18,8) (11,10) (1,17) (0,2) (2,15) (9,10) (3,16) (0,1) (3,15) (14,0) (8,2) (7,4) (10,6) (14,9) (16,10) (18,11) (12,4) (18,2) (3,14) (7,13) (7,14) (4,2) (1,12) (3,6) (14,8) (17,2) (11,1) (0,5) (17,18) (6,5) (10,13) (2,10) (2,5) (3,18) (16,6) (13,17) (11,8) (19,1) (9,5) (12,2) (12,16) (5,8) (1,8) (13,2) (11,16) (19,3) (18,19) (14,11) (3,9) (2,1) (6,19) (0,12) (17,14) (0,4) (1,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->4->7->5->17->10->18->8->13->12->1->19->3->15->2->6->16->11->14." - } - ] - }, - { - "id": "hamilton-hard-graph129", - "image": "data/hamilton/graph_visual/Base/hard/graph129.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,11) (6,8) (10,3) (0,1) (11,6) (4,7) (12,1) (2,12) (1,3) (4,2) (10,7) (4,1) (2,5) (12,4) (2,0) (11,5) (3,6) (2,8) (3,5) (2,3) (5,12) (1,6) (2,9) (2,6) (8,4) (3,7) (5,10) (8,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->12->4->7->10->3->5->11->6->8->2->9." - } - ] - }, - { - "id": "hamilton-hard-graph364", - "image": "data/hamilton/graph_visual/Base/hard/graph364.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,9) (8,5) (15,6) (10,15) (8,9) (6,8) (14,6) (6,5) (7,9) (2,3) (4,7) (6,1) (16,11) (2,4) (1,10) (1,4) (9,11) (10,12) (7,11) (5,10) (9,5) (4,9) (7,13) (14,16) (2,10) (10,11) (5,14) (2,5) (2,9) (12,3) (15,13) (7,8) (6,9) (2,1) (4,0) (3,7) (2,6) (16,4) (10,13) (12,16) (0,3) (12,5) (13,12) (12,7) (4,15) (7,6) (8,10) (8,15) (5,11) (8,14) (14,15) (12,11) (16,8) (0,13) (15,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->7->9->10->15->13->12->3->2->5->11->16->14->8->6->1." - } - ] - }, - { - "id": "hamilton-hard-graph339", - "image": "data/hamilton/graph_visual/Base/hard/graph339.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,0) (10,4) (2,13) (10,6) (0,3) (0,13) (10,2) (15,4) (10,1) (9,15) (2,4) (8,1) (8,13) (10,9) (2,5) (6,11) (14,1) (11,8) (4,1) (7,14) (10,15) (8,2) (13,1) (9,4) (4,6) (5,11) (11,13) (6,8) (1,6) (13,15) (1,5) (12,0) (8,14) (10,14) (11,2) (2,3) (6,13) (8,7) (3,8) (2,6) (13,12) (14,9) (3,14) (15,5) (8,4) (13,10) (7,12) (15,1) (5,10) (7,13) (4,3) (15,7) (11,0) (6,5) (7,4) (1,11) (6,0) (3,9) (3,5) (15,12) (2,15) (10,7) (14,15) (12,11) (3,11) (7,2) (11,7) (3,12) (0,8) (7,1) (12,6) (4,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->4->15->9->14->1->8->13->2->5->6->11->3->12->7." - } - ] - }, - { - "id": "hamilton-hard-graph29", - "image": "data/hamilton/graph_visual/Base/hard/graph29.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,6) (1,2) (6,2) (10,6) (1,6) (10,9) (4,8) (9,2) (10,1) (4,5) (1,3) (3,6) (9,0) (1,7) (8,5) (1,4) (5,7) (10,2) (8,2) (3,5) (0,3) (10,4) (7,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->10->6->4->8->2->1->3->5->7." - } - ] - }, - { - "id": "hamilton-hard-graph534", - "image": "data/hamilton/graph_visual/Base/hard/graph534.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,16) (12,13) (12,2) (1,11) (11,4) (11,12) (3,18) (6,5) (3,1) (11,5) (2,6) (12,1) (18,1) (10,8) (0,1) (9,1) (16,8) (15,7) (4,0) (5,1) (13,7) (8,3) (7,12) (12,16) (3,16) (5,3) (10,9) (17,15) (0,12) (7,14) (6,8) (11,9) (13,0) (13,15) (4,3) (8,9) (0,18) (13,16) (4,13) (0,14) (10,18) (5,10) (10,1) (17,1) (2,17) (14,10) (3,10) (5,14) (11,16) (8,7) (17,14) (13,14) (4,5) (8,15) (7,6) (18,14) (9,4) (2,11) (12,18) (0,5) (11,10) (13,3) (10,16) (16,4) (13,6) (15,9) (17,11) (12,14) (5,13) (16,9) (14,1) (15,10) (2,0) (11,15) (3,6) (2,13) (4,18) (8,5) (13,18) (2,4) (8,17) (9,0) (17,10) (15,6) (18,11) (15,3) (18,6) (6,16) (18,2) (15,5) (18,7) (12,9) (13,9) (11,8) (18,17) (0,8) (0,3) (2,16) (11,14) (10,0) (16,18)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->16->8->10->9->11->4->3->18->14->7->15->17->2->12->13->6->5." - } - ] - }, - { - "id": "hamilton-hard-graph110", - "image": "data/hamilton/graph_visual/Base/hard/graph110.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (8,6) (2,1) (10,9) (6,10) (7,5) (0,9) (8,9) (4,6) (3,8) (10,5) (2,6) (0,1) (0,2) (11,5) (10,0) (0,8) (11,1) (9,5) (7,10) (8,10) (3,4) (0,5) (10,3) (11,7) (11,9) (6,9) (10,1) (3,0) (6,0) (11,8) (3,11) (10,4) (2,10) (4,1) (4,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->10->6->8->3->4->2->1->11->5->7." - } - ] - }, - { - "id": "hamilton-hard-graph153", - "image": "data/hamilton/graph_visual/Base/hard/graph153.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,1) (0,7) (1,12) (10,12) (12,3) (0,9) (6,7) (7,8) (5,11) (5,12) (2,8) (3,9) (2,10) (3,5) (9,12) (6,9) (5,2) (10,5) (0,10) (9,10) (3,0) (10,1) (3,7) (5,4) (1,0) (7,10) (8,5) (8,0) (8,9) (4,6) (2,11) (8,3) (4,3) (4,0) (7,9) (2,12) (6,10) (6,2) (6,11) (7,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->6->9->12->1->10->2->8->3->4->5->11." - } - ] - }, - { - "id": "hamilton-hard-graph482", - "image": "data/hamilton/graph_visual/Base/hard/graph482.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (14,3) (5,0) (7,17) (18,16) (15,5) (10,12) (1,17) (5,17) (15,2) (18,11) (4,9) (0,15) (7,11) (4,2) (17,12) (6,9) (12,18) (17,4) (12,15) (17,14) (12,4) (17,10) (6,12) (0,2) (0,14) (4,14) (16,14) (7,8) (12,9) (16,2) (8,3) (15,10) (10,8) (8,18) (9,5) (11,6) (6,14) (14,15) (10,4) (18,3) (4,8) (8,11) (12,2) (6,8) (7,1) (2,13) (10,7) (1,14) (6,7) (5,13) (12,5) (14,12) (15,18) (12,8) (18,14) (12,3) (7,18) (3,11) (10,13) (9,1) (15,8) (3,17) (0,17) (7,3) (3,10) (4,7) (2,10) (16,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->15->2->4->9->6->12->17->7->1->14->3->18->16->11->8->10->13." - } - ] - }, - { - "id": "hamilton-hard-graph576", - "image": "data/hamilton/graph_visual/Base/hard/graph576.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,5) (9,0) (0,17) (16,4) (4,13) (3,19) (15,3) (17,3) (10,1) (1,13) (18,11) (16,1) (1,17) (11,6) (6,4) (19,4) (10,9) (11,0) (11,12) (12,14) (1,19) (1,2) (17,16) (19,11) (4,8) (19,16) (13,14) (18,5) (4,5) (6,12) (7,15) (7,2) (8,18) (3,5) (0,1) (14,16) (8,13) (4,0) (17,12) (10,13) (18,6) (9,16) (15,5) (0,12) (12,10) (15,14) (7,9) (9,17) (11,9) (3,6) (14,0) (13,16) (0,19) (7,12) (9,12) (0,3) (11,13) (3,7) (14,7) (3,4) (15,13) (10,15) (17,10) (7,4) (14,6) (18,1) (3,11) (10,2) (2,12) (6,10) (10,16) (8,15) (14,4) (4,9) (1,11) (14,10) (15,2) (18,9) (5,9) (5,0) (4,11) (4,18) (17,15) (10,8) (0,8) (8,19) (11,15) (16,18) (2,3) (19,2) (11,10) (3,18) (15,9) (14,5) (2,16) (19,12) (18,14) (7,18) (14,3) (12,5) (12,15) (1,5) (7,8) (8,17) (9,6) (14,9) (9,13) (18,17) (13,0) (8,2) (1,3) (3,12) (6,2) (16,6) (5,13) (18,2) (14,2) (6,19) (6,5) (17,2) (2,4) (4,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->10->1->13->4->16->17->3->19->11->5->18->8->15->7->2->12->14->6." - } - ] - }, - { - "id": "hamilton-hard-graph533", - "image": "data/hamilton/graph_visual/Base/hard/graph533.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (2,3) (3,4) (15,13) (4,18) (6,12) (7,8) (11,7) (6,17) (1,15) (15,12) (13,7) (3,16) (16,14) (11,1) (6,5) (3,15) (9,15) (15,0) (18,0) (9,1) (9,10) (3,10) (16,13) (18,17) (5,0) (0,17) (7,3) (14,4) (3,0) (17,16) (15,6) (5,14) (8,17) (9,17) (10,1) (1,6) (10,12) (13,4) (13,18) (10,4) (15,18) (5,12) (14,9) (14,7) (11,13) (7,17) (15,11) (18,12) (3,12) (9,3) (3,1) (4,6) (6,10) (11,4) (0,1) (11,14) (9,12) (8,0) (2,5) (4,16) (16,10) (15,8) (13,14) (0,16) (12,17) (10,5) (17,2) (6,0) (2,0) (9,0) (16,11) (12,14) (12,16) (1,18) (8,6) (7,4) (13,10) (17,4) (7,0) (5,18) (9,8) (8,16) (11,10) (11,2) (2,14) (1,13) (10,8) (15,17) (5,9) (15,4) (9,11) (11,6) (5,8) (9,13) (17,14) (4,9) (6,16) (9,2) (10,17) (16,9) (13,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->15->13->7->8->17->6->12->10->9->1->11->4->3->16->14->2->5->18." - } - ] - }, - { - "id": "hamilton-hard-graph278", - "image": "data/hamilton/graph_visual/Base/hard/graph278.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,6) (12,0) (6,5) (2,14) (6,14) (7,6) (13,1) (3,13) (12,5) (14,7) (8,9) (11,0) (12,11) (11,10) (0,1) (11,1) (0,4) (8,10) (3,8) (8,4) (8,1) (13,6) (7,10) (14,0) (7,4) (10,0) (12,9) (5,2) (3,4) (13,11) (5,13) (4,12) (4,13) (10,14) (10,2) (8,14) (12,8) (4,5) (0,3) (1,14) (10,1) (14,13) (12,1) (8,7) (11,5) (9,13) (9,2) (10,13) (9,14) (7,2) (0,2) (14,3) (3,12) (11,8) (5,9) (6,4) (0,13) (11,7) (0,8) (14,12) (1,5) (7,3) (9,10) (1,9) (10,12) (5,7) (11,3) (7,13) (9,4) (10,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->5->6->2->14->7->10->11->1->13->3->8->9->4." - } - ] - }, - { - "id": "hamilton-hard-graph349", - "image": "data/hamilton/graph_visual/Base/hard/graph349.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,11) (0,12) (5,6) (9,10) (9,12) (13,14) (8,14) (10,2) (13,2) (5,14) (1,15) (12,6) (10,5) (4,13) (2,12) (10,0) (10,4) (9,14) (5,1) (10,6) (10,12) (1,3) (0,7) (12,14) (15,13) (4,6) (5,9) (8,15) (0,3) (12,7) (14,3) (8,4) (14,2) (6,3) (13,11) (9,0) (1,12) (5,3) (9,4) (5,8) (4,12) (1,6) (15,9) (3,10) (8,1) (0,4) (7,8) (8,9) (1,9) (11,8) (10,15) (4,1) (8,3) (11,3) (12,13) (1,10) (11,10) (9,7) (2,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->9->10->2->13->14->5->6->4->11->3->1->15->8->7." - } - ] - }, - { - "id": "hamilton-hard-graph318", - "image": "data/hamilton/graph_visual/Base/hard/graph318.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,8) (4,14) (5,1) (0,3) (14,3) (10,9) (10,13) (0,6) (0,11) (13,1) (9,6) (8,2) (11,3) (3,13) (9,15) (10,7) (11,12) (14,1) (7,2) (6,15) (13,12) (8,6) (7,5) (11,1) (15,1) (9,12) (4,3) (2,0) (11,8) (2,6) (8,15) (3,2) (4,2) (9,8) (15,11) (12,15) (2,11) (9,5) (7,13) (14,6) (2,14) (4,13) (4,0) (2,5) (15,14) (10,11) (1,4) (8,4) (11,6) (11,13) (5,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->14->8->2->7->10->9->6->15->11->12->13->4->1->5." - } - ] - }, - { - "id": "hamilton-hard-graph370", - "image": "data/hamilton/graph_visual/Base/hard/graph370.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,5) (13,1) (9,2) (3,7) (15,8) (3,9) (4,1) (15,16) (16,9) (6,8) (15,14) (7,16) (7,1) (16,13) (13,2) (7,9) (3,2) (1,5) (16,8) (1,11) (3,14) (15,13) (12,3) (10,5) (15,1) (11,4) (2,16) (12,1) (11,16) (16,6) (15,10) (8,2) (10,12) (0,5) (15,12) (3,11) (11,10) (0,14) (1,2) (6,3) (4,2) (0,4) (7,11) (4,10) (12,7) (2,10) (0,7) (12,0) (13,10) (14,5) (3,13) (1,10) (4,15)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->16->15->14->3->9->7->11->4->1->12->10->13->2->8->6." - } - ] - }, - { - "id": "hamilton-hard-graph535", - "image": "data/hamilton/graph_visual/Base/hard/graph535.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (15,6) (7,14) (6,18) (1,12) (1,16) (6,2) (16,10) (1,10) (12,10) (12,15) (4,6) (11,4) (1,14) (1,11) (0,2) (8,12) (7,15) (8,16) (2,8) (2,5) (7,2) (17,4) (11,8) (9,2) (11,9) (0,15) (5,10) (0,9) (14,4) (15,3) (1,6) (12,6) (0,8) (16,3) (14,15) (2,3) (2,11) (10,15) (3,14) (4,3) (10,0) (3,18) (11,10) (11,12) (16,13) (10,13) (3,13) (8,17) (1,4) (10,7) (18,8) (13,7) (1,13) (1,17) (16,4) (16,18) (15,16) (18,17) (6,5) (2,16) (1,0) (14,16) (10,3) (5,9) (2,10) (16,12) (8,9) (10,6) (7,11) (6,0) (3,9) (18,4) (8,3) (8,5) (5,15) (2,13) (18,10) (18,7) (17,0) (16,6) (13,18) (8,6) (9,12) (0,18) (9,7) (2,4) (17,10) (15,4) (4,13) (6,17) (2,17) (14,8) (14,10) (2,1) (2,15) (8,15) (5,12) (9,16)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->6->15->12->1->16->10->5->9->11->4->17->8->18->3->14->7->13." - } - ] - }, - { - "id": "hamilton-hard-graph81", - "image": "data/hamilton/graph_visual/Base/hard/graph81.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,2) (6,11) (3,7) (4,5) (8,6) (3,8) (1,7) (3,6) (7,2) (5,11) (1,5) (3,9) (7,11) (7,9) (3,10) (1,2) (1,6) (6,0) (7,10) (9,5) (0,3) (9,1) (11,3) (4,1) (4,11) (5,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->11->5->4->1->2->10->7->9->3->8." - } - ] - }, - { - "id": "hamilton-hard-graph247", - "image": "data/hamilton/graph_visual/Base/hard/graph247.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,4) (9,1) (0,2) (1,7) (11,1) (0,13) (4,8) (10,6) (6,8) (2,7) (14,13) (14,6) (7,0) (5,9) (11,14) (11,12) (2,1) (13,6) (13,7) (8,5) (2,10) (12,13) (14,2) (2,3) (11,13) (11,10) (1,8) (2,13) (0,6) (3,4) (11,9) (4,12) (10,5) (7,3) (2,9) (0,8) (1,10) (8,12) (12,7) (14,7) (10,12) (6,11) (3,9) (12,6) (1,0) (1,6) (5,3) (11,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->4->8->6->10->11->1->9->5->3->7->12->13->14." - } - ] - }, - { - "id": "hamilton-hard-graph23", - "image": "data/hamilton/graph_visual/Base/hard/graph23.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,6) (7,0) (0,1) (5,6) (10,1) (2,9) (7,9) (5,8) (3,4) (4,6) (7,10) (10,8) (2,4) (7,4) (9,0) (5,9) (8,4) (1,4) (6,1) (10,5) (3,0) (0,6) (1,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->9->2->1->10->6->5->8->4->3." - } - ] - }, - { - "id": "hamilton-hard-graph310", - "image": "data/hamilton/graph_visual/Base/hard/graph310.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,11) (6,3) (14,3) (4,2) (12,5) (7,13) (6,12) (2,10) (0,10) (1,4) (4,9) (13,12) (2,9) (2,7) (5,15) (11,15) (4,7) (5,7) (3,11) (0,1) (13,6) (8,4) (1,5) (10,7) (2,11) (14,12) (11,8) (13,0) (15,10) (10,1) (11,6) (9,12) (14,7) (1,13) (0,3) (13,10) (4,6) (10,4) (7,0) (8,13) (0,9) (9,6) (3,13) (14,10) (15,9) (15,3) (15,2) (12,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->2->4->1->5->12->6->3->14->7->13->8->11->15->9." - } - ] - }, - { - "id": "hamilton-hard-graph544", - "image": "data/hamilton/graph_visual/Base/hard/graph544.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (7,4) (10,15) (15,3) (8,19) (18,11) (4,5) (4,0) (1,2) (5,0) (14,6) (1,3) (15,9) (9,8) (12,13) (7,15) (3,8) (18,19) (13,15) (16,4) (15,4) (17,8) (1,0) (16,3) (0,11) (12,8) (5,2) (16,13) (17,14) (2,7) (0,3) (4,8) (13,6) (16,10) (1,12) (11,7) (17,7) (7,5) (1,4) (10,17) (19,3) (16,5) (14,13) (0,9) (18,17) (11,1) (14,8) (18,4) (6,17) (19,7) (1,15) (7,0) (19,1) (15,5) (6,4) (3,18) (4,10) (17,4) (6,0) (15,6) (1,8) (12,4) (10,11) (11,16) (10,8) (15,0) (1,13) (13,19) (3,17) (13,4) (12,19) (14,19) (6,18) (19,0) (0,10) (2,11) (13,0) (15,17) (9,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->7->15->10->16->3->1->12->13->6->14->17->18->19->8->9->11->2->5." - } - ] - }, - { - "id": "hamilton-hard-graph457", - "image": "data/hamilton/graph_visual/Base/hard/graph457.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (8,16) (8,7) (10,17) (15,14) (12,1) (17,6) (3,1) (1,15) (15,12) (14,10) (15,5) (7,9) (2,1) (1,10) (13,15) (3,10) (9,0) (4,10) (15,16) (15,0) (15,8) (8,14) (9,2) (5,1) (14,2) (13,12) (8,11) (4,8) (8,9) (14,11) (4,5) (10,7) (2,5) (2,17) (8,17) (9,3) (17,11) (11,9) (8,6) (8,3) (6,7) (13,5) (10,5) (17,14) (14,12) (4,9) (17,12) (10,11) (10,9) (0,11) (2,7) (0,6) (6,3) (7,4) (0,4) (3,17) (14,1) (0,5) (6,16) (3,4) (0,17) (17,15) (1,4) (12,2) (0,3) (6,4) (6,2) (6,15) (3,12) (3,14) (6,10) (17,5) (1,11) (14,4) (16,14) (7,12) (9,5) (4,17) (17,1) (13,6) (10,0) (14,7) (2,0) (10,15) (13,16) (13,4) (5,8) (9,12) (8,12) (13,3) (1,6) (2,3) (12,11) (1,13) (10,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->7->8->16->15->14->10->17->6->3->1->2->5->4->13->12->11." - } - ] - }, - { - "id": "hamilton-hard-graph168", - "image": "data/hamilton/graph_visual/Base/hard/graph168.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,7) (12,3) (4,5) (10,6) (11,0) (1,9) (4,7) (6,3) (4,3) (4,9) (7,6) (5,9) (2,12) (9,10) (11,10) (11,8) (12,11) (4,6) (1,6) (9,12) (8,9) (6,9) (9,7) (1,3) (1,8) (9,11) (2,4) (1,11) (10,3) (3,2) (6,12) (0,12) (1,10) (0,7) (4,12) (2,5) (5,7) (2,7) (0,4) (0,1) (7,8) (4,1) (1,12) (8,0) (4,10) (0,10) (8,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->7->4->5->9->1->6->10->3->12->2->8." - } - ] - }, - { - "id": "hamilton-hard-graph319", - "image": "data/hamilton/graph_visual/Base/hard/graph319.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,10) (10,13) (2,9) (10,8) (10,6) (12,14) (0,6) (15,8) (15,4) (13,5) (1,0) (2,0) (13,14) (14,3) (2,3) (12,8) (11,12) (9,11) (7,12) (0,4) (2,5) (11,5) (3,8) (3,12) (6,9) (2,10) (10,1) (1,5) (6,12) (10,14) (4,7) (14,5) (10,5) (8,0) (3,9) (13,7) (5,12) (14,1) (1,7) (15,3) (2,15) (0,3) (6,13) (12,2) (7,5) (9,1) (10,3) (15,13) (13,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->10->11->12->14->13->5->2->9->3->8->15->4->7->1." - } - ] - }, - { - "id": "hamilton-hard-graph392", - "image": "data/hamilton/graph_visual/Base/hard/graph392.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (13,6) (0,4) (15,3) (11,4) (10,1) (16,8) (12,1) (7,14) (8,2) (4,5) (7,3) (0,15) (3,1) (11,12) (15,13) (5,8) (5,2) (15,5) (1,14) (6,9) (2,13) (9,2) (4,2) (1,0) (9,11) (15,4) (7,9) (8,14) (13,7) (10,7) (8,13) (13,5) (6,11) (10,9) (16,3) (6,14) (8,0) (10,4) (0,5) (5,11) (2,0) (16,15) (1,4) (14,4) (5,10) (16,1) (6,1) (16,9) (14,0) (8,1) (13,0) (15,2) (12,5) (5,7) (9,12) (10,16) (13,16) (6,12) (13,4) (8,11) (9,13) (7,15) (5,14) (13,14) (5,1) (8,9) (10,2) (3,0) (9,5) (14,11) (6,4) (7,11) (4,16) (13,1) (6,15) (15,8) (3,12) (16,11) (11,1) (4,7) (7,2) (10,6) (3,13) (2,6) (4,9) (12,15) (3,4) (15,11) (6,16) (10,0) (3,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->11->12->1->10->7->14->8->16->3->15->13->6->9->2->5." - } - ] - }, - { - "id": "hamilton-hard-graph412", - "image": "data/hamilton/graph_visual/Base/hard/graph412.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (6,8) (0,11) (8,15) (11,9) (7,12) (6,3) (8,5) (16,3) (15,5) (2,13) (10,8) (9,6) (12,15) (5,13) (15,7) (9,1) (12,1) (16,9) (12,14) (14,9) (10,3) (16,7) (6,5) (12,6) (15,0) (2,3) (5,0) (4,16) (2,1) (6,14) (1,13) (0,9) (0,1) (1,15) (11,7) (6,10) (1,6) (9,13) (8,4) (8,1) (14,4) (0,4) (15,2) (8,7) (10,7) (12,11) (0,12) (2,12) (0,14) (7,9) (11,14) (1,14) (5,16) (0,2) (9,10) (4,6) (10,4) (13,0) (5,1) (9,4) (16,10) (3,0) (6,16) (11,16) (12,13) (14,7) (7,3) (5,14) (12,3) (13,6) (13,15) (2,9) (15,6) (4,12) (3,5) (11,4) (2,4) (15,4) (0,6) (16,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->9->6->8->15->5->13->2->3->16->7->12->1->14->4->10." - } - ] - }, - { - "id": "hamilton-hard-graph236", - "image": "data/hamilton/graph_visual/Base/hard/graph236.