data/hamilton/QA/Text_Only_test.json

[
    {
        "id": "hamilton-easy-graph220",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,4) (0,5) (5,4) (2,7) (4,7) (3,9) (3,4) (6,7) (1,0) (5,2) (8,2) (8,1) (7,0) (6,2) (6,1) (3,8) (8,0) (8,7)\nQ: Is there a path in this graph that visits every 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->7->6->1->8->3->9."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph129",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,3) (4,2) (7,4) (8,7) (0,4) (8,5) (5,0) (6,5) (2,3) (8,1) (3,0) (5,3) (8,0) (3,6) (7,5) (7,2)\nQ: Is there a path in this graph that visits every 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->3->6->5->7->8->1."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph227",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,1) (4,5) (7,4) (6,4) (1,0) (7,3) (8,4) (9,7) (1,7) (9,2) (3,0) (8,7) (2,1) (4,3) (2,4) (3,2) (5,6) (7,2) (8,9) (4,0) (9,5)\nQ: Is there a path in this graph that visits every 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->8->4->6->5->9->2."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph68",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,6) (3,0) (1,5) (2,3) (0,7) (5,6) (5,4) (2,0) (5,7) (3,4) (7,1) (1,3)\nQ: Is there a path in this graph that visits every 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->5->1->7->6."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph29",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (1,4) (2,3) (6,5) (1,2) (6,0) (3,6) (0,2) (4,0) (1,0) (3,5) (6,1) (1,5)\nQ: Is there a path in this graph that visits every 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->2->1->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph196",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,4) (9,4) (4,2) (8,3) (0,6) (7,6) (4,5) (4,7) (8,2) (5,1) (9,3) (2,5) (1,8) (1,2) (5,6) (1,3) (8,4) (8,0) (8,9) (0,3) (1,9) (4,1) (0,9)\nQ: Is there a path in this graph that visits every 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->9->3->8->2->5->1."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph50",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,1) (3,2) (2,0) (3,4) (6,0) (5,6) (4,6) (1,5) (4,5) (3,6)\nQ: Is there a path in this graph that visits every 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->6->4->3->2."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph169",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,0) (3,5) (1,2) (8,5) (3,4) (4,1) (2,8) (2,3) (7,3) (4,5) (6,3) (1,3) (1,5) (6,4) (0,1) (7,4) (4,8) (7,1) (3,8) (7,5) (2,4) (0,7) (2,6) (5,0) (8,1) (6,0)\nQ: Is there a path in this graph that visits every 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->7->1->8->2->6."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph151",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (6,1) (2,4) (4,6) (0,8) (3,7) (3,1) (1,8) (6,7) (5,1) (3,6) (6,5) (0,1) (5,2) (0,6) (3,2) (2,6) (0,3) (2,1) (0,5) (7,5) (5,4)\nQ: Is there a path in this graph that visits every 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->4->2->5->7->3."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph233",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (0,2) (8,7) (5,0) (1,5) (8,4) (1,9) (9,7) (6,9) (8,9) (5,7) (6,3) (8,5) (8,0) (4,2) (1,8)\nQ: Is there a path in this graph that visits every 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->7->5->1->9->6->3."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph147",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,0) (6,3) (7,4) (8,7) (4,3) (2,6) (7,3) (6,5) (4,8) (5,1) (2,1) (5,3) (2,4) (4,5) (4,1) (8,6) (0,4) (2,8)\nQ: Is there a path in this graph that visits every 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->4->3->6->2->1->5."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph202",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,8) (1,5) (2,1) (0,3) (0,2) (6,3) (4,6) (2,6) (9,0) (4,3) (9,3) (9,6) (0,7) (6,7) (4,8) (8,3) (9,5) (1,0)\nQ: Is there a path in this graph that visits every 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->5->9->3->8->4->6->7."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph134",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,6) (4,3) (6,8) (3,5) (1,3) (7,2) (3,2) (1,5) (4,5) (2,0) (4,7) (8,4) (6,7)\nQ: Is there a path in this graph that visits every 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->3->1->5->6->8."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph122",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,3) (7,6) (2,5) (4,6) (5,7) (3,4) (7,1) (5,6) (5,3) (3,2) (5,8) (4,7) (5,4) (4,2) (0,6) (0,3) (1,8) (1,5) (2,0)\nQ: Is there a path in this graph that visits every 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->5->2->4->3->8->1."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph270",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (1,4) (4,8) (6,2) (9,2) (0,3) (4,7) (8,5) (1,0) (9,0) (4,0) (8,3) (5,0) (8,6) (0,6) (2,4) (9,6) (5,9) (2,7) (3,2) (3,5) (9,1) (7,0) (7,1) (8,1) (2,5) (3,9) (3,4) (3,7)\nQ: Is there a path in this graph that visits every 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->1->5->9->6->2->7."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph81",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (5,3) (6,2) (6,7) (2,4) (7,5) (5,0) (0,3) (1,2) (4,7) (1,3) (2,0) (7,3) (0,4) (5,2) (6,3) (6,0) (5,6) (4,1)\nQ: Is there a path in this graph that visits every 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->1->2->6->7->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph257",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,3) (2,3) (7,2) (8,1) (8,6) (1,5) (0,6) (9,6) (9,2) (9,1) (1,0) (5,6) (3,4) (4,6) (2,0) (6,2) (4,8) (8,7) (9,8) (4,2) (9,5) (1,6) (3,7) (7,6)\nQ: Is there a path in this graph that visits every 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->1->5->9->2->7->3->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph162",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,2) (4,6) (2,0) (3,2) (7,5) (1,4) (4,2) (6,3) (3,7) (4,3) (0,8) (5,3) (4,5) (8,3) (4,8) (3,0) (8,1) (0,6) (4,0)\nQ: Is there a path in this graph that visits every 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->7->3->6->4->1->8."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph288",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,3) (3,1) (1,5) (7,4) (5,3) (0,1) (8,0) (3,6) (8,2) (0,5) (5,7) (5,8) (6,5) (2,6) (2,1) (9,0) (9,3) (9,7) (4,3) (1,8) (3,0) (6,9) (2,5) (1,6) (9,2) (8,9)\nQ: Is there a path in this graph that visits every 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->2->5->6->9->7->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph96",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (6,5) (3,4) (2,3) (4,5) (1,6) (3,7) (2,7) (6,4) (0,3) (5,3) (3,6) (2,1)\nQ: Is there a path in this graph that visits every 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->3->4->5->6->1."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph289",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (3,6) (5,9) (0,4) (9,1) (5,8) (2,3) (4,7) (7,1) (6,2) (9,6) (0,5) (1,0) (1,8) (6,5) (7,5) (0,8) (7,8) (5,1) (4,1) (2,0) (9,7) (9,4) (6,7) (3,4) (9,3) (5,2) (9,0)\nQ: Is there a path in this graph that visits every 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->9->8->5->6->3->2."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph281",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (1,8) (9,4) (4,2) (3,8) (2,6) (5,9) (6,9) (4,6) (8,6) (2,5) (3,9) (2,8) (0,8) (7,0) (0,9) (1,4) (5,7) (1,2) (5,0) (2,9) (1,7) (7,3) (1,9) (6,1) (6,7)\nQ: Is there a path in this graph that visits every 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->2->6->9->3."