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,2) (6,13) (10,12) (10,6) (5,9) (4,7) (10,0) (8,3) (9,4) (10,3) (3,13) (8,1) (12,9) (9,1) (5,1) (12,6) (0,3) (8,7) (1,10) (11,7) (11,9) (11,5) (2,4) (0,1) (6,11) (11,12) (7,1) (2,1) (7,12) (0,5) (5,12) (2,11) (3,2) (12,2) (7,0) (3,11) (11,8) (11,0) (5,4) (11,10) (4,6) (10,7) (10,5) (13,8) (8,10) (6,3) (13,1) (6,7) (0,8) (6,9) (2,5) (5,6) (11,1) (6,8) (0,6) (0,4) (12,8) (3,1) (2,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->12->9->5->1->8->3->13->6->11->7->2->4." - } - ] - }, - { - "id": "hamilton-hard-graph244", - "image": "data/hamilton/graph_visual/Base/hard/graph244.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,4) (10,1) (10,7) (0,5) (9,8) (7,14) (7,1) (0,2) (12,7) (6,3) (1,0) (5,7) (11,14) (9,7) (2,6) (14,1) (11,0) (9,2) (7,0) (8,6) (14,3) (7,13) (10,12) (2,1) (6,5) (4,0) (13,14) (6,10) (12,6) (8,13) (12,11) (10,9) (7,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->7->13->8->9->2->1->10->6->3->14->11->12->4." - } - ] - }, - { - "id": "hamilton-hard-graph311", - "image": "data/hamilton/graph_visual/Base/hard/graph311.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,14) (14,5) (3,11) (4,9) (3,6) (10,8) (3,9) (4,11) (8,6) (6,15) (7,2) (14,2) (15,2) (3,7) (7,12) (1,14) (2,4) (5,3) (15,3) (1,10) (9,2) (14,4) (15,14) (12,9) (5,15) (5,11) (6,11) (3,10) (0,3) (11,13) (5,9) (11,1) (5,10) (6,1) (4,3) (2,12) (7,13) (8,12) (4,7) (5,1) (14,10) (10,4) (7,9) (13,2) (13,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->11->4->9->2->14->5->15->6->1->10->8->12->7->13." - } - ] - }, - { - "id": "hamilton-hard-graph542", - "image": "data/hamilton/graph_visual/Base/hard/graph542.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,1) (8,1) (17,10) (19,15) (13,12) (0,1) (4,0) (16,9) (2,18) (18,1) (0,14) (6,17) (6,1) (6,9) (15,2) (8,5) (19,3) (14,2) (7,9) (1,13) (17,4) (16,15) (1,19) (19,6) (6,3) (18,15) (14,19) (5,12) (1,15) (2,8) (7,18) (1,12) (11,17) (3,11) (19,0) (18,9) (8,18) (17,18) (2,13) (16,13) (14,4) (4,12) (8,19) (19,18) (10,9) (4,5) (8,15) (12,19) (5,7) (5,2) (12,11) (14,7) (16,19) (8,0) (16,1) (18,13) (2,1) (16,4) (13,19) (1,10) (1,3) (7,13) (13,8) (17,0) (17,7) (11,6) (10,3) (2,19) (17,16) (13,14) (5,19) (9,14) (4,9) (6,12) (11,15) (3,0) (13,5) (7,19) (3,18) (13,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->9->16->15->19->3->6->11->12->13->2->18->8->5->4->14->7->17->10." - } - ] - }, - { - "id": "hamilton-hard-graph332", - "image": "data/hamilton/graph_visual/Base/hard/graph332.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,2) (9,4) (13,6) (4,2) (0,6) (0,10) (10,9) (7,15) (12,10) (13,2) (0,14) (7,5) (8,4) (2,9) (10,6) (0,5) (1,11) (4,12) (5,13) (8,10) (10,15) (15,13) (14,1) (11,7) (13,11) (7,4) (3,7) (12,13) (3,0) (7,6) (15,1) (15,11) (9,0) (1,4) (13,9) (15,3) (12,15) (1,6) (3,2) (7,14) (8,12) (10,5) (11,12) (2,5) (10,14) (9,1) (13,3) (0,1) (15,14) (1,3) (10,3) (9,8) (8,11) (9,11) (8,5) (12,7) (8,3) (10,7) (8,2) (13,4) (15,0) (6,14) (4,10) (3,12) (8,0) (15,8) (1,2) (0,2) (10,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->13->2->12->10->9->4->8->11->1->14->15->3->7->5." - } - ] - }, - { - "id": "hamilton-hard-graph524", - "image": "data/hamilton/graph_visual/Base/hard/graph524.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (2,8) (15,14) (10,5) (5,0) (6,9) (10,17) (11,18) (11,1) (1,16) (6,5) (13,2) (4,10) (13,8) (15,3) (2,11) (12,2) (0,11) (2,10) (5,8) (13,18) (13,7) (7,0) (6,11) (18,15) (0,4) (3,9) (1,5) (2,15) (16,10) (3,6) (17,5) (16,14) (13,0) (10,15) (14,11) (12,18) (1,7) (4,15) (15,0) (16,15) (16,0) (3,17) (4,7) (3,7) (10,1) (0,18) (6,7) (12,8) (14,18) (10,12) (8,0) (6,12) (17,4) (0,17) (7,8) (17,14) (16,17) (3,1) (8,11) (3,0) (17,18) (13,14) (1,9) (4,14) (9,7) (11,7) (7,17) (9,5) (12,4) (2,7) (9,4) (18,9) (3,18) (0,12) (8,6) (6,13) (6,4) (2,3) (4,8) (2,5) (5,18) (18,7) (10,9) (12,11) (12,9) (3,10) (14,1) (4,2) (1,0) (3,5) (15,6) (16,12) (8,18) (10,13) (10,14) (13,17) (10,18) (2,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->10->17->3->15->14->16->1->11->18->13->2->8->12->6->9->7->4." - } - ] - }, - { - "id": "hamilton-hard-graph33", - "image": "data/hamilton/graph_visual/Base/hard/graph33.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,9) (3,8) (3,1) (4,0) (4,1) (3,7) (6,0) (6,10) (0,9) (5,1) (4,2) (7,5) (9,5) (6,7) (4,3) (7,8) (9,8) (2,9) (10,0) (8,5) (8,4) (6,5) (0,2) (0,1) (6,1) (2,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->1->3->8->7->5->9->10->6->2." - } - ] - }, - { - "id": "hamilton-hard-graph312", - "image": "data/hamilton/graph_visual/Base/hard/graph312.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (1,3) (14,5) (12,1) (4,1) (4,6) (13,6) (14,3) (12,11) (15,0) (15,7) (7,14) (3,13) (9,1) (7,4) (11,1) (9,8) (15,4) (2,15) (6,9) (14,10) (12,15) (2,11) (0,10) (8,2) (12,13) (3,11) (11,6) (7,13) (9,15) (6,1) (9,11) (2,9) (6,14) (1,7) (13,8) (11,13) (3,10) (12,8) (1,10) (5,15) (14,1) (4,10) (15,14) (14,4) (10,8) (5,13) (7,10) (15,8) (2,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->15->7->14->5->13->6->4->1->3->10->8->9->2->11->12." - } - ] - }, - { - "id": "hamilton-hard-graph62", - "image": "data/hamilton/graph_visual/Base/hard/graph62.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,1) (11,2) (11,6) (5,7) (0,7) (7,11) (10,6) (8,2) (0,8) (1,10) (1,11) (5,2) (6,3) (6,0) (7,1) (7,3) (9,2) (1,3) (7,9) (7,2) (1,8) (2,10) (9,11) (4,10) (5,8) (5,10) (9,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->5->2->8->1->3->6->11->9->10->4." - } - ] - }, - { - "id": "hamilton-hard-graph258", - "image": "data/hamilton/graph_visual/Base/hard/graph258.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,8) (7,14) (13,10) (4,8) (11,1) (13,8) (9,10) (13,9) (14,9) (0,3) (1,8) (7,2) (7,5) (13,1) (10,4) (13,12) (2,0) (7,1) (6,8) (5,11) (0,8) (6,5) (9,7) (11,6) (14,1) (12,11) (0,14) (0,7) (2,4) (9,8) (12,9) (8,10) (5,14) (6,14) (3,14) (5,10) (12,8) (9,11) (6,12) (3,11) (11,7) (13,7) (3,6) (5,12) (9,3) (9,0) (1,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->14->7->8->13->9->12->6->11->1->5->10->4->2." - } - ] - }, - { - "id": "hamilton-hard-graph421", - "image": "data/hamilton/graph_visual/Base/hard/graph421.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (8,16) (0,16) (3,9) (15,2) (5,10) (14,16) (13,11) (8,0) (10,14) (14,17) (16,1) (4,13) (8,12) (8,2) (3,8) (6,14) (0,1) (5,7) (4,14) (14,2) (7,17) (11,14) (9,16) (1,9) (11,10) (1,4) (17,0) (9,6) (4,16) (1,3) (3,13) (11,5) (2,5) (6,10) (16,5) (12,14) (8,10) (16,15) (12,5) (2,1) (3,6) (1,13) (13,9) (15,3) (15,10) (10,0) (6,1) (15,13) (14,7) (8,5) (7,12) (3,0) (2,11) (10,13) (3,11) (3,10) (12,11) (14,5) (17,11) (17,5) (6,8) (0,12) (9,7) (7,0) (8,11) (4,15) (12,16) (5,0) (16,7) (8,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->16->8->12->14->10->5->7->17->11->13->4->1->9->6->3->15->2." - } - ] - }, - { - "id": "hamilton-hard-graph520", - "image": "data/hamilton/graph_visual/Base/hard/graph520.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (6,3) (0,11) (7,4) (9,16) (11,5) (16,0) (4,16) (18,15) (8,3) (8,17) (2,8) (4,11) (14,12) (1,2) (11,8) (17,3) (5,18) (13,9) (4,10) (10,15) (10,16) (2,14) (3,10) (2,4) (2,16) (11,12) (5,10) (9,8) (15,8) (12,15) (0,2) (15,1) (1,11) (11,7) (2,13) (8,10) (7,16) (6,2) (0,5) (14,6) (6,17) (11,15) (11,9) (11,3) (0,18) (10,17) (9,3) (11,18) (4,12) (1,3) (18,2) (7,2) (0,15) (13,4) (6,0) (13,5) (16,12) (10,13) (6,12) (7,6) (2,17) (14,10) (18,7) (13,8) (16,1) (13,7) (17,12) (9,10) (6,15) (8,16) (3,0) (10,12) (5,3) (7,12) (17,4) (14,11) (13,11) (16,17) (2,15) (7,14) (7,15) (0,14) (15,5) (4,8) (0,17) (13,12) (0,8) (6,9) (17,18) (6,10) (7,1) (7,3) (9,5) (5,12) (4,3) (11,6) (1,12) (15,13) (9,14) (1,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->5->18->15->10->4->7->16->9->13->2->8->3->17->6->14->12->1." - } - ] - }, - { - "id": "hamilton-hard-graph192", - "image": "data/hamilton/graph_visual/Base/hard/graph192.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,9) (0,5) (6,8) (5,3) (12,9) (12,13) (1,8) (13,8) (10,13) (13,4) (11,6) (5,12) (2,5) (0,13) (13,1) (0,7) (10,9) (1,2) (3,10) (9,8) (5,6) (9,1) (7,5) (4,7) (10,11) (11,12) (11,7) (2,8) (10,5) (4,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->3->10->13->12->9->1->2->8->6->11->7->4." - } - ] - }, - { - "id": "hamilton-hard-graph379", - "image": "data/hamilton/graph_visual/Base/hard/graph379.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (14,4) (2,15) (15,3) (12,3) (16,14) (2,3) (16,10) (11,16) (13,6) (16,6) (16,3) (9,7) (1,16) (6,3) (4,11) (11,13) (5,13) (0,10) (6,10) (13,1) (11,6) (6,12) (4,9) (15,6) (5,2) (13,0) (6,8) (2,1) (9,12) (8,9) (2,8) (5,14) (6,9) (9,15) (14,2) (14,13) (14,11) (5,9) (6,4) (2,0) (5,8) (0,12) (2,6) (2,9) (3,5) (10,5) (12,1) (16,8) (7,1) (7,2) (10,3) (15,5) (16,15)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->16->14->4->11->13->6->3->15->2->5->8->9->7->1->12." - } - ] - }, - { - "id": "hamilton-hard-graph465", - "image": "data/hamilton/graph_visual/Base/hard/graph465.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (13,17) (15,1) (5,3) (3,0) (16,6) (0,17) (17,10) (17,4) (9,11) (4,8) (7,4) (5,8) (4,13) (14,1) (7,10) (9,13) (0,12) (11,15) (9,0) (1,10) (12,15) (10,6) (5,14) (4,2) (16,9) (4,16) (6,0) (16,1) (2,10) (12,1) (4,5) (16,11) (15,7) (3,10) (2,8) (13,15) (15,14) (9,10) (5,11) (3,15) (2,1) (10,15) (0,2) (6,4) (1,5) (3,12) (3,2) (16,0) (10,4) (3,14) (4,14) (6,3) (2,6) (8,11) (1,9) (11,4) (13,3) (17,16) (7,13) (11,14) (2,15) (8,15) (7,9) (2,7) (14,7) (7,6) (13,12) (12,14) (3,1) (16,10) (3,9) (7,11) (3,4) (0,15) (13,14) (10,0) (6,9) (9,5) (1,13) (10,14) (14,9) (6,8) (4,15) (3,8) (2,9) (12,7) (14,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->5->8->4->17->13->9->11->15->1->14->12->7->10->2->6->16." - } - ] - }, - { - "id": "hamilton-hard-graph313", - "image": "data/hamilton/graph_visual/Base/hard/graph313.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,14) (0,9) (1,5) (7,14) (10,14) (3,12) (13,14) (11,6) (8,5) (6,4) (1,0) (11,5) (14,8) (12,15) (12,14) (6,5) (0,10) (6,10) (1,6) (15,3) (10,12) (6,7) (11,13) (1,2) (0,15) (4,13) (13,0) (2,11) (12,9) (0,8) (5,3) (8,2) (13,7) (8,9) (11,0) (15,6) (7,15) (5,7) (12,4) (2,9) (13,5) (6,8) (2,13) (2,7) (2,12) (15,9) (5,2) (10,3) (6,13) (4,2) (3,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->12->3->15->7->14->10->6->11->13->4->2->1->5->8." - } - ] - }, - { - "id": "hamilton-hard-graph298", - "image": "data/hamilton/graph_visual/Base/hard/graph298.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,12) (8,7) (0,9) (11,6) (13,12) (11,7) (13,7) (14,3) (12,10) (5,13) (11,14) (13,10) (6,8) (7,2) (1,0) (10,5) (6,13) (9,10) (2,9) (4,6) (3,0) (8,3) (10,0) (3,1) (14,12) (8,10) (1,2) (1,7) (8,0) (2,5) (1,5) (10,2) (11,13) (12,5) (2,12) (14,5) (1,13) (5,11) (13,2) (14,2) (3,7) (7,6) (13,0) (8,1) (14,8) (2,11) (12,0) (14,7) (4,8) (13,14) (0,6) (8,11) (11,12) (4,0) (2,0) (4,10) (7,12) (5,0) (2,3) (1,6) (14,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->10->12->8->7->11->6->13->5->2->1->3->14->4." - } - ] - }, - { - "id": "hamilton-hard-graph300", - "image": "data/hamilton/graph_visual/Base/hard/graph300.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,7) (0,13) (10,3) (8,12) (13,8) (2,13) (10,8) (5,6) (9,11) (4,5) (12,4) (4,10) (4,14) (5,15) (3,14) (2,7) (7,13) (0,15) (3,5) (0,2) (7,15) (5,11) (7,3) (7,14) (3,2) (8,15) (8,2) (1,7) (15,2) (3,8) (3,11) (2,14) (9,12) (14,12) (14,1) (13,10) (5,7) (7,10) (6,8) (2,12) (9,1) (11,12) (7,9) (4,11) (11,8) (6,14) (15,6) (13,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->8->12->4->5->6->14->2->15->7->1->9->11->3->10." - } - ] - }, - { - "id": "hamilton-hard-graph145", - "image": "data/hamilton/graph_visual/Base/hard/graph145.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (10,4) (9,2) (11,1) (3,12) (6,5) (10,0) (9,3) (2,1) (10,9) (12,8) (10,8) (9,8) (0,4) (11,3) (5,2) (1,0) (8,5) (0,7) (10,5) (5,11) (0,12) (7,9) (4,3) (12,1) (6,3) (11,0) (12,5) (6,11) (6,1) (6,9) (3,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->4->3->12->8->5->6->11->1->2->9->7." - } - ] - }, - { - "id": "hamilton-hard-graph268", - "image": "data/hamilton/graph_visual/Base/hard/graph268.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,3) (1,6) (13,6) (1,3) (0,14) (0,9) (13,3) (14,6) (0,8) (14,1) (1,10) (3,5) (7,4) (10,11) (7,14) (9,7) (9,6) (2,11) (10,0) (12,7) (9,3) (5,4) (2,8) (13,8) (11,1) (0,11) (12,14) (7,13) (2,13) (0,1) (1,5) (10,8) (2,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->14->6->9->3->10->8->13->2->11->1->5->4->7->12." - } - ] - }, - { - "id": "hamilton-hard-graph277", - "image": "data/hamilton/graph_visual/Base/hard/graph277.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (2,8) (10,2) (8,7) (7,9) (6,4) (1,12) (4,11) (7,3) (12,5) (3,12) (6,7) (13,10) (10,4) (12,10) (9,1) (1,10) (11,9) (0,11) (14,0) (14,12) (7,2) (3,10) (10,14) (1,8) (5,0) (8,14) (0,7) (5,11) (4,0) (12,2) (3,4) (11,14) (8,13) (3,1) (11,12) (1,6) (8,0) (10,7) (4,7) (13,11) (6,0) (12,8) (9,10) (8,5) (12,7) (14,1) (3,2) (5,6) (9,6) (6,3) (6,8) (11,1) (3,13) (14,5) (13,2) (6,12) (13,12) (10,8) (8,11) (3,9) (14,7) (5,1) (2,4) (10,0) (3,5) (7,1) (7,13) (14,6) (11,2) (13,1) (2,5) (1,2) (5,9) (14,2) (0,12) (2,9) (6,10) (7,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->7->8->2->10->13->11->4->6->1->12->14->5->9." - } - ] - }, - { - "id": "hamilton-hard-graph79", - "image": "data/hamilton/graph_visual/Base/hard/graph79.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,3) (9,4) (6,8) (5,2) (2,7) (1,8) (11,7) (3,5) (1,9) (2,8) (3,6) (9,3) (5,8) (11,1) (4,0) (8,3) (7,1) (5,6) (6,0) (1,5) (2,3) (10,5) (9,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->9->1->8->6->3->10->5->2->7->11." - } - ] - }, - { - "id": "hamilton-hard-graph50", - "image": "data/hamilton/graph_visual/Base/hard/graph50.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,1) (2,3) (9,0) (2,0) (7,5) (4,7) (9,4) (2,6) (7,0) (5,8) (6,8) (1,8) (4,6) (0,4) (10,1) (1,3) (9,8) (10,6) (0,1) (1,2) (6,1) (7,1) (2,10) (9,7) (7,10) (8,7) (9,6) (9,10) (4,3) (3,9) (10,0) (4,2) (10,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->4->1->8->5->7->10->6->2->3." - } - ] - }, - { - "id": "hamilton-hard-graph240", - "image": "data/hamilton/graph_visual/Base/hard/graph240.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,5) (14,1) (1,12) (4,6) (13,6) (8,6) (0,6) (9,3) (11,7) (10,6) (12,4) (3,14) (4,5) (2,5) (11,5) (6,2) (13,3) (2,11) (3,12) (3,1) (8,13) (7,6) (3,8) (14,12) (4,8) (9,7) (7,10) (4,10) (10,14) (5,7) (7,0) (12,13) (12,11) (0,5) (13,14) (2,13) (0,10) (4,3) (2,8) (10,13) (12,5) (5,14) (8,10) (0,9) (8,11) (1,10) (0,11) (11,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->4->12->1->5->2->11->7->9->3->14->10->13->8." - } - ] - }, - { - "id": "hamilton-hard-graph290", - "image": "data/hamilton/graph_visual/Base/hard/graph290.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,6) (12,2) (12,3) (13,3) (9,1) (0,5) (3,11) (14,4) (2,14) (12,10) (7,13) (2,8) (1,7) (9,13) (0,2) (4,9) (6,11) (5,10) (14,8) (2,5) (0,4) (9,7) (11,7) (10,8) (3,8) (11,13) (10,11) (3,0) (3,9) (2,6) (12,11) (13,4) (9,10) (5,3) (5,1) (0,1) (1,2) (7,3) (14,3) (12,5) (3,2) (11,14) (14,0) (14,1) (1,12) (7,5) (7,10) (2,7) (10,13) (9,0) (6,9) (11,4) (8,7) (10,1) (8,4) (6,13) (5,13) (1,8) (9,11) (13,1) (5,4) (8,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->10->6->11->3->12->2->14->4->9->1->8->7->13." - } - ] - }, - { - "id": "hamilton-hard-graph32", - "image": "data/hamilton/graph_visual/Base/hard/graph32.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,0) (10,2) (0,5) (3,10) (2,4) (5,2) (6,9) (8,10) (5,9) (2,0) (9,0) (5,3) (4,0) (1,2) (6,2) (7,6) (0,7) (8,5) (10,0) (0,3) (4,5) (4,10) (1,6) (3,1) (7,3) (1,4) (8,4) (8,3) (8,1) (6,5) (2,8) (7,8) (3,6) (1,0) (7,2) (4,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->9->5->2->10->3->1->4->8->7." - } - ] - }, - { - "id": "hamilton-hard-graph87", - "image": "data/hamilton/graph_visual/Base/hard/graph87.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,10) (11,10) (8,11) (0,6) (4,0) (8,10) (5,0) (4,2) (3,4) (4,7) (1,11) (5,3) (1,4) (6,8) (7,5) (9,1) (7,1) (1,3) (9,3) (5,1) (4,6) (5,6) (2,6) (7,11) (0,1) (10,0) (8,4) (6,9) (3,0) (10,4) (5,4) (3,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->8->11->10->9->1->7->5->3->4->2." - } - ] - }, - { - "id": "hamilton-hard-graph523", - "image": "data/hamilton/graph_visual/Base/hard/graph523.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (13,8) (1,16) (14,8) (16,9) (1,8) (8,10) (0,13) (4,15) (6,10) (5,0) (0,11) (6,1) (17,6) (6,11) (16,4) (2,1) (15,10) (11,9) (16,6) (12,5) (14,3) (10,11) (15,6) (10,0) (17,16) (9,12) (10,1) (1,7) (4,5) (2,4) (3,2) (8,16) (17,14) (5,2) (12,1) (0,12) (14,4) (9,14) (16,7) (15,1) (11,15) (16,3) (18,11) (9,18) (0,7) (4,9) (6,0) (15,8) (12,16) (3,4) (1,14) (13,12) (8,4) (14,13) (8,5) (13,2) (17,10) (16,0) (17,4) (6,4) (7,15) (13,18) (6,18) (9,5) (0,8) (17,7) (5,11) (2,17) (2,6) (5,18) (14,2) (4,11) (0,4) (11,16) (9,2) (18,4) (16,13) (5,1) (13,5) (18,12) (13,17) (0,14) (11,17) (12,10) (9,13) (1,0) (16,15) (15,12) (18,17) (15,5) (10,13) (3,1) (17,3) (7,11) (1,17) (2,12) (4,1) (17,0) (3,0) (15,9) (17,15) (13,15) (16,18) (12,3) (12,7) (18,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->8->14->3->2->1->16->9->11->6->10->15->4->5->12->18->17->7." - } - ] - }, - { - "id": "hamilton-hard-graph351", - "image": "data/hamilton/graph_visual/Base/hard/graph351.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (8,3) (3,14) (6,12) (3,1) (14,12) (4,8) (6,8) (8,15) (13,2) (1,2) (7,11) (10,1) (7,2) (1,0) (6,10) (0,12) (11,13) (13,3) (3,6) (5,6) (2,5) (9,14) (12,11) (9,12) (9,13) (9,10) (8,9) (10,13) (7,0) (11,6) (1,15) (3,12) (6,9) (7,14) (4,6) (8,11) (9,7) (8,13) (9,1) (6,2) (15,14) (2,14) (15,11) (2,9) (2,4) (8,7) (12,10) (12,8) (13,6) (2,8) (0,5) (8,14) (3,10) (14,11) (10,7) (12,4) (0,10) (5,10) (9,5) (5,11) (0,9) (8,5) (9,3) (3,4) (13,7) (4,5) (15,0) (13,0) (8,0) (4,1) (7,4) (4,10) (9,11) (1,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->8->4->6->12->14->9->13->2->7->10->5->11->15." - } - ] - }, - { - "id": "hamilton-hard-graph417", - "image": "data/hamilton/graph_visual/Base/hard/graph417.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (9,12) (9,14) (1,15) (16,10) (10,12) (2,11) (7,2) (1,13) (3,1) (6,14) (8,3) (4,8) (5,6) (0,2) (1,12) (14,12) (0,16) (7,6) (9,15) (8,2) (3,10) (11,13) (2,6) (10,8) (12,6) (16,7) (1,0) (10,2) (15,11) (10,14) (9,6) (7,12) (8,7) (7,9) (10,13) (14,11) (8,14) (14,1) (3,11) (4,5) (3,4) (15,12) (4,1) (12,0) (15,16) (3,7) (13,4) (1,11) (2,1) (0,7) (10,15) (4,16) (13,14) (4,0) (2,16) (13,12) (2,5) (3,13) (11,8) (0,15) (2,3) (1,9) (5,8) (7,5) (14,5) (3,12) (5,0) (11,6) (7,4) (15,6) (14,15) (5,15) (9,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->11->13->1->15->9->12->10->16->7->6->14->8->3->4->5." - } - ] - }, - { - "id": "hamilton-hard-graph31", - "image": "data/hamilton/graph_visual/Base/hard/graph31.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,2) (10,0) (8,4) (7,8) (4,1) (4,9) (7,10) (1,10) (5,0) (8,6) (6,10) (10,9) (7,9) (7,4) (4,5) (10,5) (9,5) (1,2) (2,6) (1,0) (6,1) (1,7) (2,3) (8,3) (0,9) (6,0) (0,4) (9,3) (3,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->7->8->4->1->6->2->3->9->5." - } - ] - }, - { - "id": "hamilton-hard-graph209", - "image": "data/hamilton/graph_visual/Base/hard/graph209.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (9,11) (0,11) (10,3) (3,1) (10,5) (3,6) (4,7) (8,13) (3,8) (12,6) (0,6) (13,7) (12,2) (3,4) (2,7) (1,12) (4,11) (4,9) (0,7) (7,3) (3,9) (13,0) (4,10) (2,1) (7,12) (9,0) (12,13) (11,2) (0,2) (6,4) (12,8) (9,2) (7,11) (4,2) (2,13) (0,3) (9,6) (2,10) (11,13) (11,6) (12,9) (1,9) (5,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->9->4->7->13->8->3->6->12->1->2->10->5." - } - ] - }, - { - "id": "hamilton-hard-graph141", - "image": "data/hamilton/graph_visual/Base/hard/graph141.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,11) (5,8) (3,1) (11,1) (4,9) (7,4) (12,5) (0,1) (10,4) (4,6) (1,7) (12,1) (1,4) (10,2) (2,9) (11,10) (8,9) (5,4) (6,1) (2,1) (3,8) (9,10) (11,8) (6,9) (7,10) (3,10) (6,12) (2,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->11->10->2->9->8->5->12->6->4->7." - } - ] - }, - { - "id": "hamilton-hard-graph13", - "image": "data/hamilton/graph_visual/Base/hard/graph13.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,1) (6,5) (8,7) (9,1) (5,10) (5,8) (7,3) (0,7) (7,5) (4,3) (8,3) (1,4) (1,6) (9,5) (3,1) (7,6) (2,3) (5,0) (0,4) (9,3) (5,3) (4,10) (10,7) (10,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->10->5->8->7->6->1->9->3->2." - } - ] - }, - { - "id": "hamilton-hard-graph590", - "image": "data/hamilton/graph_visual/Base/hard/graph590.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (18,12) (19,18) (7,0) (8,6) (14,18) (12,9) (18,11) (0,14) (0,17) (15,7) (16,18) (12,16) (11,3) (6,2) (12,5) (6,14) (5,8) (16,5) (13,0) (2,15) (1,7) (6,5) (17,3) (4,1) (15,18) (9,18) (19,8) (2,17) (6,7) (5,18) (16,19) (13,7) (13,10) (17,7) (15,5) (8,3) (14,17) (3,12) (13,16) (18,8) (1,14) (18,3) (19,4) (19,15) (6,11) (5,19) (0,16) (2,7) (7,14) (19,9) (13,6) (19,17) (10,4) (4,6) (17,8) (0,6) (1,19) (11,16) (8,9) (5,4) (11,2) (10,2) (8,13) (12,17) (9,11) (3,0) (11,1) (13,3) (1,16) (8,4) (3,16) (0,15) (10,7) (1,3) (19,10) (17,11) (16,10) (3,2) (17,5) (15,11) (1,12) (7,16) (13,14) (5,11) (12,8) (17,1) (14,19) (17,18) (8,2) (2,1) (1,8) (10,3) (6,1) (4,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->15->2->6->8->5->12->18->19->16->13->10->4->1->14->17->3->11->9." - } - ] - }, - { - "id": "hamilton-hard-graph464", - "image": "data/hamilton/graph_visual/Base/hard/graph464.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (3,12) (17,4) (13,15) (7,4) (3,6) (14,10) (12,5) (1,3) (0,13) (17,3) (15,14) (7,11) (8,16) (6,8) (2,3) (2,13) (14,9) (16,7) (1,17) (5,0) (4,8) (17,14) (14,0) (15,4) (11,0) (0,17) (4,10) (1,12) (16,1) (9,15) (8,15) (8,11) (10,16) (0,3) (13,5) (10,6) (6,9) (9,17) (1,5) (17,6) (9,5) (6,16) (5,3) (13,10) (9,0) (2,16) (7,15) (10,12) (6,7) (15,1) (6,15) (10,7) (16,15) (10,17) (16,9) (7,9) (1,11) (17,12) (12,15) (2,6) (5,16) (16,0) (6,1) (9,12) (5,2) (0,15) (12,8) (4,2) (13,7) (1,4) (11,12) (4,9) (8,13) (17,11) (8,3) (11,13) (6,0) (4,5) (5,15) (11,2) (10,5) (4,3) (5,8) (16,4) (6,4) (4,11) (2,14) (7,14) (14,13) (4,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->15->14->10->4->17->3->12->5->1->16->8->6->9->7->11->2." - } - ] - }, - { - "id": "hamilton-hard-graph212", - "image": "data/hamilton/graph_visual/Base/hard/graph212.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,9) (0,12) (8,10) (4,0) (8,0) (13,2) (2,7) (5,11) (3,10) (7,5) (13,10) (9,7) (10,9) (5,0) (4,5) (10,1) (3,4) (11,6) (8,7) (12,13) (11,10) (2,0) (1,13) (2,11) (12,4) (10,0) (3,8) (7,0) (11,12) (11,0) (9,6) (5,9) (3,11) (5,13) (8,9) (6,5) (1,8) (3,0) (12,5) (2,4) (13,11) (3,1) (8,6) (3,7) (0,13) (3,9) (8,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->7->2->13->10->8->1->3->4->5->6->11->12." - } - ] - }, - { - "id": "hamilton-hard-graph514", - "image": "data/hamilton/graph_visual/Base/hard/graph514.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,18) (17,5) (14,17) (0,15) (3,7) (2,18) (9,18) (6,16) (2,13) (5,15) (13,14) (2,8) (3,1) (9,4) (10,1) (9,15) (17,0) (5,3) (9,12) (18,4) (2,1) (11,14) (2,15) (1,16) (8,17) (4,10) (8,1) (12,3) (6,14) (14,5) (15,1) (7,0) (2,3) (7,10) (9,16) (6,18) (8,10) (16,5) (11,2) (18,3) (17,10) (13,12) (5,1) (7,18) (14,0) (3,8) (13,15) (4,17) (1,4) (7,9) (16,11) (3,9) (18,5) (10,5) (18,13) (11,10) (16,4) (10,6) (1,9) (13,9) (18,10) (8,15) (4,15) (11,9) (18,17) (18,16) (5,9) (14,18) (10,3) (7,1) (4,14) (16,14) (14,15) (15,16) (16,2) (8,6) (4,11) (13,16) (0,8) (10,15) (8,12) (6,4) (1,18) (3,15) (18,15) (14,12) (3,16) (3,0) (5,4) (1,17) (5,6) (17,2) (1,12) (11,13) (4,0) (4,8) (4,12) (15,6) (6,12) (3,11) (11,8) (8,5) (6,3) (5,7) (7,6) (4,13) (7,8) (9,17) (15,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->15->5->17->14->13->2->18->8->1->3->7->10->4->9->12->6->16->11." - } - ] - }, - { - "id": "hamilton-hard-graph564", - "image": "data/hamilton/graph_visual/Base/hard/graph564.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,9) (17,16) (10,15) (6,5) (7,16) (6,19) (7,2) (7,9) (6,16) (11,6) (12,0) (12,8) (1,18) (6,7) (10,2) (3,8) (4,16) (6,2) (7,8) (15,16) (4,12) (9,13) (13,7) (14,19) (0,17) (9,5) (17,6) (5,14) (10,5) (10,18) (16,1) (1,7) (7,4) (9,4) (1,15) (12,3) (2,13) (0,15) (5,16) (13,11) (12,15) (9,19) (6,3) (10,17) (12,6) (8,4) (11,19) (4,1) (0,4) (7,11) (18,3) (16,12) (4,14) (2,14) (13,18) (13,1) (10,11) (17,12) (16,2) (1,19) (17,5) (0,14) (7,14) (4,11) (15,7) (5,12) (9,6) (11,2) (10,1) (10,7) (3,10) (3,13) (1,5) (5,13) (12,1) (12,11) (18,6) (15,19) (1,17) (14,12) (10,8) (12,9) (17,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->8->3->6->5->9->1->18->10->15->7->2->13->11->19->14->4->16->17." - } - ] - }, - { - "id": "hamilton-hard-graph325", - "image": "data/hamilton/graph_visual/Base/hard/graph325.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,6) (3,7) (7,14) (10,5) (13,14) (12,9) (3,15) (14,8) (2,4) (1,10) (15,5) (13,1) (9,11) (3,11) (3,13) (7,1) (3,4) (8,12) (11,6) (12,6) (3,0) (2,7) (15,7) (6,5) (9,1) (2,8) (8,9) (11,4) (5,9) (8,6) (12,7) (2,11) (2,12) (12,15) (6,13) (8,1) (4,7) (14,9) (4,13) (3,5) (3,8) (6,0) (1,0) (1,12) (6,3) (14,2) (8,13) (1,4) (15,10) (8,4) (3,2) (4,14) (0,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->7->14->13->1->10->5->15->12->9->11->6->2->4->8." - } - ] - }, - { - "id": "hamilton-hard-graph443", - "image": "data/hamilton/graph_visual/Base/hard/graph443.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (12,0) (4,10) (17,5) (3,0) (5,15) (16,2) (13,9) (12,17) (6,4) (10,12) (12,6) (2,5) (0,5) (8,10) (12,16) (9,14) (10,17) (12,1) (3,5) (13,12) (11,13) (14,11) (5,9) (10,2) (1,7) (0,7) (13,2) (7,4) (8,5) (1,2) (1,6) (2,6) (17,3) (8,6) (8,0) (12,5) (5,7) (1,13) (8,14) (11,9) (2,8) (10,1) (16,14) (16,4) (3,14) (2,12) (9,3) (12,15) (9,1) (6,7) (17,4) (16,10) (9,8) (1,5) (13,14) (3,12) (4,0) (8,11) (2,17) (3,2) (10,9) (15,7) (7,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->17->5->15->7->1->2->16->14->3->9->13->11->8->10->4->6." - } - ] - }, - { - "id": "hamilton-hard-graph279", - "image": "data/hamilton/graph_visual/Base/hard/graph279.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,2) (10,9) (5,10) (14,12) (0,7) (11,9) (2,7) (4,1) (13,7) (1,6) (8,2) (4,9) (12,13) (14,0) (13,11) (3,5) (7,9) (2,5) (8,0) (13,5) (2,4) (4,14) (11,14) (7,4) (13,8) (5,12) (10,3) (5,4) (9,2) (3,4) (4,11) (10,8) (0,9) (10,6) (0,1) (0,12) (3,7) (7,14) (4,6) (7,5) (0,5) (10,11) (9,8) (12,8) (7,10) (13,3) (2,13) (12,9) (0,11) (3,8) (9,3) (11,12) (2,14) (11,5) (12,1) (6,8) (4,0) (13,9) (6,11) (7,6) (14,3) (6,2) (9,6) (14,8) (14,6) (9,14) (7,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->2->3->5->10->9->11->13->12->14->4->1->6->8." - } - ] - }, - { - "id": "hamilton-hard-graph45", - "image": "data/hamilton/graph_visual/Base/hard/graph45.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,1) (10,2) (10,5) (10,7) (1,2) (3,10) (10,9) (4,3) (7,1) (9,4) (4,5) (1,0) (3,5) (5,6) (9,3) (3,0) (5,1) (7,2) (0,7) (10,4) (6,3) (0,10) (4,0) (7,8) (8,0) (7,5) (1,3) (7,4) (6,0) (8,4) (8,5) (10,1) (1,4) (5,2) (5,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->8->7->10->2->5->4->9->3->6." - } - ] - }, - { - "id": "hamilton-hard-graph238", - "image": "data/hamilton/graph_visual/Base/hard/graph238.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (5,7) (4,8) (13,4) (9,1) (11,7) (6,7) (3,1) (3,2) (1,10) (8,6) (0,10) (2,13) (10,11) (4,6) (3,13) (0,5) (12,13) (2,1) (12,9) (10,7) (8,7) (13,6) (12,6) (7,13) (12,11) (2,0) (7,3) (8,2) (12,4) (2,5) (12,8) (7,12) (4,10) (5,13) (11,1) (5,1) (4,9) (5,10) (4,0) (5,3) (11,3) (9,11) (9,5) (6,10) (8,13) (13,0) (3,8) (9,3) (12,5) (10,3) (6,0) (6,9) (8,10) (8,5) (11,13) (1,0) (2,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->1->9->12->13->4->8->6->7->5->2->3->11." - } - ] - }, - { - "id": "hamilton-hard-graph353", - "image": "data/hamilton/graph_visual/Base/hard/graph353.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (8,13) (2,15) (13,4) (5,2) (11,8) (5,0) (4,9) (12,8) (3,4) (0,2) (9,5) (6,7) (8,2) (14,1) (11,12) (13,6) (11,10) (13,15) (10,3) (11,6) (9,3) (10,15) (14,5) (11,3) (2,13) (8,9) (9,0) (4,1) (12,4) (3,7) (13,5) (11,15) (6,4) (14,15) (12,13) (2,10) (2,6) (7,13) (10,5) (14,10) (10,4) (6,0) (7,5) (4,15) (4,11) (7,12) (10,12) (8,5) (15,1) (9,15) (12,0) (15,7) (13,10) (15,0) (1,11) (1,6) (2,11) (6,8) (3,5) (13,1) (12,14) (15,12) (12,1) (3,15) (0,1) (1,2) (11,7) (14,9) (1,5) (3,8) (6,14) (8,10) (11,9) (11,0) (4,7) (9,10) (10,1) (14,4) (7,9) (1,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->2->15->13->8->11->12->4->9->3->10->14->1->6->7." - } - ] - }, - { - "id": "hamilton-hard-graph347", - "image": "data/hamilton/graph_visual/Base/hard/graph347.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (5,2) (11,5) (7,15) (7,6) (0,9) (10,1) (7,0) (1,4) (4,8) (6,3) (7,2) (7,14) (9,15) (11,15) (9,12) (13,2) (6,4) (1,15) (12,0) (14,3) (3,4) (4,7) (14,4) (1,3) (1,7) (12,4) (4,0) (11,1) (2,1) (10,4) (1,5) (13,7) (0,8) (10,5) (0,5) (3,7) (1,0) (8,12) (9,3) (3,15) (11,10) (9,8) (13,3) (11,13) (11,7) (0,14) (10,2) (10,12) (5,14) (6,10) (3,12) (2,4) (5,15) (2,8) (8,6) (0,3) (4,9) (0,11) (15,2) (6,2) (12,2) (8,3) (15,4) (8,15) (14,11) (8,1) (11,2) (14,12) (15,6) (8,13) (4,11) (12,11) (0,10) (7,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->15->7->6->3->14->4->1->10->5->2->13->11->12->8." - } - ] - }, - { - "id": "hamilton-hard-graph159", - "image": "data/hamilton/graph_visual/Base/hard/graph159.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,2) (6,10) (1,0) (3,2) (1,12) (7,2) (6,11) (12,10) (8,10) (10,4) (4,1) (8,7) (4,11) (7,12) (6,12) (1,6) (9,10) (1,10) (3,5) (9,0) (5,10) (9,1) (4,8) (6,5) (1,7) (4,9) (2,4) (4,5) (5,9) (3,7) (9,7) (11,10) (0,6) (4,12) (12,2) (8,3) (6,4) (11,12) (11,9) (6,3) (5,0) (3,11) (5,7) (4,3) (1,2) (0,4) (7,0) (8,9) (3,9) (6,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->12->10->6->11->2->3->5->4->8->7->9." - } - ] - }, - { - "id": "hamilton-hard-graph44", - "image": "data/hamilton/graph_visual/Base/hard/graph44.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,2) (6,4) (6,3) (9,0) (3,9) (9,8) (4,3) (7,10) (5,1) (7,4) (2,4) (3,0) (9,10) (5,9) (6,5) (0,7) (2,9) (10,6) (0,5) (2,6) (4,9) (8,7) (8,10) (8,2) (3,2) (8,5) (2,1) (0,4) (0,1) (2,5) (3,5) (3,7) (9,1) (4,8) (8,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->4->6->3->9->10->7->8->5->1." - } - ] - }, - { - "id": "hamilton-hard-graph271", - "image": "data/hamilton/graph_visual/Base/hard/graph271.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,6) (9,2) (10,5) (11,12) (5,12) (3,9) (2,12) (1,5) (5,14) (6,4) (10,11) (4,3) (2,6) (4,14) (12,4) (11,0) (14,2) (10,8) (7,10) (11,14) (12,10) (10,3) (8,13) (11,9) (7,6) (11,13) (3,13) (3,5) (7,13) (1,3) (10,0) (4,1) (9,13) (14,10) (8,4) (6,11) (3,0) (10,9) (5,13) (12,0) (4,0) (9,1) (0,7) (7,4) (6,10) (14,0) (9,8) (13,6) (5,8) (2,8) (8,7) (3,7) (2,5) (7,2) (10,2) (3,12) (12,9) (13,1) (13,4) (8,6) (9,4) (2,4) (1,11) (8,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->4->3->9->2->12->11->10->5->1->13->7->8->14." - } - ] - }, - { - "id": "hamilton-hard-graph477", - "image": "data/hamilton/graph_visual/Base/hard/graph477.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (5,8) (15,8) (3,14) (2,12) (0,9) (1,2) (3,4) (16,4) (10,0) (7,5) (11,15) (5,9) (10,6) (7,6) (0,13) (10,8) (13,1) (9,2) (16,3) (9,8) (13,11) (3,1) (14,8) (15,7) (2,13) (6,0) (7,9) (16,15) (1,9) (4,9) (17,16) (5,12) (4,8) (13,7) (4,1) (16,7) (3,17) (0,3) (5,0) (17,12) (4,7) (4,12) (8,12) (9,12) (0,16) (5,1) (5,6) (11,1) (6,8) (15,9) (3,2) (14,1) (6,1) (8,1) (7,11) (17,8) (0,1) (5,15) (6,12) (2,6) (14,17) (9,14) (0,17) (2,10) (14,0) (5,14) (1,7) (1,15) (5,17) (4,6) (10,14) (11,10) (4,14) (4,15) (12,15) (12,7) (13,14) (0,8) (11,17) (3,15) (13,10) (0,7) (7,10) (2,7) (9,11) (14,2) (16,13) (5,11) (3,13) (13,4) (3,7) (12,1) (16,2) (6,16)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->5->8->15->11->13->1->2->12->17->16->4->3->14->10->6->7." - } - ] - }, - { - "id": "hamilton-hard-graph419", - "image": "data/hamilton/graph_visual/Base/hard/graph419.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (1,8) (6,4) (10,5) (6,16) (12,0) (8,4) (0,2) (2,13) (13,7) (9,3) (16,11) (12,2) (3,5) (3,11) (10,2) (10,8) (5,1) (10,13) (16,9) (16,13) (11,1) (15,8) (9,12) (9,0) (1,9) (11,2) (13,8) (5,12) (8,9) (16,2) (8,5) (2,8) (7,9) (16,0) (0,1) (8,0) (15,12) (0,14) (3,0) (9,10) (16,10) (4,16) (16,7) (8,16) (4,13) (14,1) (5,4) (15,13) (7,15) (12,11) (16,12) (12,3) (15,0) (2,7) (15,6) (4,7) (13,6) (14,13) (3,1) (6,5) (15,5) (3,2) (10,12) (7,0) (10,0) (6,10) (7,12) (14,16) (12,1) (6,8) (6,2) (10,11) (6,11) (9,4) (0,13) (8,11) (6,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->2->13->7->9->3->5->10->8->4->16->14->1->11->6->15." - } - ] - }, - { - "id": "hamilton-hard-graph241", - "image": "data/hamilton/graph_visual/Base/hard/graph241.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,8) (13,14) (11,8) (2,3) (0,4) (12,6) (13,3) (12,7) (3,5) (4,13) (6,7) (4,8) (14,3) (12,5) (12,14) (9,2) (12,8) (9,7) (3,10) (4,5) (5,6) (8,13) (9,13) (13,5) (10,1) (9,14) (13,1) (1,2) (12,4) (8,1) (10,7) (9,12) (3,7) (10,14) (5,0) (14,7) (10,5) (11,12) (11,13) (8,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->13->14->3->2->9->7->12->6->5->10->1->8->11." - } - ] - }, - { - "id": "hamilton-hard-graph448", - "image": "data/hamilton/graph_visual/Base/hard/graph448.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (2,11) (16,7) (8,11) (12,6) (10,1) (11,10) (2,9) (6,5) (10,12) (10,6) (5,16) (2,6) (5,4) (15,17) (3,2) (2,4) (6,1) (4,3) (1,4) (6,7) (14,3) (11,4) (14,6) (3,1) (14,13) (5,12) (3,9) (17,0) (2,1) (13,4) (6,3) (4,6) (2,14) (11,9) (14,0) (3,13) (11,0) (1,14) (16,17) (8,15) (15,12) (17,13) (14,5) (17,8) (7,11) (7,1) (3,10) (0,2) (17,5) (12,7) (13,0) (13,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->17->15->8->11->2->9->3->4->5->16->7->6->12->10->1->14->13." - } - ] - }, - { - "id": "hamilton-hard-graph193", - "image": "data/hamilton/graph_visual/Base/hard/graph193.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (10,3) (12,5) (0,3) (10,13) (12,0) (10,12) (10,1) (7,12) (10,2) (0,5) (4,7) (9,10) (5,4) (10,7) (13,7) (6,10) (2,8) (6,7) (12,11) (0,8) (5,11) (2,11) (2,1) (13,0) (2,5) (4,10) (11,10) (13,8) (13,12) (7,5) (9,12) (12,4) (11,0) (6,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->10->1->2->8->13->7->6->11->5->4->12->9." - } - ] - }, - { - "id": "hamilton-hard-graph393", - "image": "data/hamilton/graph_visual/Base/hard/graph393.