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph97",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (3,1) (1,7) (4,1) (7,4) (4,0) (3,0) (7,0) (2,6) (5,1) (2,0) (6,7) (0,1) (4,3) (5,3) (6,3) (2,1) (2,3) (5,0)\nQ: Is there a path in this graph that visits every 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->7->6->2->3->5."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph109",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (2,0) (6,8) (0,5) (6,7) (3,1) (3,5) (6,0) (1,4) (2,1) (2,3) (2,6) (4,0) (6,3) (8,3) (2,4) (6,1) (1,8)\nQ: Is there a path in this graph that visits every 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->6->7->8->3->5."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph161",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,4) (5,3) (2,0) (8,4) (6,3) (3,4) (8,2) (2,5) (1,2) (6,1) (1,4) (5,8) (7,8) (7,1) (2,3) (1,0) (2,7) (7,0) (8,6) (5,7) (7,4)\nQ: Is there a path in this graph that visits every 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->5->3->6->1->7."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph108",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,4) (7,4) (1,5) (0,3) (0,2) (0,7) (7,5) (1,3) (8,2) (2,6) (6,4) (8,1) (4,5)\nQ: Is there a path in this graph that visits every 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->5->7->4->8->2->6."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph22",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (0,1) (4,3) (3,5) (2,1) (2,5) (5,4) (2,0) (1,5) (3,0)\nQ: Is there a path in this graph that visits every 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-graph258",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,7) (2,5) (1,4) (8,2) (2,4) (9,3) (9,7) (5,3) (6,3) (9,0) (6,9) (8,3) (4,5) (1,8) (1,2) (5,6) (2,0) (6,7) (8,4) (0,7) (1,3) (5,8) (7,3) (1,9) (2,6) (7,4) (1,7) (5,1) (7,5) (3,2)\nQ: Is there a path in this graph that visits every 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->5->2->8->1->4->7->6."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph235",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (2,7) (0,8) (9,0) (1,9) (0,3) (1,3) (1,5) (1,7) (6,8) (5,3) (1,2) (5,9) (7,5) (6,2) (8,2) (2,5) (8,7) (5,4) (6,4) (2,9) (1,8) (4,9)\nQ: Is there a path in this graph that visits every 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->2->7->1->9->4->5->3."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph171",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,1) (8,2) (8,5) (5,2) (0,3) (6,0) (7,4) (5,1) (0,1) (7,5) (8,6) (4,5) (8,7) (1,3) (6,4) (0,2) (0,7)\nQ: Is there a path in this graph that visits every 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->5->2->8->6."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph285",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,3) (5,6) (5,7) (9,2) (4,6) (7,2) (4,5) (0,4) (7,6) (6,0) (2,5) (3,5) (9,8) (3,2) (8,3) (8,2) (4,3) (6,9) (3,9) (8,0) (9,1) (7,8) (0,3) (9,4) (3,7)\nQ: Is there a path in this graph that visits every 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->7->2->9->8->3->1."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph274",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,2) (5,6) (0,9) (5,8) (6,4) (3,4) (6,8) (9,3) (0,8) (7,5) (8,9) (2,8) (3,5) (7,1) (6,2) (0,4) (1,4) (8,4) (5,4) (6,1) (7,6) (8,3) (2,7) (0,5) (2,9) (9,1)\nQ: Is there a path in this graph that visits every 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->6->5->8->2->1->7."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph84",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (6,1) (1,4) (3,0) (5,3) (7,6) (1,7) (6,2) (4,6) (1,5) (5,7) (2,4) (3,7) (1,0) (4,3) (6,3) (0,5) (5,6) (1,2) (5,2) (7,4) (4,5)\nQ: Is there a path in this graph that visits every 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->1->6->7->4->2."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph283",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,4) (8,3) (1,6) (5,7) (3,2) (6,8) (9,1) (4,6) (6,2) (9,4) (4,1) (6,9) (7,0) (0,3) (6,3) (9,5) (4,2) (3,9) (1,8) (0,4) (2,0) (0,1) (0,5) (8,4) (6,5) (1,5) (7,9) (9,2) (7,6) (8,7) (3,1) (4,5) (8,5) (2,5)\nQ: Is there a path in this graph that visits every 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->9->1->6->8->3->4->2."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph222",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,3) (8,7) (7,9) (7,0) (1,4) (0,6) (7,1) (9,8) (3,7) (2,5) (7,2) (5,1) (3,1) (3,2) (0,8) (6,3) (7,4) (8,4) (1,2)\nQ: Is there a path in this graph that visits every 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->8->4->1->5->2->3->6."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph292",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,9) (8,9) (0,1) (3,5) (7,8) (5,9) (6,2) (8,1) (7,1) (1,9) (4,8) (1,6) (6,7) (6,5) (7,0) (1,5) (4,0) (4,7) (0,6) (2,8) (8,6) (1,4) (8,5) (3,8) (0,2) (3,2) (3,0)\nQ: Is there a path in this graph that visits every 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->4->7->6->2->3->5."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph279",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,8) (7,9) (1,8) (3,1) (1,6) (5,3) (5,0) (2,3) (2,8) (5,8) (9,6) (2,7) (0,2) (5,7) (0,4) (7,3) (1,5) (0,7) (9,8) (8,7) (4,7) (5,2) (3,6)\nQ: Is there a path in this graph that visits every 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->1->6->9->8->2->7->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph297",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (4,8) (3,0) (1,6) (1,5) (7,2) (9,5) (8,0) (8,6) (9,2) (7,8) (6,9) (8,9) (9,1) (7,9) (4,3) (2,6) (8,5) (3,5) (7,3) (4,2) (3,6) (9,3) (1,8) (7,4) (5,6) (2,1) (6,4) (9,0) (0,4)\nQ: Is there a path in this graph that visits every 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->6->1->5->9->2->7."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph159",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,3) (1,2) (2,3) (4,0) (5,8) (7,0) (7,2) (0,1) (7,6) (5,1) (8,3) (3,4) (8,4) (6,0) (6,4) (3,7) (1,8) (2,8) (1,7) (3,1) (1,6) (7,5) (4,2) (5,0) (0,3) (1,4)\nQ: Is there a path in this graph that visits every 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->8->1->2->7->6."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph25",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (0,5) (0,6) (4,1) (1,3) (5,1) (6,4) (4,5) (1,0) (0,4) (4,2) (2,3)\nQ: Is there a path in this graph that visits every 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->3->2->4->6."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph145",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,3) (6,4) (2,0) (6,5) (7,1) (4,2) (4,3) (1,8) (4,1) (3,7) (5,8) (8,0) (6,3) (1,2) (7,8) (5,3) (8,6)\nQ: Is there a path in this graph that visits every 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->5->8->1->3->7."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph103",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (7,3) (0,1) (2,3) (4,2) (1,6) (6,5) (3,6) (6,4) (5,0) (3,5) (5,1) (5,2) (4,0) (2,7) (2,6)\nQ: Is there a path in this graph that visits every 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->5->3->7->2->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph182",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,3) (6,2) (2,0) (1,6) (7,2) (7,8) (2,3) (0,3) (0,6) (0,1) (5,0) (1,5) (3,7) (8,4) (5,6) (8,6) (8,5) (4,7)\nQ: Is there a path in this graph that visits every 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->3->7->4->8->5."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph187",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (5,1) (0,2) (1,8) (5,7) (4,8) (3,2) (1,6) (3,7) (4,0) (2,1) (1,7) (6,3) (6,2) (5,0) (5,2) (3,5) (3,4) (0,1) (7,2) (8,2) (4,2) (8,7) (0,7) (6,8)\nQ: Is there a path in this graph that visits every 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->7->5->1->6->8->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph199",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,8) (2,1) (2,3) (1,7) (6,8) (8,7) (4,2) (9,6) (0,8) (0,2) (5,1) (2,8) (2,7) (4,8) (7,4) (3,4) (5,6)\nQ: Is there a path in this graph that visits every 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->4->3->2->1->5->6->9."