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,10) (16,14) (2,7) (5,2) (6,0) (1,5) (11,16) (1,3) (4,1) (12,13) (0,14) (15,6) (13,16) (8,0) (10,14) (8,1) (2,16) (4,0) (3,0) (3,6) (10,5) (10,8) (3,13) (5,6) (3,15) (7,5) (7,4) (2,12) (0,12) (7,16) (4,9) (6,8) (12,16) (10,11) (11,9) (10,12) (2,0) (8,15) (13,0) (13,9) (9,16) (2,15) (7,9) (5,15) (4,3) (10,0) (11,7) (8,2) (11,1) (14,3) (13,10) (2,3) (9,5) (10,9) (0,5) (6,2) (15,14) (2,9) (16,15) (4,6) (6,12) (6,9) (2,4) (11,13) (2,11) (16,0) (10,15) (8,16) (4,11) (13,8) (12,15) (9,12) (3,12) (4,15) (8,4) (1,6) (10,16) (13,15) (11,14) (4,16) (15,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->15->3->1->5->2->7->10->14->16->11->9->4->8->13->12." - } - ] - }, - { - "id": "hamilton-hard-graph577", - "image": "data/hamilton/graph_visual/Base/hard/graph577.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,7) (6,13) (9,14) (4,12) (19,10) (19,18) (6,9) (4,6) (14,13) (3,15) (15,10) (9,16) (5,19) (2,4) (11,7) (8,1) (3,19) (14,2) (16,3) (18,13) (19,9) (15,19) (10,14) (16,14) (19,11) (5,2) (15,12) (8,10) (2,8) (6,14) (15,4) (10,9) (9,4) (15,5) (7,6) (7,9) (10,16) (2,1) (9,18) (7,17) (0,2) (9,15) (0,11) (16,1) (16,7) (16,17) (1,13) (13,5) (3,13) (18,0) (7,12) (16,12) (12,1) (16,18) (15,8) (19,14) (12,9) (8,6) (6,19) (10,13) (0,6) (8,11) (8,12) (14,12) (7,0) (18,15) (11,12) (1,18) (14,0) (7,3) (2,7) (0,1) (12,2) (16,8) (14,17) (13,7) (5,4) (5,9) (0,19) (11,15) (1,4) (3,11) (3,10) (14,15) (18,5) (12,5) (10,17) (2,15) (19,1) (16,13) (18,8) (14,1) (4,16) (2,17) (9,1) (3,6) (4,11) (5,16) (12,19) (0,15) (13,15) (12,10) (1,5) (4,18) (2,13) (3,17) (8,19) (11,5) (1,3) (2,11) (0,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->4->12->15->3->19->10->14->9->6->13->18->16->17->7->1->8->11->5." - } - ] - }, - { - "id": "hamilton-hard-graph264", - "image": "data/hamilton/graph_visual/Base/hard/graph264.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (4,3) (0,8) (14,5) (1,14) (12,2) (10,13) (13,9) (12,9) (2,13) (5,3) (5,7) (7,13) (3,12) (6,1) (6,8) (14,13) (14,4) (0,5) (11,3) (11,14) (14,8) (10,2) (14,3) (8,11) (0,1) (12,0) (13,0) (2,4) (10,7) (7,11) (13,8) (11,12) (2,14) (6,5) (0,10) (1,9) (6,11) (1,11) (4,5) (1,8) (11,13) (1,13) (6,10) (12,6) (4,10) (8,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->6->1->14->5->3->4->2->12->9->13->10->7->11." - } - ] - }, - { - "id": "hamilton-hard-graph507", - "image": "data/hamilton/graph_visual/Base/hard/graph507.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,16) (11,16) (1,12) (8,1) (14,12) (4,11) (18,2) (17,9) (13,1) (13,14) (3,12) (12,16) (18,8) (17,13) (12,8) (12,9) (12,7) (13,6) (11,2) (1,5) (5,12) (3,4) (16,14) (0,6) (10,1) (3,2) (4,5) (7,6) (10,7) (18,13) (9,2) (11,7) (10,8) (15,11) (11,5) (7,14) (10,14) (5,8) (3,10) (4,9) (0,17) (16,18) (7,17) (13,9) (5,18) (4,15) (2,14) (9,5) (2,8) (13,15) (10,15) (13,7) (17,12) (9,3) (4,2) (6,9) (8,3) (6,1) (18,9) (15,1) (14,18) (16,9) (13,4) (14,17) (14,1) (0,14) (17,10) (10,9) (0,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->13->1->12->14->16->8->18->2->11->7->17->9->5->4->3->10->15." - } - ] - }, - { - "id": "hamilton-hard-graph224", - "image": "data/hamilton/graph_visual/Base/hard/graph224.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (11,7) (5,1) (3,12) (1,2) (8,0) (12,4) (0,2) (4,13) (7,1) (8,12) (3,0) (8,9) (6,11) (1,10) (6,5) (11,10) (0,10) (3,5) (3,1) (5,10) (13,6) (5,2) (0,6) (4,11) (10,4) (1,8) (3,10) (2,12) (3,11) (9,10) (10,12) (8,13) (6,12) (9,4) (2,13) (7,13) (8,11) (4,2) (3,2) (11,9) (0,11) (4,7) (2,6) (0,5) (1,13) (6,4) (9,5) (3,13) (9,13) (9,3) (11,13) (10,7) (9,2) (0,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->12->3->5->1->2->13->4->9->10->7->11->6." - } - ] - }, - { - "id": "hamilton-hard-graph173", - "image": "data/hamilton/graph_visual/Base/hard/graph173.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,4) (11,10) (6,7) (2,1) (4,10) (2,12) (11,4) (4,3) (2,3) (9,2) (12,3) (0,1) (12,10) (10,0) (8,12) (5,9) (1,4) (1,7) (6,9) (3,7) (7,2) (0,9) (5,6) (9,1) (11,2) (12,6) (4,7) (4,0) (2,0) (6,8) (5,11) (9,4) (9,7) (7,11) (11,9) (8,10) (0,11) (0,6) (1,11) (3,9) (3,0) (12,1) (2,10) (9,12) (11,3) (0,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->2->4->10->11->5->9->6->7->3->12->8." - } - ] - }, - { - "id": "hamilton-hard-graph433", - "image": "data/hamilton/graph_visual/Base/hard/graph433.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (8,14) (11,9) (8,9) (5,14) (16,6) (11,2) (0,8) (4,1) (16,2) (1,3) (3,5) (4,11) (15,12) (15,13) (11,5) (7,1) (6,0) (5,4) (16,10) (4,7) (5,15) (12,11) (12,17) (1,16) (13,11) (2,4) (4,16) (3,4) (4,14) (15,11) (10,15) (17,3) (16,13) (11,3) (9,5) (15,7) (8,1) (8,12) (13,17) (16,11) (14,10) (17,0) (6,12) (4,13) (3,2) (16,8) (6,15) (0,4) (3,16) (12,5) (10,2) (4,12) (2,14) (9,7) (9,15) (8,3) (14,15) (0,16) (7,13) (7,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->14->5->3->1->4->11->9->7->15->13->17->12->6->16->2->10." - } - ] - }, - { - "id": "hamilton-hard-graph151", - "image": "data/hamilton/graph_visual/Base/hard/graph151.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (10,12) (8,6) (4,5) (3,2) (12,3) (12,8) (0,9) (9,5) (1,12) (2,0) (11,1) (0,8) (10,5) (7,8) (0,4) (6,11) (10,0) (2,4) (9,11) (4,6) (1,4) (9,1) (0,5) (1,3) (11,10) (8,11) (6,3) (10,6) (1,8) (7,4) (3,5) (12,2) (5,11) (2,7) (5,6) (0,12) (1,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->5->4->2->3->12->10->6->11->1->8->7." - } - ] - }, - { - "id": "hamilton-hard-graph536", - "image": "data/hamilton/graph_visual/Base/hard/graph536.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (2,11) (7,14) (2,14) (2,0) (4,9) (4,13) (5,7) (6,15) (4,12) (1,16) (10,5) (14,4) (9,18) (0,12) (18,6) (12,11) (12,6) (2,18) (1,7) (11,3) (13,15) (11,0) (2,10) (16,8) (11,4) (15,2) (9,17) (16,11) (1,11) (12,8) (16,13) (6,14) (10,1) (5,9) (4,15) (0,5) (7,8) (6,5) (0,10) (15,9) (13,17) (6,11) (18,0) (7,3) (1,6) (1,14) (0,9) (18,5) (13,5) (2,6) (14,17) (15,14) (17,4) (15,12) (2,8) (17,3) (1,5) (12,16) (8,4) (9,14) (8,1) (17,12) (1,3) (16,4) (3,5) (3,6) (10,17) (11,5) (15,10) (4,5) (17,1) (18,12) (2,12) (17,0) (16,9) (4,1) (16,5) (12,7) (17,7) (5,17) (2,9) (12,10) (16,15) (10,18) (11,10) (15,7) (10,8) (0,3) (10,13) (18,17) (7,2) (4,10) (13,3) (17,6) (15,8) (15,3) (6,13) (15,1) (16,3) (11,17) (18,13) (7,9) (13,14) (7,0) (8,17) (12,9) (0,16)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->11->12->4->9->18->6->15->13->16->1->7->14->17->3->5->10->8." - } - ] - }, - { - "id": "hamilton-hard-graph15", - "image": "data/hamilton/graph_visual/Base/hard/graph15.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,0) (0,7) (4,10) (2,6) (1,8) (7,3) (3,0) (10,0) (5,2) (7,5) (2,9) (6,3) (6,0) (2,3) (2,7) (5,1) (10,6) (4,7) (8,2) (1,6) (9,5) (8,4) (9,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->6->3->7->5->9->1->8->4->10." - } - ] - }, - { - "id": "hamilton-hard-graph233", - "image": "data/hamilton/graph_visual/Base/hard/graph233.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (4,5) (10,3) (8,1) (5,10) (13,5) (2,11) (0,11) (2,7) (3,0) (9,3) (2,6) (13,0) (5,11) (3,13) (9,10) (1,10) (0,1) (5,7) (7,9) (1,6) (1,12) (6,10) (6,7) (6,0) (4,6) (13,2) (4,3) (2,9) (11,9) (1,11) (0,2) (2,3) (0,9) (1,5) (9,12) (8,7) (13,8) (8,3) (9,5) (9,1) (8,2) (8,6) (0,10) (8,11) (9,6) (7,12) (0,12) (12,10) (13,1) (4,9) (4,12) (7,11) (9,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->2->7->5->4->6->1->8->13->3->10->9->12." - } - ] - }, - { - "id": "hamilton-hard-graph229", - "image": "data/hamilton/graph_visual/Base/hard/graph229.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,0) (13,5) (7,6) (10,8) (8,13) (0,2) (0,4) (11,9) (5,10) (11,3) (1,11) (3,12) (0,10) (9,6) (2,4) (1,0) (0,12) (6,12) (11,13) (4,7) (10,7) (12,13) (6,3) (6,5) (11,0) (12,8) (6,11) (11,4) (0,3) (3,8) (7,13) (13,0) (10,11) (2,7) (5,8) (3,4) (2,1) (6,8) (5,0) (3,7) (4,5) (2,13) (7,9) (3,9) (4,6) (5,9) (2,9) (6,1) (0,9) (2,3) (12,5) (5,1) (1,9) (13,6) (3,13) (1,7) (4,9) (11,2) (12,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->6->9->11->3->12->13->8->10->5->4->2->1." - } - ] - }, - { - "id": "hamilton-hard-graph4", - "image": "data/hamilton/graph_visual/Base/hard/graph4.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,5) (7,5) (9,5) (0,2) (3,10) (5,8) (4,0) (5,10) (8,10) (9,10) (8,9) (9,1) (6,10) (2,10) (5,2) (1,4) (8,3) (7,0) (1,10) (4,9) (0,9) (7,4) (2,4) (7,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->10->3->8->5->6->7->4->1->9." - } - ] - }, - { - "id": "hamilton-hard-graph176", - "image": "data/hamilton/graph_visual/Base/hard/graph176.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,5) (9,7) (1,7) (8,9) (3,7) (12,3) (8,2) (12,0) (5,11) (7,10) (8,0) (8,10) (5,2) (1,4) (11,2) (1,2) (12,5) (9,10) (10,3) (6,12) (1,11) (9,3) (1,10) (0,4) (10,5) (5,8) (10,6) (4,9) (8,1) (5,9) (12,11) (7,4) (1,3) (11,3) (1,9) (6,3) (8,12) (2,6) (8,7) (7,2) (0,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->3->5->11->2->8->9->7->4->1->10->6." - } - ] - }, - { - "id": "hamilton-hard-graph368", - "image": "data/hamilton/graph_visual/Base/hard/graph368.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (15,10) (10,4) (1,2) (4,2) (0,13) (11,6) (3,1) (5,6) (6,14) (8,1) (6,10) (2,13) (3,9) (10,7) (0,8) (4,3) (12,13) (8,2) (5,16) (15,5) (3,13) (7,16) (15,1) (16,12) (15,3) (13,14) (14,16) (0,5) (12,3) (2,14) (14,5) (14,8) (4,1) (9,8) (15,0) (0,16) (5,7) (10,1) (4,16) (16,1) (10,11) (6,2) (15,9) (7,1) (14,7) (1,0) (8,7) (7,3) (1,13) (3,2) (11,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->2->1->3->9->8->7->14->6->11->5->15->10->4->16->12." - } - ] - }, - { - "id": "hamilton-hard-graph385", - "image": "data/hamilton/graph_visual/Base/hard/graph385.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,10) (4,8) (1,0) (13,8) (9,6) (15,3) (10,7) (3,1) (15,16) (15,9) (16,3) (5,7) (8,6) (9,14) (8,12) (11,3) (10,6) (4,13) (2,1) (10,13) (12,1) (11,10) (7,3) (11,5) (9,8) (4,12) (16,14) (14,10) (5,6) (14,2) (11,7) (5,8) (0,2) (7,13) (14,7) (14,8) (9,5) (8,0) (12,11) (16,11) (7,4) (2,3) (4,16) (12,5) (15,4) (9,3) (0,15) (4,9) (0,5) (1,7) (7,8) (13,2) (2,6) (9,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->15->16->14->9->6->8->4->12->10->11->5->7->13->2." - } - ] - }, - { - "id": "hamilton-hard-graph17", - "image": "data/hamilton/graph_visual/Base/hard/graph17.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,9) (0,4) (9,2) (10,4) (7,5) (9,4) (7,3) (2,3) (10,8) (1,3) (7,2) (8,4) (0,1) (0,7) (2,10) (6,3) (5,9) (8,2) (2,4) (3,0) (10,5) (9,3) (9,0) (1,2) (2,6) (8,9) (1,4) (3,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->10->8->9->5->7->3->1->2->6." - } - ] - }, - { - "id": "hamilton-hard-graph531", - "image": "data/hamilton/graph_visual/Base/hard/graph531.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (18,7) (14,2) (16,18) (8,2) (7,11) (18,11) (8,6) (15,12) (18,6) (13,11) (12,17) (13,4) (6,1) (4,10) (16,13) (16,0) (14,5) (12,18) (5,8) (6,2) (10,14) (18,14) (9,4) (16,2) (7,13) (16,14) (12,13) (3,4) (9,15) (1,0) (13,18) (7,10) (6,4) (0,12) (0,10) (11,8) (11,12) (8,9) (4,12) (1,10) (18,8) (6,10) (6,17) (10,3) (17,2) (5,6) (5,15) (3,7) (15,13) (14,17) (14,11) (10,9) (7,9) (18,9) (1,12) (9,6) (9,0) (7,8) (15,2) (14,4) (1,8) (15,7) (11,0) (13,3) (8,3) (13,0) (8,0) (1,16) (16,12) (5,16) (6,15) (4,17) (17,5) (9,2) (5,3) (9,5) (12,14) (2,7) (8,14) (9,13) (1,14) (7,12) (13,6) (0,17) (8,15) (12,2) (18,5) (10,8) (14,7) (8,4) (4,0) (15,3) (17,18) (10,5) (3,16) (17,1) (2,13) (12,8) (18,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->16->18->7->11->13->4->10->14->2->8->6->1->12->17->5->3->15->9." - } - ] - }, - { - "id": "hamilton-hard-graph541", - "image": "data/hamilton/graph_visual/Base/hard/graph541.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,19) (0,11) (13,15) (12,11) (7,9) (16,2) (4,9) (19,17) (19,9) (18,9) (17,16) (6,13) (4,11) (15,10) (16,19) (4,15) (16,11) (1,6) (11,19) (16,12) (3,15) (16,7) (10,8) (2,13) (17,1) (7,15) (4,8) (15,8) (0,7) (8,14) (19,15) (19,12) (13,14) (5,14) (17,10) (6,4) (19,1) (2,1) (13,16) (17,11) (3,14) (19,14) (5,8) (18,1) (1,5) (19,4) (12,6) (0,4) (17,8) (16,1) (2,15) (4,1) (7,12) (8,16) (3,2) (15,9) (18,3) (14,1) (17,15) (6,15) (4,3) (7,11) (5,18) (12,18) (9,13) (0,17) (6,3) (5,7) (2,19) (5,15) (19,7) (17,5) (8,11) (11,5) (1,8) (7,18)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->12->16->2->13->15->10->8->4->9->7->5->14->19->17->1->6->3->18." - } - ] - }, - { - "id": "hamilton-hard-graph27", - "image": "data/hamilton/graph_visual/Base/hard/graph27.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,9) (2,8) (6,9) (8,1) (1,10) (10,2) (10,6) (5,1) (9,2) (4,9) (2,1) (5,3) (8,10) (5,6) (10,3) (4,10) (3,0) (7,5) (7,4) (7,6) (10,7) (0,9) (3,1) (1,6) (4,3) (5,4) (7,9) (2,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->9->6->10->2->8->1->5->7->4." - } - ] - }, - { - "id": "hamilton-hard-graph592", - "image": "data/hamilton/graph_visual/Base/hard/graph592.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (10,0) (5,6) (6,19) (16,3) (8,12) (19,13) (18,4) (2,10) (5,7) (7,17) (2,3) (4,2) (19,9) (10,17) (10,8) (15,1) (9,7) (19,17) (18,0) (3,18) (0,15) (4,3) (19,1) (19,10) (0,1) (13,17) (6,9) (5,0) (7,8) (18,14) (15,2) (11,9) (12,3) (13,10) (17,16) (17,1) (7,11) (2,14) (12,6) (3,14) (7,19) (7,6) (16,1) (6,18) (2,19) (6,3) (8,19) (1,14) (11,1) (17,18) (7,10) (1,12) (19,3) (13,6) (18,7) (4,6) (0,14) (11,18) (17,4) (5,11) (13,2) (10,11) (14,12) (11,17) (19,5) (4,0) (14,4) (9,3) (12,17) (15,16) (12,0) (6,2) (16,19) (11,14) (10,5) (2,1) (12,18) (15,11) (19,15) (12,2) (3,10) (4,16) (19,4) (0,6) (2,5) (8,3) (15,14) (10,12) (2,9) (17,8) (17,3) (5,15) (4,8) (1,18) (8,1) (0,8) (15,8) (18,13) (3,7) (15,17) (14,6) (8,11) (10,18) (2,11) (4,7) (17,0) (8,13) (9,18) (3,0) (4,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->2->3->16->17->7->5->6->19->13->18->4->14->1->12->8->15->11->9." - } - ] - }, - { - "id": "hamilton-hard-graph599", - "image": "data/hamilton/graph_visual/Base/hard/graph599.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (11,19) (13,9) (3,11) (6,19) (10,17) (19,17) (15,2) (0,14) (11,5) (3,14) (14,12) (19,2) (5,12) (15,18) (10,15) (2,13) (7,15) (18,7) (16,8) (4,17) (9,0) (9,15) (18,3) (1,15) (8,19) (11,14) (12,7) (8,12) (10,12) (2,12) (16,4) (13,19) (11,9) (9,18) (9,1) (5,9) (16,0) (15,0) (16,1) (3,15) (15,5) (12,9) (4,5) (7,5) (0,10) (5,3) (12,17) (16,5) (14,2) (16,3) (18,6) (14,15) (4,18) (9,7) (6,4) (1,17) (17,9) (9,14) (6,14) (5,18) (11,18) (11,10) (19,9) (10,16) (13,0) (1,10) (19,14) (1,6) (16,9) (4,3) (4,9) (9,10) (17,18) (16,19) (15,17) (7,2) (3,19) (12,19) (8,6) (17,16) (1,8) (5,8) (18,16) (12,16) (13,10) (6,7) (2,10) (7,16) (5,13) (2,0) (19,15) (2,18) (14,5) (3,2) (15,16) (5,17) (4,1) (13,15) (10,6) (19,10) (19,5) (4,2) (16,13) (16,11) (10,14) (16,2) (16,6) (11,15) (5,10) (5,6) (18,13) (14,1) (2,17) (7,14) (1,2) (3,13) (7,11) (12,1) (4,11) (5,1) (17,3) (0,4) (17,11) (0,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->14->3->11->19->6->18->15->2->13->9->1->16->8->12->7->5->4->17->10." - } - ] - }, - { - "id": "hamilton-hard-graph309", - "image": "data/hamilton/graph_visual/Base/hard/graph309.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (10,11) (7,3) (15,5) (14,15) (14,2) (13,9) (7,9) (15,2) (12,6) (5,4) (12,5) (10,7) (3,14) (5,7) (5,13) (9,14) (4,14) (3,4) (2,10) (0,15) (3,8) (9,8) (11,15) (10,12) (5,3) (10,3) (8,6) (9,11) (14,5) (3,2) (4,7) (7,15) (6,2) (8,13) (0,10) (5,6) (9,3) (14,1) (9,10) (12,13) (8,2) (4,9) (7,14) (8,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->15->5->4->3->7->9->11->10->12->13->8->6->2->14->1." - } - ] - }, - { - "id": "hamilton-hard-graph330", - "image": "data/hamilton/graph_visual/Base/hard/graph330.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (8,1) (4,3) (9,15) (4,11) (4,13) (6,3) (0,12) (0,2) (14,0) (10,4) (5,7) (0,1) (10,14) (0,3) (7,13) (10,0) (6,7) (8,2) (8,9) (5,14) (13,2) (9,14) (0,8) (8,4) (0,7) (14,13) (5,6) (10,7) (10,8) (5,12) (5,8) (6,10) (5,13) (15,11) (5,4) (9,10) (0,6) (8,15) (12,11) (9,12) (11,13) (2,6) (12,1) (15,14) (6,13) (8,11) (12,3) (2,7) (12,4) (7,3) (1,2) (4,6) (3,15) (1,9) (13,1) (12,10) (15,1) (7,1) (13,10) (3,13) (0,11) (6,14) (6,15) (2,12) (7,14) (2,10) (3,14) (11,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->5->7->13->4->3->6->10->14->9->15->11->8->1->2." - } - ] - }, - { - "id": "hamilton-hard-graph511", - "image": "data/hamilton/graph_visual/Base/hard/graph511.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (18,1) (3,4) (4,17) (6,5) (15,0) (13,12) (6,13) (11,18) (18,0) (18,7) (6,4) (11,16) (10,7) (12,0) (3,13) (13,1) (9,11) (7,16) (7,11) (9,14) (0,5) (1,6) (17,2) (3,10) (11,8) (6,16) (13,9) (1,9) (3,7) (17,12) (2,3) (17,14) (11,2) (1,11) (14,18) (17,11) (3,1) (3,8) (7,8) (13,10) (8,4) (8,16) (1,8) (17,1) (3,6) (15,9) (15,18) (12,2) (4,9) (6,14) (5,7) (5,15) (2,7) (13,15) (5,17) (0,11) (8,17) (10,16) (15,16) (3,9) (2,5) (16,13) (0,4) (16,12) (17,15) (0,8) (18,8) (7,1) (1,0) (0,6) (5,16) (13,11) (3,15) (14,16) (9,2) (12,11) (14,2) (3,14) (14,10) (10,11) (4,2) (10,5) (9,7) (6,9) (14,4) (2,1) (13,5) (1,12) (14,15) (12,9) (8,2) (1,4) (4,16) (14,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->15->9->11->18->1->13->12->17->4->3->10->7->16->8->2->5->6->14." - } - ] - }, - { - "id": "hamilton-hard-graph156", - "image": "data/hamilton/graph_visual/Base/hard/graph156.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (4,12) (6,0) (4,3) (7,1) (10,11) (2,8) (11,8) (10,3) (12,8) (2,11) (6,12) (0,12) (4,9) (11,7) (9,8) (3,12) (5,1) (2,3) (2,5) (4,2) (10,12) (4,8) (4,6) (7,12) (3,5) (0,7) (12,2) (9,1) (8,0) (5,11) (5,7) (1,3) (12,5) (5,10) (9,7) (10,0) (6,9) (2,6) (9,5) (6,11) (10,6) (9,11) (7,8) (8,10) (10,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->12->4->3->10->11->8->2->5->1->7->9." - } - ] - }, - { - "id": "hamilton-hard-graph399", - "image": "data/hamilton/graph_visual/Base/hard/graph399.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,9) (14,3) (8,4) (13,3) (1,13) (3,10) (16,4) (9,1) (15,11) (16,10) (13,14) (15,7) (14,2) (4,9) (9,5) (1,11) (9,13) (2,8) (8,14) (9,8) (3,15) (14,16) (11,5) (1,8) (12,5) (1,16) (8,6) (9,15) (13,16) (10,8) (12,3) (4,2) (4,13) (12,8) (7,8) (9,0) (1,0) (16,0) (5,16) (13,2) (11,8) (4,0) (3,8) (3,16) (14,1) (1,15) (6,0) (7,0) (0,10) (3,5) (0,5) (7,12) (12,14) (0,14) (3,0) (16,15) (12,15) (12,0) (15,14) (3,9) (9,2) (15,13) (6,2) (12,4) (0,11) (3,1) (9,11) (7,6) (2,5) (16,2) (0,13) (5,15) (14,5) (14,11) (12,11) (16,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->10->3->14->13->1->11->15->7->8->4->12->5->16->2->6." - } - ] - }, - { - "id": "hamilton-hard-graph460", - "image": "data/hamilton/graph_visual/Base/hard/graph460.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (4,10) (2,15) (16,14) (5,1) (15,14) (6,13) (9,14) (11,10) (12,3) (0,16) (14,10) (6,0) (7,4) (10,0) (4,3) (15,4) (12,1) (17,0) (11,13) (13,15) (0,2) (12,16) (15,1) (15,17) (6,10) (15,3) (7,12) (17,11) (5,13) (2,8) (6,3) (1,8) (14,11) (12,11) (13,4) (15,12) (2,6) (15,8) (3,9) (3,2) (16,9) (6,5) (5,16) (0,4) (11,6) (13,8) (12,5) (5,4) (9,2) (17,6) (8,7) (8,12) (8,9) (14,5) (6,7) (9,15) (5,11) (12,14) (6,14) (3,13) (1,0) (12,6) (10,8) (16,6) (0,14) (17,5) (1,4) (7,2) (17,13) (1,16) (7,13) (1,10) (7,17) (10,3) (12,4) (6,1) (11,0) (3,1) (12,17) (2,10) (7,5) (8,14) (9,10) (4,2) (12,0) (17,9) (8,5) (0,15)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->16->14->15->2->8->1->5->13->6->10->4->7->12->3->9->17->11." - } - ] - }, - { - "id": "hamilton-hard-graph341", - "image": "data/hamilton/graph_visual/Base/hard/graph341.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (2,10) (0,13) (3,2) (1,11) (7,3) (7,8) (1,12) (8,11) (4,1) (9,6) (2,14) (9,10) (8,2) (15,9) (2,12) (7,9) (3,4) (9,14) (9,3) (0,9) (10,11) (11,13) (2,15) (4,5) (6,1) (9,2) (3,14) (2,1) (12,13) (2,5) (5,7) (10,15) (10,4) (13,9) (5,12) (6,11) (7,4) (12,11) (6,5) (9,5) (6,8) (14,11) (15,14) (13,14) (6,4) (11,5) (12,9) (7,13) (0,14) (14,10) (13,15) (3,5) (5,8) (2,13) (1,14) (5,15) (10,6) (2,11) (7,10) (3,6) (12,15) (11,15) (7,0) (9,11) (1,7) (14,8) (5,14) (15,4) (12,7) (0,5) (12,0) (6,2) (13,6) (9,8) (12,6) (3,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->11->1->12->2->10->9->6->5->4->3->7->8->14->15." - } - ] - }, - { - "id": "hamilton-hard-graph106", - "image": "data/hamilton/graph_visual/Base/hard/graph106.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (3,7) (1,10) (0,10) (3,2) (2,5) (8,6) (5,6) (1,8) (5,1) (4,3) (11,4) (4,9) (1,6) (10,8) (2,9) (2,10) (6,4) (5,8) (7,4) (1,11) (7,8) (3,5) (11,0) (7,1) (0,8) (6,2) (10,4) (11,10) (2,11) (9,10) (3,9) (3,6) (0,5) (6,11) (3,11) (2,8) (7,10) (9,1) (5,10) (6,0) (4,1) (7,9) (2,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->1->8->6->5->2->3->7->9->4->11." - } - ] - }, - { - "id": "hamilton-hard-graph103", - "image": "data/hamilton/graph_visual/Base/hard/graph103.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,2) (4,9) (6,0) (7,2) (8,6) (6,3) (3,10) (0,5) (10,5) (1,6) (10,7) (0,3) (10,8) (6,5) (0,2) (7,0) (0,8) (4,7) (9,6) (5,7) (3,1) (11,8) (4,2) (7,6) (5,9) (4,0) (10,4) (6,10) (5,11) (4,6) (3,7) (0,11) (8,5) (11,9) (9,8) (7,8) (2,6) (10,9) (1,7) (1,4) (2,1) (11,7) (1,0) (11,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->8->10->3->1->7->2->4->9->5->11." - } - ] - }, - { - "id": "hamilton-hard-graph316", - "image": "data/hamilton/graph_visual/Base/hard/graph316.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,14) (14,9) (1,8) (9,1) (7,0) (2,13) (9,8) (1,0) (5,9) (11,5) (7,9) (8,7) (1,5) (6,12) (3,14) (3,4) (4,2) (11,12) (1,7) (2,6) (12,13) (15,7) (3,12) (10,2) (4,13) (12,5) (3,2) (10,1) (3,9) (0,13) (14,4) (10,5) (14,0) (3,6) (11,10) (8,6) (0,5) (11,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->8->9->5->11->10->2->13->12->6->3->4->14->7->15." - } - ] - }, - { - "id": "hamilton-hard-graph377", - "image": "data/hamilton/graph_visual/Base/hard/graph377.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,14) (6,3) (10,13) (10,4) (0,7) (6,10) (12,11) (14,10) (12,4) (0,6) (12,5) (3,13) (3,8) (13,5) (0,3) (5,10) (8,0) (9,10) (11,4) (5,2) (7,9) (0,4) (15,14) (1,13) (8,4) (14,9) (11,10) (6,14) (4,2) (15,6) (14,3) (14,13) (13,15) (6,8) (9,13) (8,5) (6,7) (9,3) (15,10) (2,15) (0,13) (7,15) (10,8) (1,14) (4,13) (0,14) (12,15) (16,8) (2,10) (9,5) (4,16) (8,12) (14,4) (15,11) (11,1) (12,0) (16,15) (4,3) (15,8) (1,9) (13,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->9->10->13->3->6->14->12->4->2->5->8->16->15->11->1." - } - ] - }, - { - "id": "hamilton-hard-graph342", - "image": "data/hamilton/graph_visual/Base/hard/graph342.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (5,2) (12,4) (4,0) (9,8) (14,13) (13,9) (15,14) (5,7) (10,2) (3,4) (5,15) (7,2) (6,14) (1,4) (8,15) (3,12) (13,7) (0,7) (11,12) (5,13) (0,5) (5,14) (9,4) (7,9) (11,14) (2,11) (6,7) (15,11) (15,0) (2,15) (3,5) (13,0) (13,4) (4,14) (7,1) (6,8) (11,9) (10,13) (1,12) (9,6) (8,14) (10,0) (11,5) (8,10) (9,15) (14,3) (1,6) (2,1) (12,14) (10,11) (3,8) (1,3) (9,12) (4,15) (4,8) (14,0) (6,5) (6,12) (5,10) (7,14) (9,14) (8,0) (10,1) (4,11) (12,15) (2,3) (11,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->12->3->5->2->10->13->14->15->8->9->7->1->6->11." - } - ] - }, - { - "id": "hamilton-hard-graph201", - "image": "data/hamilton/graph_visual/Base/hard/graph201.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,12) (4,2) (13,11) (6,4) (3,2) (3,4) (1,3) (7,0) (7,4) (10,0) (1,10) (0,3) (5,6) (6,11) (6,9) (13,2) (3,12) (13,9) (7,5) (10,13) (1,9) (10,6) (2,7) (8,6) (4,9) (7,3) (8,11) (9,5) (12,2) (8,13) (7,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->4->2->3->12->1->10->13->11->8->6->5->9." - } - ] - }, - { - "id": "hamilton-hard-graph566", - "image": "data/hamilton/graph_visual/Base/hard/graph566.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,7) (13,2) (16,9) (11,6) (10,1) (15,18) (19,14) (4,18) (5,15) (0,18) (13,12) (6,16) (19,0) (3,12) (7,19) (0,15) (6,14) (5,17) (12,7) (0,17) (18,7) (3,17) (1,5) (1,16) (3,15) (14,9) (17,10) (8,17) (14,11) (5,14) (10,5) (0,2) (12,14) (0,6) (4,15) (18,10) (4,0) (17,15) (4,6) (18,12) (0,7) (8,14) (17,7) (7,11) (16,4) (8,15) (8,10) (13,3) (13,14) (18,1) (19,6) (3,6) (13,0) (3,0) (16,12) (8,2) (0,10) (13,1) (11,2) (3,4) (12,15) (4,14) (3,7) (13,7) (12,5) (2,17) (12,10) (3,14) (18,19) (14,15) (12,19) (10,2) (10,15) (1,7) (16,14) (12,2) (10,3) (3,8) (15,9) (7,15) (13,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->18->15->5->17->3->12->13->2->8->10->1->16->9->14->19->7->4->6->11." - } - ] - }, - { - "id": "hamilton-hard-graph449", - "image": "data/hamilton/graph_visual/Base/hard/graph449.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,16) (14,12) (6,16) (3,11) (5,6) (3,8) (13,6) (2,1) (0,5) (10,16) (2,13) (8,13) (3,12) (12,8) (8,4) (11,13) (13,15) (16,1) (14,10) (13,0) (1,5) (11,0) (1,0) (14,9) (15,0) (3,0) (0,2) (3,1) (7,6) (11,16) (3,15) (8,17) (13,3) (5,9) (11,10) (5,12) (15,5) (17,13) (12,2) (17,7) (4,13) (7,9) (8,2) (10,12) (1,4) (7,16) (11,9) (8,1) (11,8) (0,10) (15,10) (4,12) (3,10) (7,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->6->16->15->13->2->1->3->11->10->14->12->4->8->17->7->9." - } - ] - }, - { - "id": "hamilton-hard-graph372", - "image": "data/hamilton/graph_visual/Base/hard/graph372.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (2,5) (15,8) (2,8) (4,10) (14,13) (6,11) (5,10) (13,16) (7,1) (11,5) (2,13) (15,5) (13,8) (3,9) (11,1) (3,10) (11,2) (0,12) (7,16) (13,11) (12,3) (0,9) (3,16) (8,16) (9,2) (10,7) (1,13) (9,12) (0,10) (5,7) (16,11) (12,1) (12,7) (9,15) (14,10) (1,3) (14,15) (16,4) (1,14) (6,0) (7,2) (12,10) (14,7) (6,5) (13,6) (15,12) (15,0) (0,4) (8,0) (5,4) (0,7) (11,12) (11,14) (1,4) (14,3) (3,2) (14,0) (16,14) (11,0) (3,5) (12,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->3->9->2->5->10->4->16->13->8->15->14->7->1->11->6." - } - ] - }, - { - "id": "hamilton-hard-graph133", - "image": "data/hamilton/graph_visual/Base/hard/graph133.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,8) (9,6) (3,11) (11,4) (4,5) (4,6) (9,2) (12,11) (7,1) (5,1) (4,0) (10,2) (6,3) (12,5) (0,2) (2,7) (9,0) (8,0) (3,4) (2,4) (7,6) (5,3) (2,3) (1,0) (7,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->11->12->7->1->5->4->3->6->9->2->10." - } - ] - }, - { - "id": "hamilton-hard-graph521", - "image": "data/hamilton/graph_visual/Base/hard/graph521.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (7,1) (6,1) (0,11) (6,12) (13,1) (5,8) (7,13) (12,5) (8,12) (0,3) (12,14) (4,5) (5,15) (13,10) (3,11) (9,18) (8,18) (7,9) (4,18) (2,9) (16,6) (6,0) (8,7) (10,18) (16,12) (16,5) (17,18) (1,9) (8,9) (17,10) (11,1) (9,3) (6,18) (12,9) (6,13) (14,0) (12,3) (0,12) (0,8) (17,12) (11,17) (5,10) (1,2) (5,14) (15,0) (4,17) (8,6) (15,9) (5,13) (14,15) (6,2) (3,14) (3,7) (18,15) (3,5) (5,11) (7,17) (11,16) (16,14) (7,11) (2,7) (11,13) (7,15) (5,0) (14,10) (16,4) (11,9) (10,2) (13,16) (6,14) (0,17) (15,10) (17,5) (10,0) (14,4) (1,0) (17,3) (11,18) (5,6) (18,0) (7,6) (12,4) (10,1) (7,5) (14,13) (6,4) (16,15) (18,16) (14,9) (4,0) (18,13) (13,12) (16,9) (10,7) (10,11) (11,15) (1,3) (12,11) (8,2) (3,15) (2,18) (15,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->11->3->9->18->8->5->12->6->1->7->13->16->15->14->4->17->10->2." - } - ] - }, - { - "id": "hamilton-hard-graph562", - "image": "data/hamilton/graph_visual/Base/hard/graph562.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (17,5) (11,16) (1,14) (8,19) (0,17) (16,18) (9,2) (13,10) (7,16) (14,19) (14,17) (9,6) (8,14) (14,9) (6,19) (4,11) (17,13) (4,8) (10,5) (13,7) (17,12) (3,1) (2,3) (11,1) (14,18) (15,10) (14,16) (9,18) (2,15) (18,19) (5,3) (1,5) (15,1) (5,18) (11,10) (1,18) (6,1) (5,2) (14,12) (15,8) (1,17) (12,1) (4,16) (16,17) (8,16) (9,19) (10,8) (1,2) (19,5) (5,16) (6,13) (14,10) (4,14) (11,14) (15,7) (16,0) (0,7) (1,10) (12,2) (13,16) (16,1) (7,12) (3,18) (11,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->17->5->10->13->7->16->11->4->8->19->14->12->1->15->2->3->18->9->6." - } - ] - }, - { - "id": "hamilton-hard-graph39", - "image": "data/hamilton/graph_visual/Base/hard/graph39.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,5) (0,3) (1,2) (5,10) (3,4) (2,6) (8,0) (1,3) (2,3) (3,5) (9,0) (4,0) (6,1) (7,0) (7,9) (8,6) (4,8) (0,2) (6,9) (9,8) (1,9) (10,7) (0,10) (9,3) (0,5) (7,5) (8,10) (2,9) (6,7) (2,7) (5,6) (4,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->4->5->10->7->9->8->6->2->1." - } - ] - }, - { - "id": "hamilton-hard-graph248", - "image": "data/hamilton/graph_visual/Base/hard/graph248.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,5) (10,5) (12,5) (14,4) (12,11) (4,10) (9,6) (2,3) (14,8) (2,11) (4,8) (2,7) (12,7) (6,13) (2,13) (6,4) (2,14) (10,1) (8,3) (0,13) (11,0) (13,10) (6,14) (8,5) (1,9) (9,7) (11,1) (3,14) (7,0) (14,5) (13,7) (0,3) (7,11) (5,4) (0,6) (4,9) (0,1) (8,0) (3,6) (11,5) (10,9) (13,11) (14,1) (12,2) (7,10) (7,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->10->4->14->8->3->2->11->12->7->13->6->9->1." - } - ] - }, - { - "id": "hamilton-hard-graph274", - "image": "data/hamilton/graph_visual/Base/hard/graph274.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,12) (2,8) (2,7) (3,5) (0,10) (7,14) (12,11) (13,12) (9,11) (12,14) (11,0) (1,10) (0,2) (4,13) (7,10) (6,9) (8,3) (12,0) (10,14) (1,4) (14,6) (3,10) (5,6) (5,4) (5,9) (3,14) (14,9) (11,6) (10,6) (7,1) (3,2) (6,4) (10,4) (2,1) (2,9) (13,14) (11,13) (13,0) (11,8) (14,11) (13,7) (6,13) (5,10) (0,5) (0,8) (0,9) (4,9) (3,11) (6,0) (4,2) (2,10) (8,13) (5,12) (12,8) (3,7) (9,7) (14,5) (4,12) (4,7) (3,9) (7,8) (3,6) (7,11) (9,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->1->4->13->12->9->11->6->14->7->2->8->3->5." - } - ] - }, - { - "id": "hamilton-hard-graph506", - "image": "data/hamilton/graph_visual/Base/hard/graph506.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,3) (6,11) (9,5) (9,10) (12,17) (5,7) (17,14) (10,3) (14,5) (12,13) (14,11) (15,11) (9,3) (4,17) (2,9) (3,4) (4,13) (8,18) (10,12) (16,2) (15,9) (6,4) (12,18) (17,13) (9,7) (5,15) (13,1) (18,0) (5,12) (2,4) (18,2) (11,17) (1,16) (11,5) (14,10) (0,9) (15,8) (17,7) (11,8) (10,15) (6,1) (13,7) (14,9) (2,14) (15,1) (1,7) (0,14) (16,5) (1,18) (2,5) (15,12) (7,10) (8,12) (17,0) (6,10) (5,1) (11,10) (18,6) (9,6) (1,2) (15,4) (5,18) (0,12) (2,7) (4,1) (4,12) (8,16) (16,7) (6,0) (8,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->10->9->5->7->17->12->13->4->6->11->14->2->16->1->15->8->18." - } - ] - }, - { - "id": "hamilton-hard-graph382", - "image": "data/hamilton/graph_visual/Base/hard/graph382.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,7) (11,9) (12,8) (4,16) (0,16) (11,6) (11,4) (2,16) (0,15) (13,16) (14,13) (6,1) (6,12) (11,3) (15,5) (3,4) (4,12) (6,3) (2,15) (13,7) (3,12) (5,0) (9,14) (14,2) (10,14) (8,16) (3,5) (5,2) (8,4) (6,8) (3,14) (1,5) (14,11) (11,5) (1,14) (11,15) (2,12) (6,10) (4,1) (4,9) (16,14) (6,16) (11,10) (2,8) (14,8) (12,16) (3,1) (3,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->16->7->13->14->9->11->4->3->12->8->2->15->5->1->6->10." - } - ] - }, - { - "id": "hamilton-hard-graph308", - "image": "data/hamilton/graph_visual/Base/hard/graph308.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (5,2) (6,5) (1,7) (1,5) (14,0) (13,11) (6,8) (6,13) (6,7) (11,10) (8,12) (10,0) (11,0) (8,14) (1,8) (4,15) (12,15) (7,10) (6,11) (4,13) (11,15) (10,12) (12,11) (4,14) (7,5) (14,10) (5,9) (8,13) (13,3) (13,15) (0,8) (5,3) (10,8) (0,15) (7,4) (5,12) (0,5) (3,11) (2,3) (9,8) (6,10) (0,4) (9,13) (4,9) (14,13) (10,5) (6,9) (1,13) (15,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->14->8->6->5->2->3->13->9->4->15->12->11->10->7->1." - } - ] - }, - { - "id": "hamilton-hard-graph272", - "image": "data/hamilton/graph_visual/Base/hard/graph272.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,4) (4,14) (12,13) (2,5) (7,13) (6,5) (1,6) (2,7) (14,3) (5,13) (7,6) (4,6) (7,1) (9,6) (8,5) (2,4) (4,7) (10,1) (8,11) (3,11) (2,9) (14,2) (0,5) (0,11) (11,4) (6,8) (0,14) (3,8) (9,1) (11,7) (11,12) (5,14) (1,12) (10,11) (2,10) (5,4) (14,9) (1,2) (6,0) (12,7) (3,6) (13,1) (2,8) (2,0) (3,9) (13,3) (13,0) (2,12) (7,9) (7,14) (13,4) (12,5) (8,10) (3,4) (14,6) (0,10) (2,3) (11,13) (8,12) (3,1) (8,13) (10,6) (14,8) (11,14) (12,6) (9,8) (10,5) (9,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->2->7->13->12->11->8->4->14->3->6->9->1->10." - } - ] - }, - { - "id": "hamilton-hard-graph147", - "image": "data/hamilton/graph_visual/Base/hard/graph147.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,1) (0,9) (2,9) (9,4) (8,10) (3,10) (12,9) (3,0) (2,8) (4,7) (6,9) (4,5) (6,0) (4,0) (0,10) (9,5) (10,5) (5,6) (5,8) (6,8) (4,8) (7,9) (12,0) (11,12) (4,1) (12,5) (8,3) (5,0) (7,6) (10,11) (12,10) (12,8) (10,6) (8,7) (12,1) (7,5) (0,7) (11,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->2->8->5->6->7->4->1->12->11->10->3." - } - ] - }, - { - "id": "hamilton-hard-graph557", - "image": "data/hamilton/graph_visual/Base/hard/graph557.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (17,6) (3,14) (4,16) (18,1) (16,11) (0,8) (3,12) (1,15) (15,19) (3,17) (2,5) (11,17) (7,18) (13,3) (0,7) (7,5) (0,14) (6,8) (5,14) (5,8) (11,7) (3,11) (2,17) (1,12) (19,3) (12,11) (17,14) (2,10) (10,7) (15,0) (3,5) (15,8) (9,1) (6,19) (8,2) (6,3) (12,0) (4,19) (4,12) (18,13) (1,8) (16,17) (5,1) (4,1) (14,18) (6,2) (17,18) (7,14) (7,9) (18,5) (1,13) (3,15) (9,4) (11,14) (9,15) (2,9) (6,4) (10,0) (10,5) (12,17) (14,15) (0,1) (13,16) (5,9) (9,19) (6,15) (17,7) (19,14) (10,11) (18,3) (14,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->6->17->3->14->5->2->10->7->18->1->15->19->9->4->12->11->16->13." - } - ] - }, - { - "id": "hamilton-hard-graph376", - "image": "data/hamilton/graph_visual/Base/hard/graph376.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (2,12) (5,4) (3,5) (3,9) (0,10) (8,0) (4,8) (12,3) (1,5) (9,12) (16,0) (7,11) (5,10) (5,2) (9,5) (1,15) (6,5) (2,15) (8,2) (3,11) (13,12) (6,12) (12,11) (7,8) (8,3) (6,14) (9,15) (4,9) (2,16) (13,10) (0,3) (15,3) (11,10) (4,7) (9,6) (7,13) (16,8) (16,13) (3,2) (16,12) (7,6) (14,11) (4,3) (6,2) (9,7) (0,5) (5,8) (8,6) (3,13) (13,15) (1,11) (0,12) (1,7) (12,1) (16,4) (2,4) (11,15) (11,6) (11,16) (13,0) (11,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->5->4->8->2->12->3->9->15->1->11->14->6->7->13->16." - } - ] - }, - { - "id": "hamilton-hard-graph291", - "image": "data/hamilton/graph_visual/Base/hard/graph291.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (3,10) (7,6) (2,12) (11,8) (9,10) (11,4) (4,12) (1,7) (14,8) (7,12) (14,13) (12,1) (7,8) (12,9) (3,13) (5,10) (3,7) (5,9) (9,3) (4,13) (10,12) (2,13) (6,5) (8,12) (3,2) (14,10) (3,6) (14,12) (0,5) (2,6) (8,1) (3,12) (2,5) (11,14) (4,1) (9,4) (11,9) (0,2) (10,2) (10,1) (10,4) (11,2) (6,11) (2,1) (6,14) (5,8) (9,2) (12,0) (0,14) (6,10) (3,11) (13,7) (4,6) (9,0) (2,14) (9,13) (14,3) (7,4) (13,8) (1,13) (0,13) (7,0) (2,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->10->3->13->14->8->11->4->12->1->7->6->2->9." - } - ] - }, - { - "id": "hamilton-hard-graph476", - "image": "data/hamilton/graph_visual/Base/hard/graph476.