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph116",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,2) (1,7) (3,8) (5,6) (6,3) (8,7) (1,6) (6,4) (1,3) (6,8) (0,6) (0,3) (2,1)\nQ: Is there a path in this graph that visits every 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->1->2->4->6->5."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph118",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,3) (6,1) (3,4) (7,1) (1,8) (8,0) (7,4) (0,2) (5,8) (8,6) (2,3) (1,4) (2,7) (3,6) (7,0) (6,4) (0,1) (6,0) (6,2) (8,2)\nQ: Is there a path in this graph that visits every 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->7->4->6->8->5."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph165",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (1,7) (4,6) (2,4) (5,3) (4,0) (3,1) (2,6) (1,6) (0,1) (5,0) (6,3) (3,0) (7,8) (5,6) (5,7) (7,4) (0,2) (8,4)\nQ: Is there a path in this graph that visits every 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->3->5->8->4->6->2."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph256",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (1,0) (7,8) (0,8) (5,3) (1,9) (8,9) (6,0) (6,9) (5,0) (9,0) (6,3) (5,9) (3,8) (3,9) (2,3) (6,2) (4,9) (9,7) (2,9) (7,2) (8,2) (1,5) (4,1) (4,7) (1,6) (7,0) (6,5) (7,3) (3,0) (7,1)\nQ: Is there a path in this graph that visits every 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->8->3->5->6->2->7->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph254",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (8,9) (9,0) (1,8) (2,7) (9,5) (2,8) (0,8) (3,6) (4,6) (5,8) (3,2) (3,9) (9,7) (7,8) (9,4) (1,7) (0,3) (1,2) (7,3) (8,3) (7,5) (6,8) (6,5) (4,3) (4,8) (3,1) (2,0) (2,6) (7,6) (4,1)\nQ: Is there a path in this graph that visits every 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->1->7->2->3->5->6->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph4",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (1,0) (3,4) (3,0) (1,4) (2,4) (1,3)\nQ: Is there a path in this graph that visits every 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."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph105",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (7,0) (0,5) (4,6) (6,7) (0,6) (8,4) (3,2) (3,4) (5,1) (8,5) (7,1) (6,8) (2,6) (8,7) (8,3) (5,6) (7,2)\nQ: Is there a path in this graph that visits every 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->2->3->4->8->5->1."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph26",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (4,2) (1,5) (6,0) (0,4) (5,4) (3,4) (6,2) (2,1) (3,1)\nQ: Is there a path in this graph that visits every 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->5->1->3."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph173",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (4,8) (6,8) (8,5) (0,8) (1,8) (1,3) (3,2) (3,7) (2,7) (0,6) (5,3) (4,1) (7,5) (1,7) (6,7) (2,6)\nQ: Is there a path in this graph that visits every 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->2->6->7->5."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph246",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (9,8) (6,7) (8,6) (7,4) (8,1) (5,8) (2,6) (9,6) (2,9) (7,9) (3,9) (0,6) (4,2) (9,5) (8,7) (1,2) (8,2) (1,7) (0,8) (5,3) (5,1) (1,9) (3,1) (0,1) (0,2) (0,3) (6,3) (0,9) (3,7) (4,8) (4,9)\nQ: Is there a path in this graph that visits every 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->2->9->8->1->5->3."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph0",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 4, and the edges are: (3,1) (1,2) (4,3) (0,2) (0,4) (0,1)\nQ: Is there a path in this graph that visits every 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-graph45",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (1,4) (5,3) (6,3) (5,4) (3,0) (1,0) (4,2) (6,1)\nQ: Is there a path in this graph that visits every 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->5->4->2."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph124",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,4) (3,2) (2,7) (1,8) (7,8) (4,3) (5,2) (1,7) (6,3) (8,3) (0,1) (6,2) (2,4) (6,0) (0,3) (4,7)\nQ: Is there a path in this graph that visits every 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->4->3->6->2->5."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph164",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (6,3) (4,1) (3,2) (1,2) (4,5) (2,4) (4,6) (1,7) (0,1) (3,0) (2,0) (4,3) (7,0) (5,1) (6,5) (6,1) (7,2) (7,8) (0,6) (8,4) (2,5)\nQ: Is there a path in this graph that visits every 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->3->2->7->8."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph219",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (0,8) (7,8) (1,6) (4,7) (1,4) (1,9) (0,7) (5,2) (6,9) (6,0) (4,3) (1,0) (3,2) (3,1) (4,9) (5,1) (4,6) (5,7) (7,3)\nQ: Is there a path in this graph that visits every 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->4->3->2->5->1->6->9."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph168",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (5,7) (4,2) (4,7) (4,5) (2,8) (8,5) (0,6) (3,0) (5,1) (0,5) (4,1) (6,2) (1,7) (8,1) (4,8) (2,5) (0,4) (4,6) (8,3) (6,1)\nQ: Is there a path in this graph that visits every 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->7->5->1->8->3."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph158",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (1,6) (4,3) (3,7) (2,8) (5,0) (5,2) (0,6) (2,3) (2,0) (5,4) (8,7) (4,2) (6,4) (4,8) (1,4) (7,5) (1,3) (6,8) (5,3) (7,1) (1,0) (7,6) (1,8)\nQ: Is there a path in this graph that visits every 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->8->7->3->4->6->1."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph251",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (7,9) (3,8) (5,0) (8,4) (3,4) (7,3) (9,2) (1,3) (0,6) (6,1) (8,5) (6,8) (5,9) (0,9) (7,6) (6,5) (5,2) (9,8) (2,0) (2,6) (9,4) (9,1) (4,5) (8,7) (2,1) (9,3) (2,3)\nQ: Is there a path in this graph that visits every 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->3->4->9->7->6->1->2."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph275",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (5,3) (9,3) (4,0) (6,9) (6,8) (9,7) (0,7) (5,0) (5,1) (3,7) (6,5) (8,1) (9,0) (8,0) (1,3) (1,0) (6,0) (9,1) (7,2) (4,8) (3,4) (7,4) (2,5) (8,2) (4,1) (3,0) (5,7) (6,1) (4,9) (9,2)\nQ: Is there a path in this graph that visits every 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->6->9->3->7->2->5->1."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph60",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (6,7) (1,3) (5,0) (6,0) (4,6) (1,7) (3,5) (4,7) (2,6) (5,4)\nQ: Is there a path in this graph that visits every 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->1->7->4->6->2."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph291",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (3,0) (6,3) (2,5) (2,6) (1,0) (8,9) (8,3) (4,0) (8,0) (9,3) (6,5) (9,1) (6,9) (7,1) (4,5) (7,6) (9,2) (8,7) (4,1) (1,8) (7,2) (5,3) (8,5) (5,9) (2,1) (8,6) (3,7)\nQ: Is there a path in this graph that visits every 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->4->1->9->8->7."