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,1) (2,0) (12,17) (9,17) (0,1) (8,11) (11,9) (9,10) (10,17) (8,5) (10,0) (4,16) (3,10) (6,15) (5,1) (16,1) (8,13) (15,10) (4,1) (17,1) (16,7) (16,2) (10,14) (8,10) (1,11) (13,11) (12,14) (12,9) (14,4) (6,17) (11,17) (9,2) (3,0) (0,15) (2,10) (1,3) (14,17) (17,15) (16,5) (4,6) (8,9) (14,7) (16,8) (0,8) (1,8) (11,14) (3,11) (9,13) (7,2) (5,14) (7,1) (5,10) (3,13) (17,8) (5,9) (16,3) (4,8) (16,6) (10,12) (5,12) (6,1) (12,3) (13,1) (0,5) (17,2) (7,0) (7,8) (9,14) (7,12) (12,4) (7,15) (12,15) (14,0) (11,6) (4,17) (16,15) (5,3) (3,8) (8,6) (10,11) (13,2) (7,11) (17,3) (14,2) (12,1) (7,17) (10,6) (0,17) (14,13) (6,0) (10,4) (3,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->16->4->1->9->17->12->14->10->3->13->11->6->15->7->8->5." - } - ] - }, - { - "id": "hamilton-hard-graph234", - "image": "data/hamilton/graph_visual/Base/hard/graph234.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,3) (9,5) (0,1) (10,12) (7,12) (3,11) (10,13) (6,1) (1,4) (10,8) (1,9) (3,13) (7,13) (6,11) (10,3) (4,11) (11,1) (6,9) (1,3) (3,5) (6,12) (7,9) (5,7) (11,10) (10,5) (4,7) (0,4) (6,0) (7,6) (2,6) (11,9) (7,2) (8,4) (8,0) (1,7) (3,0) (6,8) (8,7) (4,6) (13,2) (10,4) (1,10) (5,13) (5,6) (9,13) (7,0) (11,8) (12,13) (0,5) (2,10) (0,13) (10,6) (9,12) (12,4) (8,5) (9,2) (8,13) (5,11) (2,0) (12,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->6->3->11->4->7->12->10->13->2->9->5->8." - } - ] - }, - { - "id": "hamilton-hard-graph499", - "image": "data/hamilton/graph_visual/Base/hard/graph499.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (7,8) (8,11) (2,13) (6,9) (8,12) (14,0) (11,12) (8,10) (5,12) (7,5) (18,12) (13,18) (9,1) (8,0) (4,9) (13,5) (0,1) (18,3) (11,15) (18,9) (16,17) (6,3) (18,14) (18,11) (10,17) (16,6) (4,6) (13,1) (14,1) (4,18) (10,13) (2,5) (15,9) (7,12) (14,2) (6,14) (1,17) (8,9) (9,7) (7,1) (13,6) (2,18) (12,3) (11,16) (17,0) (6,5) (7,14) (10,18) (3,13) (2,1) (17,13) (0,7) (16,12) (1,4) (4,3) (18,15) (6,1) (14,5) (16,9) (2,17) (11,13) (10,15) (9,14) (12,10) (0,16) (2,4) (14,13) (15,2) (17,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->14->18->12->8->7->5->13->2->1->9->4->3->6->16->17->10->15->11." - } - ] - }, - { - "id": "hamilton-hard-graph397", - "image": "data/hamilton/graph_visual/Base/hard/graph397.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,15) (3,12) (1,13) (16,8) (7,15) (6,10) (7,5) (5,13) (12,13) (0,13) (14,16) (14,0) (4,7) (0,1) (0,2) (1,2) (13,16) (14,13) (2,8) (5,1) (12,10) (5,12) (1,3) (11,5) (8,7) (14,1) (4,10) (8,11) (8,3) (9,6) (1,4) (11,3) (13,3) (6,14) (9,13) (12,0) (9,7) (13,7) (12,16) (16,0) (12,9) (3,15) (0,4) (8,6) (6,13) (1,15) (8,4) (3,10) (10,7) (16,1) (8,15) (0,3) (2,4) (16,5) (8,12) (14,3) (5,10) (14,2) (2,10) (2,5) (11,1) (11,9) (8,10) (2,12) (1,12) (8,1) (3,4) (9,2) (6,7) (0,9) (5,6) (15,9) (2,15) (14,10) (1,7) (0,6) (5,8) (8,9) (12,4) (11,14) (6,4) (11,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->1->2->8->16->14->6->10->12->3->11->5->7->4->15->9." - } - ] - }, - { - "id": "hamilton-hard-graph69", - "image": "data/hamilton/graph_visual/Base/hard/graph69.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,8) (11,7) (8,6) (3,7) (2,1) (4,5) (2,8) (11,5) (7,1) (3,2) (8,1) (9,10) (3,5) (0,8) (11,10) (5,0) (9,7) (9,4) (3,1) (2,10) (0,6) (11,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->4->9->10->11->7->3->2->1->8->6." - } - ] - }, - { - "id": "hamilton-hard-graph496", - "image": "data/hamilton/graph_visual/Base/hard/graph496.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (12,0) (13,16) (16,2) (17,0) (9,15) (7,0) (17,1) (15,11) (7,12) (5,12) (9,1) (14,12) (11,8) (8,16) (4,11) (10,3) (18,2) (13,12) (7,6) (16,18) (18,8) (2,14) (2,13) (15,2) (2,7) (5,17) (9,6) (14,13) (12,2) (11,6) (9,0) (4,14) (1,6) (0,14) (6,5) (7,8) (3,5) (7,15) (8,10) (17,16) (9,16) (8,9) (0,10) (18,9) (15,1) (13,10) (4,16) (12,6) (6,17) (12,3) (3,15) (3,18) (13,9) (11,2) (1,13) (14,1) (10,12) (5,13) (18,6) (8,2) (3,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->7->6->9->15->11->8->16->2->18->3->10->13->5->17->1->14->4." - } - ] - }, - { - "id": "hamilton-hard-graph14", - "image": "data/hamilton/graph_visual/Base/hard/graph14.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,10) (1,8) (0,10) (4,2) (9,4) (1,4) (9,2) (7,1) (6,10) (7,3) (4,0) (9,1) (6,1) (2,7) (1,0) (10,2) (3,5) (4,7) (7,9) (9,0) (1,10) (10,8) (5,7) (0,3) (6,5) (10,5) (9,8)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->7->3->5->6->1->8->9->4->2." - } - ] - }, - { - "id": "hamilton-hard-graph231", - "image": "data/hamilton/graph_visual/Base/hard/graph231.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,8) (1,10) (13,5) (12,6) (8,7) (9,12) (4,2) (7,12) (7,13) (2,3) (2,0) (11,9) (4,8) (9,4) (5,8) (12,2) (0,3) (4,12) (9,13) (5,9) (12,10) (12,13) (2,1) (6,3) (3,12) (2,5) (6,11) (4,13) (6,13) (9,7) (5,4) (13,3) (7,4) (5,11) (4,11) (7,1) (7,0) (6,0) (3,10) (1,4) (1,6) (7,5) (12,0) (3,1) (2,13) (10,8) (13,0) (10,13) (3,9) (0,8) (5,6) (10,2) (0,9) (7,10) (1,13) (10,0) (11,13) (9,10) (4,0) (3,7) (10,6) (7,6) (9,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->4->8->1->10->12->6->3->13->5->11->9->7." - } - ] - }, - { - "id": "hamilton-hard-graph493", - "image": "data/hamilton/graph_visual/Base/hard/graph493.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (16,8) (6,4) (16,7) (18,15) (12,8) (10,5) (3,10) (7,3) (10,15) (15,4) (17,4) (18,0) (11,2) (2,12) (8,7) (17,7) (8,6) (11,17) (3,1) (6,10) (18,5) (10,17) (3,17) (9,10) (12,6) (18,16) (12,10) (17,9) (16,12) (12,9) (12,17) (12,4) (4,16) (5,0) (3,5) (14,12) (2,15) (10,14) (15,17) (13,4) (4,8) (16,0) (18,10) (7,9) (18,1) (18,8) (13,6) (13,0) (3,16) (8,3) (15,11) (12,5) (4,1) (1,0) (2,18) (1,10) (13,10) (0,10) (13,3) (2,5) (18,6) (7,2) (8,9) (0,11) (7,13) (4,14) (9,1) (16,13) (0,6) (11,18)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->18->15->10->5->3->7->16->8->6->13->4->1->9->17->11->2->12->14." - } - ] - }, - { - "id": "hamilton-hard-graph137", - "image": "data/hamilton/graph_visual/Base/hard/graph137.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,3) (7,3) (4,0) (7,12) (2,6) (9,3) (10,11) (1,12) (0,6) (11,7) (10,6) (9,8) (11,1) (5,10) (0,9) (9,10) (4,2) (1,9) (11,4) (12,4) (12,10) (5,11) (0,12) (1,3) (8,0) (12,3) (7,1) (5,2) (3,4) (5,4) (2,9) (2,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->2->6->3->7->12->1->11->5->10->9->8." - } - ] - }, - { - "id": "hamilton-hard-graph453", - "image": "data/hamilton/graph_visual/Base/hard/graph453.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,9) (7,0) (10,13) (2,16) (15,8) (2,8) (12,3) (12,13) (14,16) (2,9) (8,5) (6,11) (0,17) (14,6) (16,0) (10,7) (1,0) (9,5) (7,14) (5,16) (16,12) (14,11) (13,16) (11,10) (16,4) (6,12) (6,8) (5,13) (1,10) (13,15) (2,12) (1,4) (8,13) (4,17) (1,17) (2,13) (9,0) (17,5) (6,13) (5,2) (8,9) (4,7) (0,2) (7,2) (13,7) (0,15) (0,4) (4,12) (10,15) (5,7) (12,11) (6,3) (6,17) (16,8) (15,1) (7,17) (15,7) (10,9) (9,15) (16,15) (6,16) (1,2) (14,13) (3,16) (11,13) (13,0) (10,14) (13,17) (13,4) (8,12) (1,14) (7,8) (17,8) (3,8) (9,1) (3,13) (6,9) (1,6) (1,12) (0,8) (7,3) (1,16) (0,11) (5,15) (13,9) (16,11) (0,14) (10,0) (2,6) (11,9) (7,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->10->13->12->3->6->11->14->16->2->8->15->1->4->17->9->5." - } - ] - }, - { - "id": "hamilton-hard-graph187", - "image": "data/hamilton/graph_visual/Base/hard/graph187.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (11,3) (4,1) (11,9) (7,1) (7,2) (4,0) (3,4) (5,12) (1,13) (11,2) (13,6) (2,8) (11,4) (7,9) (8,4) (4,2) (10,5) (7,11) (10,13) (5,9) (11,1) (0,11) (10,0) (1,10) (8,5) (13,0) (11,6) (10,8) (3,7) (13,9) (8,7) (7,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->1->10->8->2->7->3->11->6->13->9->5->12." - } - ] - }, - { - "id": "hamilton-hard-graph369", - "image": "data/hamilton/graph_visual/Base/hard/graph369.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (0,2) (9,0) (15,2) (12,14) (8,12) (3,11) (0,12) (2,8) (13,1) (8,14) (14,13) (6,0) (10,14) (5,13) (15,11) (9,5) (2,3) (11,6) (12,2) (8,9) (10,15) (9,16) (8,15) (9,3) (10,6) (12,7) (10,11) (7,9) (3,8) (7,3) (2,16) (3,6) (0,5) (0,10) (8,6) (2,4) (13,16) (6,13) (14,6) (13,9) (9,15) (13,10) (8,10) (13,4) (3,1) (7,2) (13,7) (7,15) (8,5) (14,11) (12,9) (1,2) (4,9) (14,9) (6,7) (1,16)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->15->11->3->7->12->14->10->6->8->5->13->1->16->9->4." - } - ] - }, - { - "id": "hamilton-hard-graph487", - "image": "data/hamilton/graph_visual/Base/hard/graph487.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,5) (2,12) (9,18) (9,5) (14,6) (7,18) (5,4) (5,16) (10,13) (18,4) (0,6) (4,15) (7,0) (10,6) (12,15) (2,10) (10,7) (9,7) (16,8) (4,7) (1,0) (14,4) (11,16) (6,9) (3,10) (17,12) (17,8) (16,18) (5,18) (8,6) (16,7) (2,1) (18,11) (11,14) (4,16) (11,2) (8,10) (12,10) (6,11) (14,12) (0,11) (15,13) (9,0) (12,5) (12,8) (6,16) (15,9) (11,3) (16,10) (3,16) (13,14) (13,11) (4,2) (13,0) (8,1) (0,14) (16,14) (4,17) (9,4) (4,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->9->18->7->10->13->15->4->14->6->11->3->16->8->17->12->2->1." - } - ] - }, - { - "id": "hamilton-hard-graph219", - "image": "data/hamilton/graph_visual/Base/hard/graph219.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (10,7) (4,3) (0,6) (4,13) (7,13) (2,5) (6,10) (10,5) (3,0) (13,8) (1,7) (0,9) (11,12) (13,5) (8,0) (11,9) (8,9) (8,1) (12,2) (11,13) (5,6) (3,7) (6,8) (3,6) (11,2) (9,10) (13,12) (7,11) (5,11) (11,3) (4,10) (4,11) (5,4) (11,8) (10,2) (0,11) (9,4) (10,12) (8,12) (9,2) (13,0) (7,6) (0,1) (5,1) (3,2) (1,6) (7,12) (8,3) (3,12) (1,4) (8,4) (9,1) (9,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->10->7->13->4->3->11->12->2->5->1->8->9." - } - ] - }, - { - "id": "hamilton-hard-graph456", - "image": "data/hamilton/graph_visual/Base/hard/graph456.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (5,16) (7,15) (11,8) (13,14) (6,11) (6,3) (8,2) (1,13) (3,10) (16,12) (17,12) (13,11) (12,13) (12,14) (13,4) (10,5) (4,0) (10,7) (6,7) (7,0) (13,3) (13,10) (11,16) (15,5) (8,1) (13,7) (1,7) (0,15) (0,9) (5,17) (0,3) (12,0) (7,16) (8,0) (12,1) (4,1) (3,17) (9,5) (9,2) (9,8) (10,1) (1,9) (1,16) (3,2) (8,6) (17,8) (0,1) (8,3) (6,2) (6,13) (1,5) (4,2) (15,3) (6,14) (14,8) (14,10) (2,17) (16,2) (4,14) (5,12) (10,12) (4,12) (6,12) (3,1) (16,0) (9,14) (16,15) (16,14) (7,2) (5,13) (3,11) (16,6) (15,11) (17,15) (4,10) (10,9) (3,7) (9,17) (16,8) (10,0) (10,15) (9,3) (3,4) (6,15) (13,8) (13,15) (4,6) (15,9) (0,2) (12,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->13->14->12->16->5->10->3->6->11->8->2->9->1->7->15->17." - } - ] - }, - { - "id": "hamilton-hard-graph373", - "image": "data/hamilton/graph_visual/Base/hard/graph373.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,11) (4,0) (15,13) (9,6) (1,11) (3,12) (16,4) (7,11) (5,1) (5,2) (16,3) (14,11) (14,12) (10,12) (8,10) (10,6) (4,15) (7,12) (6,3) (12,4) (4,2) (11,13) (16,7) (14,15) (12,16) (1,10) (5,7) (9,10) (11,12) (13,5) (15,12) (4,8) (6,11) (14,8) (15,11) (5,8) (8,3) (0,13) (7,4) (8,1) (6,1) (2,15) (13,9) (8,2) (14,6) (16,8) (9,0) (2,3) (6,0) (12,8) (4,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->16->11->1->5->2->15->13->9->10->8->14->6->3->12->7." - } - ] - }, - { - "id": "hamilton-hard-graph24", - "image": "data/hamilton/graph_visual/Base/hard/graph24.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,9) (9,10) (2,0) (6,2) (5,10) (0,6) (4,9) (1,8) (9,0) (10,4) (1,0) (4,5) (7,4) (8,6) (10,7) (4,8) (2,10) (9,6) (4,6) (2,8) (3,7) (4,1) (6,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->6->8->1->4->9->3->7->10->5." - } - ] - }, - { - "id": "hamilton-hard-graph386", - "image": "data/hamilton/graph_visual/Base/hard/graph386.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,6) (11,14) (5,0) (10,2) (3,2) (3,8) (16,6) (13,0) (2,6) (0,3) (5,1) (11,9) (9,1) (1,10) (16,3) (2,8) (2,5) (15,14) (13,4) (13,11) (0,14) (15,4) (13,7) (0,8) (5,13) (13,12) (4,11) (1,2) (15,7) (3,5) (12,5) (9,12) (11,3) (7,9) (7,11) (8,15) (3,9) (14,6) (14,16) (5,6) (6,12) (16,7) (15,2) (12,11) (6,13) (11,1) (16,11) (8,6) (12,3) (16,4) (10,3) (7,3) (8,5) (5,4) (15,1) (13,9) (10,12) (7,0) (9,4) (11,8) (10,7) (6,9) (10,15) (14,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->1->9->11->6->16->14->15->4->13->7->3->8->2->10->12." - } - ] - }, - { - "id": "hamilton-hard-graph237", - "image": "data/hamilton/graph_visual/Base/hard/graph237.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (6,11) (12,7) (7,10) (4,1) (1,5) (0,6) (7,6) (3,10) (11,5) (7,4) (4,3) (0,9) (11,12) (11,2) (13,4) (10,8) (11,7) (5,2) (6,5) (8,4) (4,0) (11,0) (3,9) (4,12) (8,12) (3,0) (8,11) (1,11) (6,8) (4,5) (12,9) (6,1) (13,1) (0,13) (0,2) (9,8) (4,10) (1,0) (3,5) (9,6) (8,3) (9,4) (2,4) (11,10) (3,1) (7,2) (1,9) (1,2) (3,11) (3,13) (8,5) (2,9) (1,12) (11,9) (10,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->11->5->1->4->7->12->8->10->2->9->3->13." - } - ] - }, - { - "id": "hamilton-hard-graph228", - "image": "data/hamilton/graph_visual/Base/hard/graph228.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,9) (6,11) (4,2) (5,13) (9,5) (10,11) (12,10) (2,0) (1,6) (10,7) (8,6) (6,9) (1,12) (12,11) (2,12) (8,7) (10,5) (8,5) (8,2) (2,1) (11,4) (3,8) (6,4) (2,3) (1,8) (0,9) (12,5) (3,12) (7,4) (0,1) (10,8) (5,2) (3,10) (10,0) (8,11) (6,2) (13,7) (10,13) (0,5) (9,4) (0,7) (13,11) (4,5) (13,1) (3,6) (3,13) (3,7) (2,13) (8,4) (7,5) (13,12) (11,1) (0,11) (12,0) (3,9) (10,9) (4,12) (4,3) (3,5) (0,13) (4,13) (9,8) (9,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->4->11->6->1->12->9->5->13->7->10->8->3." - } - ] - }, - { - "id": "hamilton-hard-graph101", - "image": "data/hamilton/graph_visual/Base/hard/graph101.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,4) (2,11) (10,4) (6,3) (5,7) (6,1) (9,11) (6,7) (8,1) (2,1) (6,10) (0,2) (3,4) (0,8) (1,10) (2,6) (1,0) (3,2) (0,5) (9,5) (11,7) (0,6) (6,9) (9,7) (10,11) (11,6) (4,7) (0,4) (8,3) (8,9) (3,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->4->10->6->3->11->7->5->9->8->1." - } - ] - }, - { - "id": "hamilton-hard-graph585", - "image": "data/hamilton/graph_visual/Base/hard/graph585.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (1,8) (2,14) (18,12) (13,2) (10,0) (6,9) (6,11) (11,8) (5,0) (13,10) (11,0) (13,4) (8,9) (0,6) (11,4) (9,19) (5,13) (16,19) (16,5) (5,17) (1,3) (19,1) (2,10) (12,9) (4,7) (5,4) (8,0) (9,5) (14,4) (15,19) (13,15) (10,11) (7,18) (3,12) (16,10) (17,4) (6,10) (11,9) (8,17) (12,5) (12,11) (16,13) (17,14) (2,7) (13,11) (5,14) (17,16) (6,8) (9,1) (19,11) (0,2) (17,1) (0,1) (9,10) (2,18) (18,10) (7,8) (19,17) (13,18) (1,6) (18,9) (8,2) (12,0) (6,2) (6,16) (3,2) (14,0) (19,4) (13,8) (13,0) (18,17) (5,2) (16,0) (15,6) (18,19) (13,14) (2,4) (1,16) (9,7) (3,17) (1,15) (4,12) (4,6) (16,9) (11,1) (10,14) (13,7) (7,17) (12,16) (2,19) (10,5) (9,14) (8,12) (17,11) (7,1) (5,7) (10,15) (14,15) (13,19) (7,3) (13,12) (16,15) (6,7) (4,15) (11,2) (3,15) (18,11) (4,18) (7,0) (5,3) (10,8) (3,11) (19,0) (16,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->13->2->14->4->11->6->9->8->1->3->12->18->7->17->5->16->19->15." - } - ] - }, - { - "id": "hamilton-hard-graph383", - "image": "data/hamilton/graph_visual/Base/hard/graph383.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (6,0) (5,7) (10,6) (2,10) (16,7) (4,6) (9,2) (10,5) (13,7) (7,9) (4,7) (0,8) (10,1) (14,13) (5,4) (12,14) (5,13) (15,9) (12,3) (6,16) (2,13) (2,16) (15,16) (3,7) (15,2) (5,14) (5,8) (16,9) (16,10) (1,7) (0,13) (15,12) (9,4) (15,6) (7,6) (7,10) (0,12) (5,6) (3,14) (8,11) (13,4) (11,15) (0,1) (16,14) (13,15) (9,13) (5,1) (9,12) (2,0) (11,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->10->2->9->16->7->4->13->14->3->12->15->11->8->5->1." - } - ] - }, - { - "id": "hamilton-hard-graph432", - "image": "data/hamilton/graph_visual/Base/hard/graph432.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (17,3) (14,5) (3,1) (6,8) (10,5) (13,8) (2,10) (3,12) (11,4) (14,1) (17,16) (9,15) (7,13) (15,12) (8,10) (1,7) (12,11) (10,3) (7,15) (0,16) (13,12) (1,17) (13,17) (12,2) (4,1) (7,6) (9,3) (10,4) (13,3) (13,14) (12,8) (9,13) (8,5) (4,17) (4,12) (17,12) (0,11) (14,9) (13,16) (9,10) (7,11) (3,5) (6,15) (11,9) (9,1) (8,16) (8,2) (10,7) (3,0) (0,13) (0,1) (16,15) (3,2) (9,17) (15,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->16->17->3->1->14->5->10->2->12->15->9->13->8->6->7->11->4." - } - ] - }, - { - "id": "hamilton-hard-graph301", - "image": "data/hamilton/graph_visual/Base/hard/graph301.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,12) (1,13) (6,10) (12,9) (7,2) (11,12) (8,10) (6,11) (9,10) (3,11) (0,4) (0,6) (9,1) (12,4) (7,5) (11,1) (1,7) (5,6) (5,1) (15,13) (10,14) (7,11) (8,14) (15,7) (5,8) (13,0) (1,4) (10,7) (14,13) (11,8) (1,14) (3,7) (6,3) (9,14) (2,6) (9,6) (14,5) (0,2) (0,5) (5,13) (5,12) (9,3) (13,6) (8,15) (8,7) (0,10) (10,5) (13,10) (4,8) (5,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->12->7->2->6->10->8->14->9->1->11->3->5->13->15." - } - ] - }, - { - "id": "hamilton-hard-graph491", - "image": "data/hamilton/graph_visual/Base/hard/graph491.