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph120",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (5,7) (0,6) (5,3) (4,3) (5,0) (6,7) (1,5) (0,8) (8,5) (5,2) (6,1) (7,8) (1,3) (0,7) (3,8) (3,2) (6,2)\nQ: Is there a path in this graph that visits every 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->5->1->6->2->3->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph141",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,6) (2,1) (2,7) (3,0) (0,1) (4,1) (7,8) (3,5) (2,4) (3,4) (2,3) (5,1) (6,4) (4,0) (8,3) (5,0) (5,4) (8,4)\nQ: Is there a path in this graph that visits every 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->4->1->2->7->8."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph86",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (2,3) (5,1) (6,0) (3,5) (1,7) (7,3) (0,5) (6,5) (2,6) (3,4) (4,1) (2,0) (4,6) (1,6)\nQ: Is there a path in this graph that visits every 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->7->3->2->6->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph127",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (7,3) (7,1) (1,2) (8,3) (0,1) (3,4) (2,0) (0,5) (6,1) (0,7) (4,6) (8,7) (3,2) (6,2) (4,8) (1,5) (7,6) (6,3)\nQ: Is there a path in this graph that visits every 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->7->8->4->6->1->5."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph280",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (5,8) (2,6) (1,9) (5,9) (0,1) (3,6) (2,3) (7,3) (9,7) (6,4) (0,5) (7,1) (0,6) (8,3) (2,5) (1,6) (4,9) (3,9) (5,6) (7,5) (2,9) (8,9) (8,7) (8,4) (5,4)\nQ: Is there a path in this graph that visits every 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->8->7->1->9->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph286",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,0) (9,4) (7,1) (0,1) (0,4) (5,6) (4,3) (2,9) (0,5) (3,9) (5,9) (8,6) (1,9) (6,1) (1,3) (8,0) (7,0) (9,6) (8,3) (7,3) (3,2) (3,5) (8,9) (1,2) (7,2) (5,7) (7,9) (7,4) (8,1)\nQ: Is there a path in this graph that visits every 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->9->4->3->8->1->7->2."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph66",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (4,2) (4,1) (5,0) (2,5) (3,1) (7,5) (7,0) (3,6) (4,0) (4,7) (3,7) (5,4) (0,2)\nQ: Is there a path in this graph that visits every 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->4->1->3->6."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph11",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 5, and the edges are: (3,4) (1,3) (5,2) (5,1) (0,5) (2,1) (1,4)\nQ: Is there a path in this graph that visits every 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->1->3->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph99",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (6,4) (1,5) (5,6) (2,4) (0,5) (3,2) (0,2) (7,3) (0,3) (6,7) (5,4) (4,3) (4,7) (5,3) (1,6) (1,4) (2,7) (1,2) (1,0)\nQ: Is there a path in this graph that visits every 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->2->3->7."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph252",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (6,4) (8,1) (1,5) (1,3) (9,5) (9,4) (0,9) (7,8) (0,4) (7,1) (2,6) (3,6) (0,6) (6,1) (2,5) (3,4) (2,0) (8,0) (9,7) (3,5) (1,4) (0,7) (2,4) (8,2)\nQ: Is there a path in this graph that visits every 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->3->6->4->2->8->7."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph155",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (2,7) (8,2) (4,1) (7,1) (0,7) (0,8) (8,6) (4,5) (3,6) (3,8) (5,1) (3,7) (4,7) (4,0) (2,4) (7,8) (1,3) (4,6) (1,2) (7,5) (4,8) (8,1)\nQ: Is there a path in this graph that visits every 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->8->6->3->1->4->5."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph80",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 7, and the edges are: (1,5) (7,2) (4,6) (0,1) (1,2) (2,6) (7,0) (6,3) (3,0) (1,4) (5,2) (0,6) (2,4) (4,3) (0,2) (1,3) (4,7) (1,6) (4,0) (5,0) (7,3)\nQ: Is there a path in this graph that visits every 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->7->4->6->3."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph121",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (8,0) (1,0) (1,3) (7,6) (8,2) (5,8) (7,1) (1,8) (0,5) (8,7) (6,3) (4,7) (2,6) (2,3) (6,0) (1,4)\nQ: Is there a path in this graph that visits every 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->2->8->5."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph36",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (3,0) (3,2) (3,4) (5,3) (0,1) (5,2) (6,0) (5,6) (0,2) (6,1) (5,4) (6,4) (4,1)\nQ: Is there a path in this graph that visits every 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->5->6->1->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph32",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (6,4) (3,5) (4,3) (6,2) (3,1) (5,6) (0,4) (3,0) (2,1) (1,6) (3,6)\nQ: Is there a path in this graph that visits every 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->1->3->5."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph295",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (2,5) (1,0) (1,9) (5,9) (7,5) (0,7) (5,6) (3,2) (7,3) (5,1) (5,8) (7,6) (2,6) (2,9) (6,1) (8,7) (6,0) (7,1) (4,6) (4,7) (3,6) (8,2) (4,8) (7,9) (8,3) (1,4)\nQ: Is there a path in this graph that visits every 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->5->9->1->6->7->8->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph210",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (2,6) (2,5) (0,7) (3,8) (2,1) (5,9) (1,0) (5,8) (6,3) (7,5) (6,5) (8,4) (9,1) (4,0) (9,8) (4,2) (8,1) (4,9) (6,7) (6,9) (9,2)\nQ: Is there a path in this graph that visits every 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->1->9->4->8->3->6->7."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph153",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (4,0) (8,7) (5,1) (3,2) (7,4) (7,5) (2,8) (6,4) (2,7) (3,8) (6,0) (4,5) (0,5) (0,8) (1,8) (6,8) (5,3) (6,5) (5,2)\nQ: Is there a path in this graph that visits every 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->2->3->8->1->5->6."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph132",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (5,1) (0,8) (8,5) (7,2) (7,8) (5,7) (1,0) (4,2) (3,6) (3,5) (8,3) (2,5) (3,4) (5,6)\nQ: Is there a path in this graph that visits every 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->4->3->6->5->1."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph216",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (8,4) (9,7) (9,3) (7,2) (8,3) (1,7) (4,5) (9,5) (8,1) (2,3) (2,4) (8,9) (2,1) (2,0) (6,3) (5,7)\nQ: Is there a path in this graph that visits every 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->9->5->4->8->3->6."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph287",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 9, and the edges are: (8,1) (4,5) (6,0) (6,4) (0,4) (3,5) (4,8) (1,6) (2,4) (7,8) (4,7) (0,7) (7,1) (2,1) (6,7) (9,2) (3,9) (5,6) (1,0) (6,2) (6,8) (8,5)\nQ: Is there a path in this graph that visits every 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->3->9->2->1->8->7."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph14",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (2,3) (1,2) (4,3) (3,1) (1,4) (5,0) (0,1)\nQ: Is there a path in this graph that visits every 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->2->1->4."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph178",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 8, and the edges are: (2,8) (5,1) (1,0) (1,3) (6,7) (5,0) (0,4) (0,7) (5,8) (4,8) (7,2) (8,7) (8,1) (5,2) (5,3) (5,7) (2,0) (4,6) (1,2) (6,1) (3,2) (2,4) (2,6) (1,7) (8,3)\nQ: Is there a path in this graph that visits every 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->8->4->6->7->2->3."
            }
        ]
    },
    {
        "id": "hamilton-easy-graph34",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 6, and the edges are: (6,1) (4,6) (0,3) (0,6) (6,3) (5,2) (5,4) (3,1) (1,0)\nQ: Is there a path in this graph that visits every 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->6->4->5->2."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph495",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (17,13) (18,7) (12,5) (13,8) (10,14) (17,4) (2,16) (2,1) (14,9) (10,2) (1,14) (5,13) (7,1) (1,17) (5,2) (4,16) (17,3) (15,16) (15,11) (2,8) (8,6) (3,18) (10,8) (8,15) (1,10) (6,9) (0,11) (11,10) (17,12) (16,3) (17,2) (9,3) (8,17) (3,6) (11,8) (12,6) (7,16) (2,3) (9,16) (4,3) (2,0) (15,0) (9,5) (14,18) (0,10) (14,8) (12,8) (15,4) (11,1) (15,9) (15,12) (14,4) (18,2) (13,9) (13,0) (16,17) (6,16) (14,2) (10,9) (4,1) (12,0)\nQ: Is there a path in this graph that visits every 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->15->16->2->1->14->10->8->13->5->9->6->12->17->4->3->18->7."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph461",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (5,2) (6,17) (8,2) (4,17) (12,9) (14,15) (6,11) (16,17) (11,2) (2,14) (11,16) (4,11) (13,17) (12,7) (9,1) (15,9) (17,0) (0,6) (2,10) (12,3) (14,9) (16,3) (15,11) (10,7) (14,10) (13,9) (0,7) (16,8) (0,12) (2,15) (6,1) (8,17) (2,17) (3,2) (10,0) (1,14) (15,10) (15,12) (10,9) (4,0) (14,16) (4,1) (5,6) (14,7) (7,4) (6,7) (4,14) (12,10) (8,13) (7,5) (6,3) (12,4) (5,13) (3,7) (7,11) (13,15) (2,9) (4,16) (9,3) (17,11) (4,5) (0,15) (5,0) (14,8) (6,15) (14,0) (8,12) (15,7) (11,8) (0,1) (12,14) (8,10) (3,10) (2,1) (12,5) (3,17) (8,6) (2,12) (12,13) (5,17) (5,3) (6,14) (2,0) (10,4) (1,8) (3,14) (3,0) (15,16) (8,0) (13,16) (10,5) (8,7) (12,16) (15,3) (12,6) (4,6) (9,7) (9,11)\nQ: Is there a path in this graph that visits every 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->6->11->2->5->7->12->9->1->14->15->13->8->16->3->10->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph164",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (6,7) (9,12) (6,9) (9,8) (2,0) (8,7) (2,3) (8,4) (12,7) (11,7) (10,0) (2,11) (5,4) (7,3) (9,7) (0,12) (5,3) (12,2) (3,8) (0,8) (1,7) (6,12) (10,11) (5,6) (6,11) (0,1) (5,7) (9,3) (3,12) (8,6) (7,2) (5,10) (4,6) (11,1) (10,12) (2,6) (9,2) (5,8) (4,7) (3,0) (6,0) (4,10) (6,1) (1,10) (11,9) (0,11) (7,10) (0,4) (10,3) (7,0) (3,4) (5,0) (4,9)\nQ: Is there a path in this graph that visits every 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->7->6->9->12->10->5->4->8->11->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph389",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (11,7) (7,16) (3,7) (1,7) (10,13) (11,15) (0,8) (7,9) (11,1) (10,2) (3,12) (1,13) (1,6) (15,8) (15,4) (16,9) (9,10) (5,16) (15,10) (6,5) (15,3) (12,8) (12,6) (0,3) (12,1) (16,11) (8,14) (9,11) (0,13) (11,10) (13,9) (10,16) (0,2) (6,13) (8,5) (5,11) (10,12) (9,3) (14,16) (0,10) (9,15) (12,14) (4,7) (4,5) (10,5) (5,13) (6,10) (3,14) (6,11) (6,16) (1,10) (0,11) (5,7) (16,13) (4,8) (3,6) (2,14) (1,15) (2,13) (10,4)\nQ: Is there a path in this graph that visits every 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->15->11->7->16->9->10->13->2->14->3->12->1->6->5->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph297",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (5,9) (0,6) (13,8) (11,6) (13,3) (10,0) (2,8) (9,2) (2,0) (4,10) (4,12) (13,12) (7,13) (4,5) (3,11) (14,3) (14,4) (12,14) (7,14) (3,9) (11,12) (11,9) (11,2) (4,13) (8,1) (10,9) (7,6) (5,7) (7,8) (2,12) (2,1) (6,13) (11,13) (5,3) (1,4) (14,6) (9,8) (4,9) (9,7) (6,1) (8,14) (12,10) (11,5) (4,8) (7,4) (9,12) (0,11) (2,5) (5,10) (3,2) (13,5) (6,10) (1,14) (10,11) (6,9) (9,0) (2,13) (10,13) (8,5) (1,10) (12,8)\nQ: Is there a path in this graph that visits every 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->13->8->2->9->5->4->12->10->1->14->7."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph546",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (14,1) (14,16) (6,13) (19,11) (13,5) (10,16) (8,6) (17,19) (3,0) (0,7) (8,9) (11,8) (5,6) (19,18) (16,0) (4,19) (11,12) (9,19) (7,16) (3,17) (6,16) (18,1) (8,13) (17,13) (1,0) (9,4) (19,3) (1,10) (4,3) (9,17) (18,12) (13,18) (9,3) (8,19) (0,13) (15,19) (4,10) (2,13) (7,3) (2,12) (3,11) (17,4) (7,17) (14,17) (2,9) (13,3) (18,7) (3,5) (1,7) (12,5) (19,16) (19,14) (9,15) (17,6) (1,13) (6,10) (18,0) (7,13) (10,15) (19,5) (2,4) (11,9) (15,2) (15,12) (7,8) (17,0) (12,3) (4,8) (1,17) (10,9) (2,8) (5,2) (1,5) (18,10) (3,2) (11,15) (12,19) (5,10) (16,8) (16,13) (1,3) (4,1)\nQ: Is there a path in this graph that visits every 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->17->19->11->8->6->13->5->12->18->7->16->14->1->10->4->9->2->15."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph340",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (12,5) (14,4) (9,1) (3,15) (6,3) (8,10) (3,9) (13,5) (7,6) (7,0) (13,6) (14,13) (1,10) (11,0) (2,9) (13,9) (15,7) (14,7) (7,2) (1,8) (3,12) (0,1) (9,7) (11,14) (12,6) (3,2) (15,11) (5,1) (2,15) (14,2) (14,6) (6,1) (5,0) (0,3) (7,4) (15,13) (12,10) (7,3) (9,15) (8,2) (11,7) (10,4) (0,14) (11,2) (5,8) (9,8) (4,11) (12,0) (6,4) (3,8) (4,13) (5,9) (1,13) (9,11) (4,2) (10,0) (5,11) (5,15) (13,3) (6,8) (12,7) (12,11) (8,4) (14,15) (9,14)\nQ: Is there a path in this graph that visits every 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->15->11->14->4->10->8->2->9->1->13->5->12."