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (12,0) (8,5) (10,0) (2,9) (18,2) (18,10) (4,3) (0,6) (6,2) (9,8) (7,14) (16,14) (17,2) (2,13) (2,0) (14,6) (8,4) (17,1) (16,11) (10,7) (7,6) (15,8) (13,4) (1,0) (2,15) (9,5) (9,11) (10,3) (11,0) (16,4) (10,11) (17,18) (5,4) (12,9) (18,15) (18,1) (13,17) (13,7) (18,3) (13,9) (0,5) (1,13) (14,10) (16,6) (3,16) (14,5) (14,0) (5,1) (8,0) (16,1) (8,7) (5,18) (18,11) (4,17) (14,17) (2,14) (10,4) (2,10) (13,15) (14,15) (2,11) (17,16) (5,11) (2,7) (16,8) (3,8) (9,18) (4,1) (1,12) (9,3) (12,15) (12,18)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->9->2->18->10->7->14->6->16->11->5->8->15->13->17->1->4->3." - } - ] - }, - { - "id": "hamilton-hard-graph513", - "image": "data/hamilton/graph_visual/Base/hard/graph513.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (2,1) (8,10) (12,3) (10,15) (2,4) (13,7) (16,12) (5,18) (6,13) (5,8) (14,9) (18,3) (10,16) (15,7) (16,1) (8,14) (2,16) (2,0) (4,18) (9,18) (6,7) (6,1) (7,8) (15,16) (17,12) (17,6) (15,3) (14,3) (11,5) (10,18) (12,1) (14,13) (2,14) (6,12) (13,16) (6,0) (11,7) (5,2) (0,15) (14,12) (5,9) (1,17) (11,10) (10,5) (10,2) (6,14) (11,6) (10,13) (11,9) (10,17) (15,14) (7,12) (18,16) (9,16) (5,1) (16,5) (11,15) (3,1) (10,9) (15,5) (1,0) (4,15) (5,6) (14,7) (4,6) (7,2) (2,12) (17,18) (13,9) (18,15) (15,12) (1,18) (13,2) (1,11) (14,18) (9,7) (17,9) (12,18) (9,15) (18,8) (2,9) (12,8) (0,4) (8,16) (2,17) (16,11) (14,17) (8,1) (10,0) (6,3) (3,5) (7,1) (12,5) (7,5) (6,9) (3,16)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->1->16->12->3->18->5->8->10->15->7->13->14->17->9->11->6->4." - } - ] - }, - { - "id": "hamilton-hard-graph561", - "image": "data/hamilton/graph_visual/Base/hard/graph561.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,3) (1,11) (2,6) (5,16) (8,17) (19,13) (1,2) (10,1) (17,7) (11,19) (9,5) (17,16) (2,9) (18,3) (0,2) (16,19) (17,11) (11,0) (19,2) (12,15) (5,4) (17,13) (1,19) (18,6) (7,19) (2,3) (8,19) (15,8) (7,16) (3,11) (6,4) (5,2) (12,2) (18,12) (19,18) (1,14) (10,15) (11,14) (1,8) (11,9) (12,10) (19,10) (13,15) (4,14) (18,11) (14,3) (5,13) (18,13) (18,9) (15,14) (1,15) (6,8) (7,12) (6,11) (8,11) (7,3) (8,10) (2,16) (6,5) (9,3) (4,15) (6,0) (11,5) (4,11) (3,0) (4,2) (3,8) (6,16) (12,1) (3,10) (9,12) (8,16) (5,14) (6,19) (5,19) (9,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->6->18->3->4->5->16->17->8->19->13->15->12->10->1->14->11->9->7." - } - ] - }, - { - "id": "hamilton-hard-graph114", - "image": "data/hamilton/graph_visual/Base/hard/graph114.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,9) (0,5) (4,1) (1,8) (2,4) (8,11) (11,1) (0,9) (11,2) (9,11) (7,9) (5,6) (11,3) (8,9) (3,4) (7,8) (4,9) (8,10) (6,8) (3,0) (3,7) (0,1) (5,3) (3,6) (10,1) (2,3) (5,11) (0,2) (9,10) (8,3) (3,10) (4,6) (11,4) (5,4) (7,0) (0,8) (7,10) (8,2) (2,5) (5,10) (5,1) (4,0) (10,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->6->9->11->8->1->4->2->3->7->10." - } - ] - }, - { - "id": "hamilton-hard-graph510", - "image": "data/hamilton/graph_visual/Base/hard/graph510.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (8,11) (16,8) (6,4) (14,12) (18,12) (8,5) (4,13) (10,7) (10,8) (15,17) (12,7) (6,2) (0,1) (8,2) (15,0) (16,4) (8,4) (8,0) (16,2) (12,2) (3,7) (9,11) (12,8) (0,14) (11,17) (18,13) (2,14) (15,10) (1,17) (15,2) (10,5) (18,2) (12,6) (18,1) (5,6) (7,11) (4,3) (3,13) (16,18) (0,18) (18,3) (5,1) (1,16) (0,3) (14,16) (6,0) (9,2) (16,5) (10,1) (9,17) (16,7) (9,18) (11,12) (5,17) (18,17) (3,10) (6,16) (12,16) (13,2) (1,9) (14,6) (14,17) (5,4) (0,12) (15,1) (3,8) (16,0) (11,16) (14,1) (3,12) (14,4) (11,18) (5,18) (18,15) (6,9) (12,13) (13,1) (14,5) (3,15) (14,9) (13,17) (4,18) (5,15) (0,10) (9,8) (10,4) (8,1) (11,3) (7,0) (14,11) (5,2) (14,15) (10,18) (7,4) (18,8) (16,13) (17,0) (2,11) (17,4) (17,8) (16,9) (1,2) (9,15)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->17->15->10->7->12->14->2->6->4->13->18->16->5->8->3->11->9." - } - ] - }, - { - "id": "hamilton-hard-graph356", - "image": "data/hamilton/graph_visual/Base/hard/graph356.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,8) (3,10) (4,13) (9,13) (0,5) (15,8) (14,3) (4,6) (2,14) (6,0) (14,6) (1,8) (12,1) (0,9) (14,13) (9,4) (14,4) (5,12) (6,5) (10,8) (9,15) (9,7) (10,2) (12,13) (2,15) (15,6) (9,14) (13,11) (11,14) (8,7) (12,7) (3,8) (14,5) (8,0) (0,7) (6,2) (11,10) (4,15) (13,5) (13,10) (14,10) (15,13) (3,9) (2,12) (0,11) (8,12) (1,7) (6,3) (3,1) (7,6) (10,1) (5,3) (10,15) (9,6) (15,3) (2,13) (12,11) (13,1) (5,4) (3,7) (0,1) (4,8) (5,15) (8,2) (12,14) (9,10) (3,13) (11,3) (10,0) (14,1) (12,4) (6,12) (3,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->12->1->8->14->3->10->2->15->9->7->6->4->13->11." - } - ] - }, - { - "id": "hamilton-hard-graph64", - "image": "data/hamilton/graph_visual/Base/hard/graph64.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,8) (5,1) (3,0) (3,1) (6,0) (3,10) (3,7) (9,2) (3,2) (1,6) (10,0) (7,11) (2,5) (8,10) (4,2) (1,2) (4,6) (1,9) (8,1) (2,11) (3,11) (1,4) (6,5) (7,0) (6,11) (7,2) (0,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->11->3->10->8->6->4->2->9->1->5." - } - ] - }, - { - "id": "hamilton-hard-graph529", - "image": "data/hamilton/graph_visual/Base/hard/graph529.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (18,16) (12,9) (17,11) (11,5) (14,12) (2,10) (5,18) (13,11) (6,8) (1,0) (13,4) (18,14) (0,12) (5,8) (17,10) (16,2) (11,2) (15,2) (17,5) (10,13) (3,7) (15,10) (1,5) (17,13) (0,10) (6,5) (0,7) (2,6) (13,12) (8,0) (3,16) (2,3) (8,4) (4,5) (11,4) (17,16) (1,11) (3,9) (6,18) (3,11) (7,2) (7,18) (10,6) (18,13) (18,9) (1,6) (16,13) (4,14) (3,12) (14,11) (14,15) (13,14) (9,11) (1,4) (14,0) (0,6) (12,2) (15,13) (16,11) (3,8) (9,13) (12,10) (3,6) (15,0) (7,9) (15,7) (3,0) (1,7) (9,0) (1,3) (18,11) (18,1) (15,17) (1,15) (15,18) (2,17) (8,11) (12,1) (2,0) (4,2) (16,6) (13,3) (5,16) (1,8) (17,12) (2,5) (15,11) (4,7) (9,15) (8,13) (1,9) (7,8) (4,9) (0,18) (10,3) (11,12) (14,3) (14,8) (6,7) (6,9) (8,16) (15,6) (2,9) (11,10) (4,12) (0,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->5->11->17->10->2->16->18->14->12->9->3->7->15->13->4->8->6." - } - ] - }, - { - "id": "hamilton-hard-graph199", - "image": "data/hamilton/graph_visual/Base/hard/graph199.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,8) (4,12) (6,10) (10,4) (2,5) (2,11) (8,6) (2,0) (9,8) (9,10) (0,1) (12,10) (1,11) (3,8) (3,4) (11,3) (2,7) (7,1) (12,2) (2,9) (1,3) (9,4) (12,0) (6,4) (9,13) (3,7) (6,13) (2,8) (1,4) (5,0) (5,13) (3,12) (13,11) (10,3) (8,1) (6,0) (10,5) (11,4) (8,7) (13,10) (7,0) (4,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->6->10->4->12->3->11->1->7->2->5->13->9." - } - ] - }, - { - "id": "hamilton-hard-graph398", - "image": "data/hamilton/graph_visual/Base/hard/graph398.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (4,5) (13,3) (15,13) (10,13) (11,9) (7,0) (8,15) (1,10) (2,8) (4,15) (8,16) (1,8) (9,13) (8,3) (3,2) (14,5) (6,13) (13,12) (12,0) (16,6) (0,15) (0,5) (12,2) (13,7) (3,15) (12,9) (5,15) (0,9) (6,1) (9,2) (9,15) (7,5) (11,2) (0,14) (7,2) (4,8) (8,11) (16,1) (16,5) (6,10) (8,7) (2,15) (13,2) (10,8) (15,11) (3,7) (14,8) (1,7) (1,4) (0,2) (1,11) (13,11) (10,9) (0,3) (16,14) (15,1) (12,14) (8,9) (12,1) (5,1) (6,3) (5,13) (4,13) (14,9) (6,5) (0,13) (2,1) (6,2) (11,0) (16,0) (16,12) (12,15) (16,2) (7,15) (16,10) (5,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->13->3->8->15->4->5->14->16->6->1->10->9->11->2->12." - } - ] - }, - { - "id": "hamilton-hard-graph117", - "image": "data/hamilton/graph_visual/Base/hard/graph117.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,3) (7,10) (0,9) (5,2) (3,9) (11,5) (3,7) (2,7) (6,11) (6,0) (11,10) (2,3) (11,9) (5,4) (0,1) (0,10) (6,2) (4,8) (10,6) (9,8) (11,0) (0,7) (10,4) (9,1) (6,8) (8,10) (10,3) (0,2) (0,4) (8,2) (5,8) (6,9) (1,10) (1,5) (5,10) (4,11) (0,5) (4,9) (5,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->3->4->5->11->6->8->2->7->10->1." - } - ] - }, - { - "id": "hamilton-hard-graph22", - "image": "data/hamilton/graph_visual/Base/hard/graph22.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,4) (9,0) (10,9) (0,4) (7,9) (10,7) (8,7) (1,5) (2,10) (6,1) (4,7) (10,3) (0,5) (7,1) (7,5) (2,6) (9,8) (7,2) (1,2) (6,4) (9,5) (4,9) (8,3) (6,5) (6,3) (3,9) (0,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->10->7->8->3->6->2->1->5->4." - } - ] - }, - { - "id": "hamilton-hard-graph527", - "image": "data/hamilton/graph_visual/Base/hard/graph527.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,5) (7,8) (8,13) (9,17) (0,7) (12,10) (2,15) (6,11) (7,1) (5,6) (12,13) (9,6) (3,16) (15,9) (9,5) (0,18) (4,15) (8,6) (2,12) (0,1) (16,10) (12,15) (2,11) (18,11) (17,7) (2,6) (13,6) (2,18) (3,12) (9,4) (12,16) (11,8) (13,14) (7,18) (7,3) (1,16) (7,11) (17,6) (7,12) (3,6) (18,6) (17,14) (8,9) (6,16) (8,3) (16,15) (18,4) (15,11) (9,12) (5,15) (1,9) (9,2) (10,5) (14,6) (13,10) (9,18) (16,14) (14,3) (2,13) (16,2) (15,1) (4,12) (4,16) (0,6) (15,3) (1,4) (17,15) (14,2) (4,3) (16,18) (15,8) (0,13) (0,15) (11,5) (14,18) (8,5) (2,5) (11,1) (7,16) (2,0) (4,5) (0,12) (7,14) (7,13) (4,8) (11,10) (17,18) (5,16) (2,10) (14,1) (11,16) (6,12) (3,13) (8,17) (13,11) (8,10) (12,17) (1,8) (11,9) (11,3) (16,13) (17,5) (6,1) (10,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->8->13->12->10->16->3->6->11->2->15->9->17->14->18->4->1->5." - } - ] - }, - { - "id": "hamilton-hard-graph71", - "image": "data/hamilton/graph_visual/Base/hard/graph71.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,3) (10,5) (9,1) (3,2) (11,4) (4,10) (2,11) (3,11) (3,8) (9,8) (9,3) (3,4) (1,7) (3,7) (8,2) (7,9) (4,0) (10,6) (2,1) (6,7) (0,11) (1,3) (6,4) (9,5) (1,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->11->2->3->5->10->6->7->1->9->8." - } - ] - }, - { - "id": "hamilton-hard-graph160", - "image": "data/hamilton/graph_visual/Base/hard/graph160.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,1) (4,7) (4,5) (1,5) (6,4) (4,1) (2,4) (1,11) (4,9) (11,7) (1,7) (9,3) (2,9) (4,11) (1,3) (2,12) (5,3) (3,10) (9,5) (10,0) (5,7) (3,6) (1,12) (9,12) (2,6) (7,12) (11,10) (10,4) (8,1) (0,12) (10,2) (11,2) (7,8) (11,12) (8,0) (7,2) (11,3) (0,1) (6,0) (10,9) (3,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->3->9->1->5->4->6->2->12->11->7->8." - } - ] - }, - { - "id": "hamilton-hard-graph98", - "image": "data/hamilton/graph_visual/Base/hard/graph98.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,8) (2,3) (1,3) (5,6) (10,7) (0,7) (2,9) (8,5) (6,10) (3,6) (10,11) (9,10) (4,8) (11,5) (8,2) (8,11) (9,0) (10,3) (2,11) (1,8) (4,2) (9,6) (8,9) (9,7) (1,4) (10,2) (2,6) (5,0) (11,9) (10,0) (7,3) (5,2) (7,11) (11,3) (6,0) (9,5) (2,1) (1,0) (10,5) (6,1) (3,9) (7,4) (11,0) (7,6) (1,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->10->6->8->5->11->2->9->3->1->4." - } - ] - }, - { - "id": "hamilton-hard-graph430", - "image": "data/hamilton/graph_visual/Base/hard/graph430.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (0,13) (10,2) (3,1) (3,14) (12,17) (3,8) (7,13) (1,9) (11,3) (1,14) (1,16) (6,4) (8,12) (10,7) (11,10) (11,9) (5,6) (0,5) (13,1) (11,13) (17,9) (0,8) (6,13) (17,5) (5,9) (2,1) (3,5) (1,10) (16,2) (4,5) (14,0) (6,12) (12,3) (6,7) (1,4) (16,0) (17,3) (0,2) (14,15) (5,15) (14,7) (15,17) (0,4) (8,4) (1,17) (13,9) (16,7) (4,12) (10,0) (17,0) (5,12) (7,3) (15,7) (11,17) (3,9) (10,14) (16,5) (8,9) (8,15) (15,1) (8,7)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->7->10->2->1->3->14->15->17->11->9->8->12->6->4->5->16." - } - ] - }, - { - "id": "hamilton-hard-graph532", - "image": "data/hamilton/graph_visual/Base/hard/graph532.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,6) (10,12) (9,4) (14,17) (5,3) (4,18) (17,5) (1,4) (17,10) (18,10) (1,11) (9,13) (9,5) (16,6) (16,17) (1,8) (14,5) (7,4) (4,11) (9,16) (12,4) (12,7) (3,8) (13,7) (14,2) (17,7) (2,5) (3,0) (1,9) (3,4) (10,1) (0,1) (16,18) (7,8) (0,14) (3,12) (2,7) (11,3) (7,15) (3,1) (0,11) (13,14) (18,17) (4,10) (16,13) (1,18) (17,2) (5,6) (11,7) (2,4) (12,15) (6,0) (5,4) (15,14) (6,8) (13,2) (6,14) (15,2) (0,8) (13,10) (9,0) (9,17) (10,11) (15,13) (17,12) (11,18) (12,16) (16,5) (2,11) (12,5) (17,8) (18,13) (10,14) (11,14) (1,6) (10,5) (2,0) (7,6) (0,7) (15,1) (11,5) (9,14) (16,7) (7,14) (11,15) (9,7) (15,10) (2,10) (16,11) (6,13) (3,9) (6,9) (1,5) (12,8) (12,6) (13,3) (18,7) (3,18) (2,12) (8,16)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->5->17->6->16->9->4->18->10->12->7->13->14->2->15->11->1->8." - } - ] - }, - { - "id": "hamilton-hard-graph246", - "image": "data/hamilton/graph_visual/Base/hard/graph246.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (12,10) (1,5) (2,4) (8,1) (7,11) (3,4) (1,10) (0,13) (9,6) (14,5) (14,0) (4,13) (7,6) (0,5) (0,9) (6,3) (0,1) (9,1) (8,12) (2,0) (10,13) (7,12) (1,11) (7,9) (9,2) (2,3) (9,5) (3,10) (7,3) (7,10) (8,7) (4,14) (14,12) (11,13) (7,0) (3,8) (4,10) (5,8) (3,12) (5,13) (13,9) (2,7) (8,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->4->2->9->6->7->11->1->5->14->12->10->3->8." - } - ] - }, - { - "id": "hamilton-hard-graph269", - "image": "data/hamilton/graph_visual/Base/hard/graph269.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,4) (5,10) (11,0) (12,8) (3,8) (1,10) (1,6) (3,11) (5,12) (8,1) (12,14) (1,7) (8,2) (0,4) (13,12) (9,11) (11,8) (12,0) (0,10) (14,0) (12,1) (3,13) (13,4) (3,1) (5,6) (5,1) (12,7) (13,8) (0,6) (14,2) (14,5) (6,8) (1,13) (5,13) (12,3) (3,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->5->6->1->7->12->14->2->8->3->13->4->11->9." - } - ] - }, - { - "id": "hamilton-hard-graph163", - "image": "data/hamilton/graph_visual/Base/hard/graph163.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,4) (4,6) (11,10) (8,7) (12,2) (12,5) (10,6) (0,8) (10,1) (6,7) (8,5) (12,0) (12,6) (6,11) (6,2) (12,1) (5,11) (4,7) (6,8) (9,2) (5,6) (8,3) (2,11) (3,9) (0,1) (9,0) (5,4) (2,8) (1,2) (9,10) (7,0) (9,8) (11,3) (9,1)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->7->6->4->11->5->12->2->1->10->9->3." - } - ] - }, - { - "id": "hamilton-hard-graph97", - "image": "data/hamilton/graph_visual/Base/hard/graph97.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,8) (10,9) (3,1) (11,7) (6,5) (5,10) (2,3) (9,11) (8,2) (0,9) (8,6) (7,9) (0,2) (2,7) (7,10) (2,1) (0,1) (2,5) (10,0) (4,0) (6,0) (4,1) (2,10) (10,11) (11,0) (9,4) (3,4) (0,7) (1,11) (5,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->10->5->6->8->11->7->2->3->1->4." - } - ] - }, - { - "id": "hamilton-hard-graph462", - "image": "data/hamilton/graph_visual/Base/hard/graph462.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,14) (8,0) (14,11) (12,8) (0,17) (7,15) (12,13) (2,13) (5,8) (4,6) (15,17) (1,0) (16,6) (5,17) (6,11) (12,11) (17,11) (12,15) (2,15) (3,9) (16,17) (17,1) (16,4) (4,2) (9,8) (8,3) (2,14) (4,11) (13,5) (11,10) (7,12) (6,3) (11,9) (16,1) (12,2) (15,14) (8,16) (8,6) (5,11) (13,9) (0,3) (5,4) (17,3) (1,5) (17,2) (10,12) (9,0) (15,10) (4,17) (7,0) (7,6) (4,10) (15,16) (11,3) (12,4) (0,4) (0,12) (11,13) (16,3) (13,4) (9,10) (9,5) (17,7) (16,2) (13,3) (14,13) (14,10) (14,6) (16,7) (10,5) (10,6) (3,5) (12,16) (11,1) (2,6) (6,15) (8,4) (5,12) (1,15) (0,11) (17,13) (0,13) (11,15) (15,5) (1,8) (2,0) (0,6) (6,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->12->13->2->15->7->6->4->16->14->11->17->1->5->10->9->3." - } - ] - }, - { - "id": "hamilton-hard-graph49", - "image": "data/hamilton/graph_visual/Base/hard/graph49.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (3,2) (9,3) (3,4) (5,4) (0,5) (4,6) (5,6) (8,1) (9,2) (0,10) (7,2) (9,0) (0,2) (9,8) (3,10) (8,3) (6,9) (10,2) (2,8) (6,10) (6,3) (5,7) (6,0) (4,7) (0,8) (6,2) (1,6) (0,7) (5,8) (1,10) (10,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->4->3->9->8->1->6->10->2->7." - } - ] - }, - { - "id": "hamilton-hard-graph182", - "image": "data/hamilton/graph_visual/Base/hard/graph182.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,7) (13,7) (5,10) (13,3) (12,3) (0,12) (1,6) (1,0) (2,3) (11,12) (10,13) (11,8) (11,5) (10,7) (5,6) (5,4) (2,1) (2,6) (9,1) (11,1) (9,4) (4,11) (0,8) (4,1) (13,8) (13,9) (11,3) (0,11) (1,13) (12,2) (3,10) (4,12) (9,12) (7,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->7->13->3->10->5->6->2->1->9->4->11->8." - } - ] - }, - { - "id": "hamilton-hard-graph479", - "image": "data/hamilton/graph_visual/Base/hard/graph479.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (13,17) (10,2) (7,17) (1,0) (16,6) (6,8) (3,4) (6,2) (13,4) (6,13) (13,0) (16,11) (17,9) (8,11) (12,7) (11,0) (3,1) (17,16) (15,1) (10,4) (8,1) (1,17) (4,1) (6,17) (5,10) (11,6) (2,11) (5,1) (11,1) (15,5) (9,12) (3,15) (9,7) (16,10) (2,12) (4,8) (11,5) (8,13) (4,9) (3,10) (0,3) (0,5) (9,8) (10,11) (12,15) (11,13) (15,2) (15,8) (16,13) (0,2) (9,14) (8,7) (2,17) (12,13) (8,3) (10,8) (2,3) (1,10) (6,3) (10,0) (11,3) (6,14) (17,0) (7,15) (3,12) (17,12) (14,3) (7,6) (12,10) (11,15) (15,9) (13,7) (9,13) (16,4) (1,2) (13,10) (14,13) (16,7) (14,17) (16,8) (2,8) (9,6) (5,3) (2,16) (3,9) (7,0) (12,11) (15,0) (5,17) (1,13) (7,3) (2,13) (0,14) (5,4) (14,4) (5,16) (16,1) (7,2) (17,3) (13,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->1->3->4->13->17->7->12->9->8->11->16->10->5->15->2->6->14." - } - ] - }, - { - "id": "hamilton-hard-graph336", - "image": "data/hamilton/graph_visual/Base/hard/graph336.