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph185",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (10,12) (6,2) (13,0) (13,9) (10,11) (13,3) (3,5) (4,7) (12,6) (11,3) (1,0) (7,8) (9,3) (10,2) (12,0) (1,3) (1,2) (11,13) (8,2) (12,2) (4,11) (13,7) (5,12) (10,8) (4,6) (4,9) (6,10) (10,4) (13,1) (6,3) (5,7) (8,1) (1,5)\nQ: Is there a path in this graph that visits every 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->9->3->5->12->10->11->4->7->8->1->2->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph442",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (12,15) (2,10) (11,15) (16,2) (17,2) (12,3) (6,3) (12,1) (10,6) (1,13) (14,11) (1,6) (6,12) (12,16) (12,10) (11,5) (11,2) (12,13) (17,7) (0,3) (9,17) (16,6) (6,8) (6,13) (14,9) (8,11) (0,17) (3,10) (9,12) (9,0) (3,9) (17,16) (7,5) (15,16) (2,9) (10,7) (16,0) (11,4) (8,7) (5,3) (2,12) (14,16) (0,1) (15,7) (5,16) (14,17) (10,13) (13,16) (5,8) (2,13) (8,14) (11,16) (7,1) (1,17) (6,0) (17,13) (16,9) (9,13) (17,15) (7,13) (13,11) (14,2) (6,2) (5,0) (14,4) (2,15)\nQ: Is there a path in this graph that visits every 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->15->11->5->7->17->9->16->2->10->13->1->6->8->14->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph282",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (7,2) (8,7) (13,12) (9,11) (0,10) (10,8) (5,1) (2,9) (5,10) (10,12) (14,4) (14,11) (9,0) (11,10) (1,13) (12,4) (0,1) (1,10) (7,1) (0,3) (8,4) (4,2) (14,6) (4,9) (11,8) (10,2) (8,12) (8,2) (0,11) (11,1) (13,7) (7,14) (2,11) (9,12) (13,4) (13,8) (6,9) (2,0) (8,9) (10,7) (3,14) (13,11) (2,6) (6,13) (0,8) (13,9) (12,6) (6,1) (14,13) (6,3) (7,3) (7,6) (12,1) (6,11)\nQ: Is there a path in this graph that visits every 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->7->2->9->11->14->3->6->13->4->12->1->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph257",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (14,10) (5,3) (10,7) (7,2) (3,1) (14,4) (14,8) (11,8) (14,9) (7,1) (5,0) (6,13) (9,6) (0,11) (13,1) (7,3) (4,9) (10,6) (4,8) (2,3) (2,8) (12,14) (5,12) (10,12) (1,8) (4,13) (13,0) (7,12) (3,11) (5,8) (10,1) (4,0) (1,6) (0,10) (11,14) (5,9) (14,5) (12,0) (1,2) (13,12) (5,1) (14,0) (1,12) (5,10) (7,5) (1,9) (10,4) (11,4)\nQ: Is there a path in this graph that visits every 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->14->10->7->2->8->11->4->9->6->13->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph232",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (10,4) (6,0) (4,3) (10,6) (3,9) (10,8) (11,12) (2,11) (8,1) (10,0) (6,8) (3,6) (0,9) (7,4) (4,5) (2,0) (2,1) (11,0) (0,8) (9,11) (7,5) (13,1) (5,12) (11,10) (13,11) (8,3) (4,13) (10,13) (2,4) (3,7) (5,13) (9,12) (13,3) (2,13) (5,10) (2,3) (12,3) (5,1) (10,3) (11,8) (5,3) (9,4) (5,9) (0,13) (7,12) (4,8) (1,12) (6,13) (0,3) (8,2) (6,2) (9,1) (11,4) (11,3)\nQ: Is there a path in this graph that visits every 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->4->3->9->11->12->7->5->13->1->8->2."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph445",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,2) (7,5) (7,12) (16,17) (3,16) (6,13) (11,7) (9,4) (7,10) (15,17) (5,0) (4,16) (13,4) (8,13) (15,8) (2,0) (6,15) (7,0) (16,11) (4,5) (9,7) (1,14) (15,14) (14,6) (16,0) (9,15) (4,10) (1,6) (10,12) (11,5) (6,2) (14,17) (8,17) (10,1) (10,16) (17,2) (14,16) (6,5) (9,3) (5,8) (12,13) (0,14) (7,4) (3,8) (10,17) (8,12) (11,1) (12,1) (11,13) (17,12) (4,0) (1,13)\nQ: Is there a path in this graph that visits every 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->12->10->4->9->2->6->13->8->15->17->14->1->11->16->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph26",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (10,3) (0,6) (5,10) (5,3) (9,8) (7,3) (1,10) (7,4) (1,5) (4,10) (5,9) (7,5) (6,1) (5,2) (2,8) (8,5) (4,2) (0,2) (5,6) (1,4)\nQ: Is there a path in this graph that visits every 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->10->5->9->8->2->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph299",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,9) (14,8) (2,9) (0,10) (2,8) (4,11) (2,7) (9,10) (2,14) (1,6) (13,9) (6,14) (0,4) (6,9) (5,1) (10,14) (2,5) (6,12) (7,0) (1,12) (8,6) (13,4) (7,10) (11,7) (3,9) (9,0) (13,14) (11,10) (3,4) (7,5) (3,10) (5,0) (8,7) (4,9) (7,12) (1,9) (4,1) (13,6) (6,3) (6,2) (1,14) (3,1) (8,4) (2,0) (6,0) (12,13) (4,12) (0,11) (0,14) (12,0) (7,9) (8,5) (14,12) (7,3) (3,8) (13,8) (5,11) (3,2) (12,9) (11,14) (5,9) (13,3) (11,8)\nQ: Is there a path in this graph that visits every 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->8->14->2->7->11->4->13->12->6->3->1->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph94",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (1,11) (5,11) (0,11) (4,9) (5,9) (1,6) (11,2) (1,9) (10,3) (8,2) (8,1) (3,0) (7,8) (11,8) (11,4) (0,9) (6,2) (4,0) (10,6) (9,2) (6,9) (3,11) (3,9) (4,5) (4,6) (4,10) (5,6) (10,11) (5,7) (9,8) (5,8) (7,4) (10,8) (3,8) (0,2) (2,3) (2,1) (5,0) (0,8) (1,4) (6,7) (3,7) (6,11) (3,6) (11,7) (9,10) (7,1)\nQ: Is there a path in this graph that visits every 