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,0) (10,9) (2,4) (14,6) (5,15) (1,0) (11,2) (13,5) (2,12) (15,10) (14,10) (8,13) (12,1) (8,7) (5,3) (6,11) (0,15) (11,0) (13,7) (10,3) (3,6) (15,3) (2,10) (15,13) (14,1) (0,5) (6,2) (15,4) (12,15) (7,12) (3,2) (7,9) (6,4) (10,4) (9,2) (12,13) (15,7) (11,8) (13,6) (1,11) (15,9) (14,8) (5,9) (12,4) (14,11) (13,2) (10,0) (5,1) (5,11) (9,11) (13,10) (14,5) (2,8) (8,12) (12,11) (9,14) (5,4) (9,8) (13,4) (1,10) (5,6) (15,8) (6,9) (5,2) (15,1) (15,11) (14,15) (8,0) (14,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->7->8->13->5->15->10->9->2->4->12->1->14->11->6->3." - } - ] - }, - { - "id": "hamilton-hard-graph418", - "image": "data/hamilton/graph_visual/Base/hard/graph418.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,3) (4,2) (5,12) (16,5) (15,7) (4,5) (2,5) (9,15) (2,7) (11,7) (11,6) (3,8) (11,12) (7,5) (16,11) (14,0) (16,12) (1,5) (9,2) (3,1) (8,9) (16,1) (13,1) (13,16) (10,11) (15,1) (1,2) (0,1) (14,3) (2,11) (4,9) (7,13) (9,0) (13,5) (2,15) (2,14) (7,3) (14,13) (12,3) (3,4) (8,11) (0,11) (8,2) (2,3) (5,6) (0,15) (10,1) (13,9) (3,9) (13,2) (4,8) (2,0) (6,3) (8,14) (5,10) (8,1) (9,10) (13,12) (8,13) (6,16) (14,5) (4,10) (4,0) (14,15) (13,4) (2,6) (8,0) (9,11) (15,5) (9,14) (12,10) (0,12) (16,4) (5,0) (13,11) (14,12) (14,7) (14,16) (4,1) (7,1) (12,4) (2,16) (4,14) (15,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->14->3->5->12->11->7->15->9->2->4->10->1->8->13->16->6." - } - ] - }, - { - "id": "hamilton-hard-graph172", - "image": "data/hamilton/graph_visual/Base/hard/graph172.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,4) (5,12) (3,5) (6,8) (11,9) (9,3) (0,3) (4,5) (1,6) (8,9) (9,12) (1,12) (8,4) (7,8) (8,0) (1,10) (8,11) (7,6) (0,5) (9,6) (10,0) (5,2) (4,1) (4,3) (11,2) (3,6) (12,8) (11,3) (5,7) (5,9) (2,1) (2,12) (0,11) (1,9) (8,3) (9,7) (7,10) (12,11) (0,1) (12,0) (1,11) (5,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->5->12->9->11->8->6->7->10->1->4->2." - } - ] - }, - { - "id": "hamilton-hard-graph115", - "image": "data/hamilton/graph_visual/Base/hard/graph115.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,7) (8,10) (11,4) (6,8) (9,11) (6,3) (0,10) (4,1) (11,3) (9,5) (5,0) (8,3) (5,3) (6,2) (3,2) (9,3) (3,0) (4,7) (11,1) (7,6) (2,4) (5,10) (2,7) (1,8) (4,0) (10,2) (1,0) (1,7) (6,11) (5,2) (2,9) (8,2) (7,3) (10,1) (1,3) (7,11) (0,9) (6,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->8->6->3->11->4->1->7->5->9->2." - } - ] - }, - { - "id": "hamilton-hard-graph70", - "image": "data/hamilton/graph_visual/Base/hard/graph70.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,11) (4,1) (4,5) (7,1) (3,7) (3,2) (4,9) (7,8) (7,4) (4,6) (6,11) (11,1) (1,10) (7,9) (11,10) (7,6) (4,8) (2,9) (11,3) (8,2) (0,5) (5,8) (5,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->8->7->1->10->11->6->4->9->2->3." - } - ] - }, - { - "id": "hamilton-hard-graph19", - "image": "data/hamilton/graph_visual/Base/hard/graph19.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,9) (1,10) (8,2) (9,6) (2,9) (3,8) (0,8) (10,9) (7,6) (4,1) (8,10) (4,10) (6,5) (10,5) (8,7) (0,6) (8,5) (9,0) (8,1) (3,1) (7,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->2->7->6->5->10->9->4->1->3." - } - ] - }, - { - "id": "hamilton-hard-graph206", - "image": "data/hamilton/graph_visual/Base/hard/graph206.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (5,7) (12,11) (7,11) (3,10) (8,7) (2,13) (9,4) (0,4) (1,11) (4,7) (4,10) (9,1) (12,0) (13,7) (13,0) (12,3) (1,13) (3,0) (8,0) (10,11) (5,8) (5,11) (9,3) (7,2) (4,5) (1,10) (9,11) (1,3) (1,8) (1,6) (0,9) (9,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->9->10->3->12->11->5->8->7->2->13->1->6." - } - ] - }, - { - "id": "hamilton-hard-graph403", - "image": "data/hamilton/graph_visual/Base/hard/graph403.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (16,12) (15,13) (9,11) (15,9) (5,14) (12,9) (3,7) (6,1) (0,5) (6,3) (12,10) (2,16) (6,7) (13,11) (1,0) (13,0) (13,14) (0,9) (3,4) (15,10) (14,1) (14,11) (6,11) (7,8) (2,9) (12,0) (16,5) (4,13) (6,13) (12,6) (8,0) (8,14) (6,2) (1,7) (7,5) (0,14) (2,13) (9,13) (9,5) (14,3) (2,4) (14,12) (14,7) (15,6) (16,1) (3,9) (11,12) (4,16) (15,5) (6,10) (7,15) (10,11) (13,12) (8,5) (14,2) (8,15) (16,13) (2,10) (2,1) (13,7) (5,2) (4,5) (12,1) (1,3) (13,5) (3,11) (1,10) (10,7) (4,14) (10,3) (15,4) (0,3) (10,5) (8,9) (15,14) (4,9) (11,1) (10,16) (5,1) (14,9) (0,16) (13,1) (16,9) (11,0) (0,4) (14,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->14->13->15->9->11->6->1->16->12->10->2->4->3->7->8." - } - ] - }, - { - "id": "hamilton-hard-graph400", - "image": "data/hamilton/graph_visual/Base/hard/graph400.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,2) (5,6) (9,1) (14,8) (4,3) (11,13) (15,2) (8,3) (12,13) (4,15) (13,14) (15,16) (3,6) (11,6) (15,13) (7,2) (14,16) (13,6) (15,1) (8,0) (6,12) (3,16) (4,14) (2,1) (7,0) (16,1) (7,10) (14,5) (2,11) (8,16) (11,14) (13,0) (1,6) (4,13) (1,5) (7,3) (1,3) (12,5) (10,16) (13,8) (7,8) (12,0) (16,9) (15,9) (4,8) (13,1) (0,10) (12,11) (12,1) (0,16) (10,6) (9,8) (9,13) (9,7) (5,11) (15,7) (11,3) (14,7) (10,14) (1,11) (11,16) (8,15) (14,1) (9,0) (6,14) (6,7) (10,8) (12,10) (1,10) (3,15) (10,11) (14,12) (4,10) (4,5) (16,13) (13,5) (6,8) (3,10)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->14->13->11->6->5->1->9->16->15->2->7->3->4->10->12." - } - ] - }, - { - "id": "hamilton-hard-graph597", - "image": "data/hamilton/graph_visual/Base/hard/graph597.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (19,16) (0,3) (7,16) (18,6) (8,5) (1,15) (5,17) (7,17) (18,15) (14,16) (1,8) (10,8) (6,10) (3,7) (10,15) (18,12) (12,3) (12,4) (15,11) (7,6) (2,5) (16,9) (17,0) (17,3) (10,2) (1,3) (6,11) (4,16) (6,16) (18,10) (11,1) (4,15) (17,8) (11,4) (15,8) (7,1) (16,17) (19,9) (14,1) (2,16) (10,1) (11,7) (9,4) (7,10) (5,4) (11,5) (11,16) (5,9) (18,0) (3,9) (11,2) (2,18) (7,15) (9,6) (9,12) (5,15) (5,16) (8,9) (13,19) (6,4) (5,6) (7,4) (11,9) (17,15) (13,7) (9,2) (12,1) (10,12) (16,0) (15,14) (5,1) (15,12) (0,5) (16,1) (15,19) (19,5) (12,8) (2,0) (16,18) (6,15) (1,18) (13,10) (14,19) (1,0) (14,17) (7,5) (6,3) (9,10) (0,12) (1,13) (10,17) (0,10) (14,5) (0,11) (4,8) (5,18) (0,19) (9,14) (14,18) (17,1) (10,19) (16,3) (3,19) (8,7) (3,5) (6,17) (14,12) (19,1) (13,11) (2,15) (2,3) (3,10) (8,19) (17,2)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->7->16->19->9->4->12->18->6->10->8->5->17->15->14->1->13->11->2." - } - ] - }, - { - "id": "hamilton-hard-graph422", - "image": "data/hamilton/graph_visual/Base/hard/graph422.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (15,3) (12,7) (9,10) (13,15) (3,16) (12,4) (16,17) (9,6) (11,10) (0,12) (5,15) (6,15) (15,12) (8,0) (4,5) (4,17) (15,1) (5,8) (5,0) (2,1) (11,1) (14,0) (2,0) (13,10) (11,12) (17,7) (10,16) (1,3) (16,11) (10,4) (10,3) (7,10) (3,7) (14,4) (3,13) (0,9) (10,8) (17,12) (0,10) (15,0) (16,7) (14,6) (1,10) (17,9) (6,5) (16,9) (11,2) (11,4) (13,8) (17,3) (17,8) (17,10) (14,16) (7,0) (0,16) (13,17) (8,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->12->7->17->16->3->15->13->10->9->8->5->6->14->4->11->1->2." - } - ] - }, - { - "id": "hamilton-hard-graph2", - "image": "data/hamilton/graph_visual/Base/hard/graph2.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,2) (1,7) (6,8) (2,9) (8,0) (6,5) (1,4) (1,6) (6,0) (9,8) (9,6) (7,6) (2,6) (8,1) (0,4) (2,8) (9,10) (3,6) (5,8) (0,10) (3,1) (1,9) (7,4) (8,10) (6,4) (10,1) (5,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->9->2->10->1->7->4->5->6->3." - } - ] - }, - { - "id": "hamilton-hard-graph390", - "image": "data/hamilton/graph_visual/Base/hard/graph390.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (13,11) (1,8) (8,14) (1,5) (11,15) (15,7) (10,16) (5,0) (7,8) (7,13) (1,6) (0,2) (15,4) (7,6) (1,2) (12,9) (12,14) (11,2) (2,6) (7,11) (6,3) (1,3) (4,14) (15,16) (12,11) (4,11) (12,2) (3,4) (16,2) (7,5) (16,13) (4,8) (6,14) (7,12) (13,10) (14,2) (12,13) (5,6) (3,7) (14,1) (3,10) (15,8) (2,7) (12,6) (16,6) (6,10) (13,8) (1,10) (0,16) (13,9) (9,8) (15,3) (15,5) (13,2) (1,9) (4,5) (16,1) (0,11) (10,12) (12,3) (13,6) (5,13) (9,0) (11,6) (2,5) (9,11) (5,12) (0,12) (4,1) (11,1) (6,0) (13,1) (7,1) (16,12) (16,8) (9,14) (5,3) (4,0) (2,8) (8,11) (4,6) (5,11) (7,4) (7,10) (5,10) (15,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->5->1->8->14->12->9->13->11->15->7->6->2->16->10->3->4." - } - ] - }, - { - "id": "hamilton-hard-graph148", - "image": "data/hamilton/graph_visual/Base/hard/graph148.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,0) (7,3) (9,11) (2,4) (4,1) (9,12) (0,5) (9,6) (8,0) (8,10) (12,7) (1,3) (1,11) (11,5) (6,7) (1,5) (5,7) (1,0) (3,10) (3,12) (10,11) (1,2) (9,0) (7,4) (0,7) (8,12) (7,11) (6,4) (5,8) (6,8) (0,12) (4,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->4->1->3->7->12->9->6->8->10->11->5." - } - ] - }, - { - "id": "hamilton-hard-graph388", - "image": "data/hamilton/graph_visual/Base/hard/graph388.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,12) (1,5) (10,0) (13,14) (0,8) (4,16) (1,10) (12,16) (1,4) (11,10) (3,9) (10,5) (13,11) (15,0) (2,9) (8,10) (8,5) (6,3) (10,13) (9,11) (7,11) (11,14) (11,2) (2,8) (13,5) (3,8) (1,14) (6,12) (4,15) (13,7) (2,13) (16,5) (10,7) (0,2) (11,16) (6,2) (4,12) (1,8) (13,1) (1,2) (4,10) (6,0) (3,11) (15,5) (7,12) (12,15) (15,16) (9,4) (14,2) (12,0) (13,15) (6,7) (1,7) (4,5) (16,8) (5,3)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->10->1->5->12->16->4->15->13->14->11->9->3->8->2->6->7." - } - ] - }, - { - "id": "hamilton-hard-graph583", - "image": "data/hamilton/graph_visual/Base/hard/graph583.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (18,5) (10,14) (14,1) (3,6) (15,13) (5,7) (13,10) (9,15) (15,17) (13,18) (18,6) (5,15) (14,19) (11,15) (9,16) (17,16) (12,8) (10,3) (6,5) (10,12) (8,14) (15,14) (12,19) (4,2) (7,11) (17,4) (1,6) (19,6) (6,7) (13,2) (19,18) (19,9) (6,4) (12,11) (4,15) (0,8) (6,8) (1,17) (15,12) (8,3) (7,12) (6,14) (18,3) (0,15) (7,10) (5,14) (16,2) (16,6) (12,13) (5,0) (3,15) (4,13) (5,1) (12,14) (6,17) (13,9) (4,7) (17,12) (12,4) (6,15) (0,1) (10,5) (0,14) (7,1) (18,1) (11,17) (2,10) (16,14) (14,4) (14,7) (14,11) (13,3) (2,9) (0,2) (9,5) (18,2) (3,4) (18,9) (4,18) (16,7) (16,12) (8,2) (1,9) (10,18) (9,11) (2,7) (13,8) (17,9) (9,12) (1,15) (19,2) (1,11) (15,2) (1,10) (18,0) (14,9) (16,1) (6,2) (1,8) (0,11) (11,5) (5,19) (13,0) (16,4) (10,4) (14,3) (1,2) (5,8) (10,16) (16,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->8->12->10->14->1->6->3->18->5->7->11->15->13->2->4->17->16->9->19." - } - ] - }, - { - "id": "hamilton-hard-graph343", - "image": "data/hamilton/graph_visual/Base/hard/graph343.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (3,11) (1,10) (15,0) (8,0) (13,10) (8,2) (9,15) (8,5) (9,0) (5,12) (2,15) (12,9) (10,15) (2,1) (3,7) (14,3) (6,1) (2,11) (6,10) (5,1) (4,15) (11,4) (14,8) (10,2) (8,6) (10,12) (4,12) (14,9) (1,14) (9,13) (6,3) (7,8) (4,2) (8,12) (1,4) (1,11) (2,3) (12,13) (7,11) (0,6) (10,3) (13,6) (0,2) (0,5) (1,15) (8,10) (8,9) (14,13) (4,3) (14,2) (5,15) (6,11) (7,15) (9,2) (9,10) (0,14) (6,12) (6,4) (7,0) (14,12) (6,2) (13,5) (9,11) (14,10) (3,15) (13,0) (11,5) (3,0) (11,15) (7,9) (14,5) (9,3) (8,1) (8,3) (9,4) (3,5)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->15->9->12->5->8->2->1->10->13->6->4->11->7->3->14." - } - ] - }, - { - "id": "hamilton-hard-graph83", - "image": "data/hamilton/graph_visual/Base/hard/graph83.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,4) (2,1) (4,11) (5,1) (8,11) (2,7) (0,4) (3,9) (2,4) (4,1) (5,8) (7,1) (6,2) (2,8) (11,0) (6,1) (3,4) (8,10) (11,3) (1,8) (7,5) (8,0) (11,2) (10,7) (10,11) (10,4) (7,6) (8,9) (10,9) (5,11)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->4->5->1->2->6->7->10->8->11->3->9." - } - ] - }, - { - "id": "hamilton-hard-graph519", - "image": "data/hamilton/graph_visual/Base/hard/graph519.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (1,11) (5,10) (8,17) (16,9) (4,3) (14,1) (15,4) (6,14) (8,1) (1,4) (6,17) (11,8) (0,9) (13,6) (16,18) (12,15) (1,5) (13,12) (15,13) (10,7) (7,3) (9,13) (9,2) (16,10) (18,3) (9,12) (13,4) (6,0) (14,8) (0,8) (2,1) (16,12) (13,14) (6,8) (16,13) (17,16) (4,0) (16,14) (16,7) (18,2) (7,13) (9,11) (6,4) (11,2) (13,11) (2,13) (15,8) (9,4) (12,2) (5,17) (11,6) (4,16) (17,14) (10,6) (0,14) (11,12) (10,1) (17,9) (15,7) (5,18) (1,0) (9,8) (14,12) (10,8) (9,10) (14,15) (10,14) (3,15) (10,13) (15,16) (8,13) (12,5) (6,18) (17,15) (2,8) (18,11) (7,9) (11,5) (12,10) (7,17) (14,5) (15,2) (17,3) (16,5) (11,14) (15,10) (11,0) (15,1) (0,3) (5,9) (17,10) (14,2) (9,1) (5,3) (3,16) (13,0) (10,0)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->9->16->18->3->4->15->12->13->6->14->1->11->2->8->17->5->10->7." - } - ] - }, - { - "id": "hamilton-hard-graph250", - "image": "data/hamilton/graph_visual/Base/hard/graph250.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,9) (5,7) (2,3) (9,14) (7,13) (4,14) (8,11) (6,0) (6,1) (1,3) (12,1) (9,1) (8,0) (10,7) (9,0) (7,14) (10,8) (6,7) (13,8) (4,5) (0,1) (9,4) (2,6) (3,9) (14,10) (5,3) (3,12) (0,3) (5,10) (2,1) (10,0) (7,3) (5,9) (6,12) (11,1) (4,13) (12,14) (10,3) (6,3) (13,12)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->1->2->3->9->14->12->13->4->5->7->10->8->11." - } - ] - }, - { - "id": "hamilton-hard-graph304", - "image": "data/hamilton/graph_visual/Base/hard/graph304.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,15) (2,8) (9,3) (4,9) (11,4) (1,10) (5,15) (3,10) (2,12) (8,4) (1,5) (2,5) (15,11) (7,9) (9,12) (0,2) (8,5) (4,13) (7,0) (7,3) (10,14) (0,1) (1,8) (12,14) (11,14) (15,4) (4,1) (8,10) (9,1) (14,9) (2,3) (13,1) (7,11) (3,5) (13,12) (13,0) (11,5) (7,2) (11,10) (1,12) (1,7) (9,0) (1,3) (6,0) (2,11) (15,13) (7,10) (6,13) (8,9) (12,11) (6,5) (3,11) (8,6) (7,13) (10,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->2->8->4->9->3->10->1->5->15->14->12->11->7->13->6." - } - ] - }, - { - "id": "hamilton-hard-graph440", - "image": "data/hamilton/graph_visual/Base/hard/graph440.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,4) (7,15) (2,5) (12,10) (12,4) (7,10) (17,6) (14,0) (14,6) (10,5) (17,13) (17,8) (4,5) (3,0) (2,6) (6,8) (16,17) (7,6) (13,14) (10,15) (4,9) (0,1) (11,10) (14,8) (0,11) (11,13) (14,16) (15,6) (8,0) (4,6) (7,16) (11,14) (4,8) (10,17) (3,12) (17,4) (16,2) (5,1) (4,3) (15,12) (14,5) (8,10) (9,13) (3,15) (16,0) (4,2) (9,3) (13,10) (0,17) (3,5) (3,8) (14,9) (0,15) (7,3) (6,5) (7,9) (13,7) (2,11) (10,0) (1,7) (1,11) (8,11) (14,12) (16,8) (16,1) (17,2) (13,4) (1,13)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->14->6->17->13->11->10->12->4->1->5->2->16->8->3->15->7->9." - } - ] - }, - { - "id": "hamilton-hard-graph74", - "image": "data/hamilton/graph_visual/Base/hard/graph74.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,8) (0,3) (10,11) (9,6) (1,4) (3,1) (5,2) (11,5) (8,9) (5,1) (0,10) (9,11) (8,10) (7,9) (6,2) (3,5) (0,2) (7,1) (3,6) (9,3) (4,7) (10,2) (0,7) (7,3) (8,4) (4,6) (9,4)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->3->1->4->7->9->6->2->5->8->10->11." - } - ] - }, - { - "id": "hamilton-hard-graph595", - "image": "data/hamilton/graph_visual/Base/hard/graph595.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (18,19) (9,3) (2,5) (16,5) (13,7) (12,14) (13,16) (15,9) (12,1) (3,18) (17,0) (12,15) (15,0) (11,2) (17,18) (19,1) (18,15) (16,9) (8,19) (9,19) (15,4) (19,12) (0,6) (13,6) (5,0) (12,16) (19,3) (9,5) (14,11) (11,1) (5,1) (15,13) (14,6) (13,18) (6,2) (7,4) (1,8) (4,13) (12,11) (18,1) (11,19) (10,17) (13,1) (0,4) (1,16) (16,17) (8,5) (17,15) (11,3) (5,4) (1,2) (1,6) (17,13) (1,17) (12,7) (4,6) (3,13) (2,19) (4,16) (9,18) (4,8) (12,0) (18,7) (15,7) (11,0) (7,8) (15,5) (5,13) (10,13) (7,2) (8,15) (3,17) (5,10) (6,11) (3,12) (9,17) (18,0) (6,12) (18,4) (16,6) (5,17) (18,2) (9,11) (13,11) (4,14) (11,4) (5,7) (5,19) (8,11) (15,16) (17,7) (1,10) (16,2) (12,8) (8,13) (5,11) (16,3) (8,17) (10,14) (6,9) (10,19) (7,16) (3,10) (2,4) (9,14) (15,1) (3,5) (15,11) (6,10) (2,14)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->17->18->19->1->12->14->11->2->5->16->13->7->4->6->10->3->9->15->8." - } - ] - }, - { - "id": "hamilton-hard-graph28", - "image": "data/hamilton/graph_visual/Base/hard/graph28.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (4,10) (4,1) (0,10) (8,4) (8,10) (0,9) (1,7) (3,0) (1,9) (5,3) (5,10) (4,0) (1,0) (4,2) (6,9) (7,10) (8,6) (2,6) (6,4) (4,3) (7,3) (7,8) (4,9) (3,6)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->6->9->1->7->3->5->10->8->4->2." - } - ] - }, - { - "id": "hamilton-hard-graph452", - "image": "data/hamilton/graph_visual/Base/hard/graph452.png", - "conversations": [ - { - "from": "human", - "value": "\nIn this undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (7,13) (3,6) (13,17) (17,14) (13,0) (10,13) (0,4) (7,16) (11,1) (16,3) (13,6) (17,6) (0,1) (13,5) (13,8) (15,2) (9,3) (3,0) (16,4) (15,5) (2,0) (8,7) (1,2) (7,10) (15,12) (12,1) (9,16) (3,1) (2,7) (11,2) (12,17) (7,17) (15,4) (6,2) (1,15) (11,14) (7,14) (5,10) (12,2) (16,0) (4,12) (6,14) (3,17) (17,1) (6,1) (17,8) (6,12) (0,15) (3,4) (9,5) (1,8) (4,2) (2,13) (16,14) (11,9) (14,2) (0,11) (8,4) (1,7) (7,12) (5,3) (16,6) (15,7) (7,6) (11,5) (10,15) (8,6) (1,16) (5,12) (4,6) (3,12) (1,5) (16,8) (8,12) (12,13) (17,9) (14,10) (0,8) (16,17) (8,3) (16,15) (2,16) (7,11) (15,13) (9,13) (16,5) (10,9)\nQ: Begin with node 0, Is there a path in this graph that visits every node exactly once? If yes, give the path. Note that in a path, adjacent nodes must be connected with edges." - }, - { - "from": "gpt", - "value": "0->13->7->16->3->6->17->14->11->1->2->15->4->8->12->5->10->9." - } - ] - } -] \ No newline at end of file +version https://git-lfs.github.com/spec/v1 +oid sha256:77841f6cccd0822ccabc699a3af28922873aa447fcedacf02d61ae543915735b +size 645339