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->1->6->2->8->7->5->9->4->10->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph472",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (2,13) (11,17) (3,10) (9,13) (9,1) (8,9) (12,14) (5,17) (17,7) (2,4) (5,9) (7,2) (8,6) (6,10) (1,0) (5,6) (17,8) (11,13) (6,13) (7,15) (13,4) (6,11) (7,3) (5,10) (0,8) (14,15) (1,16) (15,13) (11,0) (1,8) (0,17) (8,11) (10,0) (6,4) (15,8) (17,1) (5,12) (9,6) (0,16) (0,5) (2,0) (16,13) (17,16) (9,10) (16,10) (10,4) (12,17) (0,12) (1,6) (13,10) (4,9) (3,15) (11,5) (11,3) (1,11) (9,7) (14,4) (13,7) (11,7) (15,1) (10,15) (12,8) (0,14) (0,4) (1,3) (8,7) (3,16) (9,16) (5,8) (11,10) (12,7) (13,8) (6,15) (8,16) (3,9) (4,11) (12,15) (2,16) (16,4) (5,3) (16,7) (12,11) (1,14) (11,15) (1,12) (6,17) (5,16) (17,9) (14,7)\nQ: Is there a path in this graph that visits every 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->13->2->4->6->8->17->11->5->10->3->15->14->12->7->16."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph53",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (1,3) (10,9) (0,8) (6,2) (3,7) (0,9) (8,3) (5,8) (2,4) (8,9) (3,5) (3,10) (4,5) (10,6) (4,1) (0,3) (1,0) (1,7) (9,1) (5,7) (5,0) (0,10) (8,1) (6,8) (10,7) (10,2) (7,9) (4,8) (2,3) (2,9) (7,6) (5,9) (6,5) (0,4) (7,2)\nQ: Is there a path in this graph that visits every 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->1->4->2->6->10->9->7->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph428",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,15) (13,16) (11,7) (13,15) (6,17) (2,10) (2,7) (6,9) (3,10) (7,4) (2,8) (4,12) (13,14) (7,8) (13,9) (17,9) (2,15) (16,11) (12,10) (2,17) (12,1) (15,11) (12,13) (3,0) (6,2) (10,17) (1,11) (10,0) (9,5) (11,4) (9,14) (5,17) (1,2) (12,5) (12,3) (13,4) (6,7) (1,13) (10,14) (4,5) (10,16) (13,3) (16,3) (11,8) (8,14) (0,4) (4,15) (1,9) (11,9) (14,16) (11,0) (3,15) (1,4) (6,3) (12,16) (3,4) (7,9) (16,9)\nQ: Is there a path in this graph that visits every 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->2->7->11->16->13->15->6->17->5->12->4->1->9->14->8."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph284",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,3) (11,8) (13,3) (10,14) (5,7) (4,3) (7,14) (3,7) (1,8) (4,7) (14,12) (13,12) (3,8) (9,11) (8,9) (3,1) (5,10) (11,2) (13,5) (11,3) (0,4) (12,5) (8,7) (5,9) (6,1) (13,6) (6,7) (0,5) (4,13) (9,6) (9,14) (3,12) (0,6) (4,8) (5,3) (10,3) (0,8) (14,2) (13,1) (10,6) (12,9) (0,11) (14,6) (0,1) (0,7) (14,13) (0,12) (5,2) (0,10) (9,2) (3,6) (5,14) (11,5) (4,2) (12,4) (7,13) (2,0) (10,13) (8,12) (2,10) (13,8) (5,1) (6,8) (4,14) (2,12) (7,1) (4,9)\nQ: Is there a path in this graph that visits every 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->14->10->5->7->8->11->9->6->1->13->12->2."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph543",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (5,1) (19,14) (5,3) (8,9) (6,2) (14,18) (11,0) (1,6) (9,2) (1,16) (13,14) (14,3) (4,16) (17,0) (2,0) (15,6) (8,1) (3,7) (15,18) (3,9) (9,7) (6,12) (16,0) (15,19) (7,5) (0,7) (5,11) (1,7) (1,19) (11,6) (7,12) (9,19) (7,17) (11,13) (1,14) (19,4) (18,9) (4,12) (18,2) (6,0) (11,8) (7,8) (13,0) (13,9) (0,1) (19,0) (16,3) (14,11) (0,5) (4,14) (8,4) (5,17) (17,18) (3,13) (16,7) (18,3) (15,11) (16,15) (17,15) (7,6) (10,9) (16,5) (18,10) (13,17) (5,2) (8,12) (5,4) (11,7) (14,12) (10,17) (13,8) (15,2) (0,4) (11,12) (19,7) (4,1) (12,18) (5,19)\nQ: Is there a path in this graph that visits every 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->1->6->2->9->8->7->4->16->3->13->14->19->15->17->10->18->12."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph283",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (5,10) (3,2) (14,11) (10,4) (3,9) (8,1) (11,12) (8,4) (4,12) (14,1) (7,0) (11,10) (5,3) (14,9) (4,9) (9,10) (4,7) (7,2) (0,14) (3,11) (10,3) (6,7) (2,4) (5,1) (3,12) (9,8) (7,8) (0,6) (2,10) (5,11) (7,11) (10,0) (10,7) (9,2) (3,14) (1,2) (0,1) (8,12) (1,3) (2,12) (6,1) (11,13) (4,11) (13,8) (6,3) (8,3) (5,13) (9,11) (5,6) (13,9) (11,1) (7,13) (0,8) (5,14) (14,13) (1,10) (7,14) (1,7) (6,14) (8,6) (6,4) (6,11) (6,13) (13,12)\nQ: Is there a path in this graph that visits every 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->10->5->3->2->9->14->11->12->8->1->6->13."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph361",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (15,13) (4,11) (14,3) (9,3) (6,13) (16,11) (9,10) (8,12) (14,9) (7,13) (12,1) (5,1) (4,0) (11,10) (0,1) (11,14) (12,11) (10,12) (4,13) (5,8) (3,11) (8,11) (0,2) (5,4) (16,14) (16,8) (8,0) (10,13) (16,6) (13,12) (7,1) (1,2) (3,12) (12,6) (1,14) (15,3) (1,6) (3,4) (1,15) (12,5) (12,4) (7,4) (4,9) (4,8) (15,11) (0,9) (0,7) (0,16) (13,11) (2,12) (2,10) (9,13) (1,11) (3,16) (10,14) (11,5) (1,9) (4,14) (3,0) (6,3) (9,12) (8,15) (4,6) (8,9) (12,0) (5,14) (15,4)\nQ: Is there a path in this graph that visits every 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->16->14->3->9->10->2->1->7->13->15->8->5->12->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph84",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,0) (2,9) (6,0) (11,5) (4,3) (3,7) (9,4) (9,8) (10,7) (11,0) (8,4) (7,1) (7,8) (0,10) (3,11) (8,10) (1,8) (5,4) (1,9) (3,0) (9,7) (7,5) (10,1) (10,11) (11,1) (11,8) (11,6) (6,10) (3,5)\nQ: Is there a path in this graph that visits every 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->11->6->10->7->3->4->8->1->9->2."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph381",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (2,16) (3,7) (14,2) (14,10) (15,6) (3,6) (2,12) (9,4) (3,14) (9,3) (2,9) (13,4) (14,6) (6,10) (8,9) (2,3) (2,13) (10,11) (10,2) (5,4) (12,0) (11,9) (4,10) (7,9) (11,16) (3,0) (0,8) (6,0) (4,12) (15,16) (13,0) (6,4) (4,2) (15,3) (16,5) (7,1) (9,14) (1,8) (10,12) (15,1) (5,9) (2,1) (13,1) (16,13) (10,13) (14,12) (1,5) (6,11) (8,6) (0,16) (11,0) (0,9) (16,3) (3,11) (13,6)\nQ: Is there a path in this graph that visits every 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->16->11->10->14->3->7->9->8->1->15->6->13->4->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph1",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,5) (8,10) (3,9) (0,2) (2,6) (4,9) (9,10) (8,9) (9,7) (5,10) (7,4) (8,6) (9,6) (3,7) (0,1) (3,10) (8,2) (8,3) (6,0) (4,1) (9,2) (6,7) (4,10) (7,5) (5,6) (1,7) (8,0) (4,0)\nQ: Is there a path in this graph that visits every 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->5->10->9->3->7->4->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph473",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,1) (10,0) (11,7) (0,17) (11,10) (13,17) (4,11) (8,14) (17,16) (15,17) (6,5) (2,5) (9,15) (17,9) (4,7) (12,7) (12,6) (3,9) (10,16) (16,3) (4,0) (1,7) (11,12) (12,17) (10,9) (3,5) (15,11) (7,13) (8,5) (0,7) (14,11) (1,0) (9,12) (0,13) (17,10) (4,16) (11,13) (1,8) (16,2) (3,13) (12,5) (9,0) (9,6) (10,3) (0,14) (12,2) (15,2) (0,11) (4,3) (14,4) (7,3) (16,15) (8,6) (3,15) (14,1) (1,9) (9,14) (11,8) (17,8) (10,8) (12,4) (2,1) (8,3) (15,12) (14,7) (7,9) (16,9) (2,17) (8,16) (11,16) (14,17) (11,9) (13,2) (15,4) (15,14) (5,14) (11,3) (14,3) (17,5) (1,17) (2,9) (17,11) (7,10) (4,8) (2,8)\nQ: Is there a path in this graph that visits every 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->7->4->16->1->8->14->9->15->17->13->3->5->6->12->2."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph42",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,3) (4,8) (0,7) (7,4) (6,10) (10,3) (8,0) (5,0) (9,6) (9,8) (7,5) (3,7) (5,8) (10,0) (3,4) (7,8) (7,10) (0,4) (6,5) (2,10) (4,10) (7,9) (0,6) (9,4) (10,5) (3,0) (8,3) (6,8) (6,3) (6,7) (3,2) (4,5) (3,1) (4,2) (2,9)\nQ: Is there a path in this graph that visits every 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->8->9->6->5->10->2->3->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph334",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (9,0) (2,8) (7,8) (15,9) (14,0) (12,5) (0,12) (10,12) (4,10) (13,12) (5,14) (0,8) (6,10) (6,14) (15,4) (9,10) (15,12) (8,12) (3,10) (1,11) (2,14) (9,12) (3,15) (13,11) (5,13) (10,8) (15,1) (2,5) (7,11) (3,12) (4,14) (0,2) (6,12) (3,11) (15,10) (14,9) (6,5) (5,9) (13,9) (4,7) (11,6) (3,6) (7,1) (10,14) (9,6) (5,10) (4,0) (1,8) (4,12) (1,4) (0,3) (7,6) (11,10) (5,3) (2,9) (7,12) (14,12) (10,7) (8,5) (11,0) (13,10) (8,6) (2,12) (11,8) (10,0) (4,11) (13,0) (15,7) (0,1) (3,7) (7,5) (1,9) (15,11) (13,15) (2,6) (14,11)\nQ: Is there a path in this graph that visits every 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->4->10->12->5->14->6->2->8->1->7->3->11->13."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph468",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,17) (2,9) (3,9) (7,1) (10,17) (15,10) (9,17) (11,16) (8,16) (1,12) (4,17) (15,8) (17,7) (11,6) (6,1) (14,0) (0,6) (17,5) (0,1) (8,13) (8,17) (10,12) (15,13) (3,14) (0,4) (14,5) (14,11) (2,7) (14,10) (3,17) (11,13) (10,2) (7,3) (8,9) (13,6) (15,17) (9,5) (14,2) (12,2) (12,16) (11,3) (1,13) (2,15) (7,4) (3,6) (7,10) (1,4) (4,8) (12,6) (15,16) (11,4) (3,5) (11,8) (17,16) (9,0) (7,6) (9,12) (0,17) (0,12) (17,12) (6,4) (13,16) (3,10) (13,9) (15,3) (16,5) (14,15) (11,12) (1,8) (9,6) (8,14) (13,2) (15,5) (16,10) (8,12) (0,7) (15,11) (11,1) (1,16) (9,11) (1,2) (5,11) (14,4) (13,7) (2,11) (9,15) (5,8) (4,5) (6,2) (17,6) (0,3) (0,13) (4,3) (1,14)\nQ: Is there a path in this graph that visits every 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->9->2->7->1->17->10->15->8->16->12->6->13->11->4->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph558",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (9,6) (17,12) (15,13) (7,12) (19,11) (12,3) (13,19) (2,17) (2,18) (15,17) (2,11) (4,9) (14,11) (9,14) (7,4) (9,13) (17,6) (0,18) (3,1) (5,7) (16,7) (18,17) (6,8) (2,13) (18,5) (10,2) (17,1) (11,0) (19,18) (8,1) (18,8) (15,0) (19,6) (6,0) (18,10) (5,10) (2,8) (13,5) (14,13) (3,2) (4,19) (14,15) (18,11) (14,12) (0,16) (1,6) (3,17) (1,7) (2,1) (0,1) (19,10) (19,8) (14,6) (16,17) (17,10) (16,8) (8,14) (19,14) (1,10) (14,16) (6,13) (5,3) (0,8) (2,14) (9,8) (13,1) (2,6) (9,5) (17,7) (19,15) (19,7) (13,0) (16,6)\nQ: Is there a path in this graph that visits every 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->2->17->12->7->4->9->6->8->16->14->11->19->10->5->3->1->13->15."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph359",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (7,15) (8,9) (14,3) (7,13) (1,15) (12,7) (9,1) (3,2) (9,2) (0,9) (3,0) (4,1) (8,5) (11,12) (6,3) (10,15) (15,5) (6,10) (5,1) (15,14) (14,9) (10,4) (10,14) (10,12) (3,8) (4,9) (10,3) (8,7) (1,12) (12,2) (11,9) (3,4) (5,4) (5,2) (7,6) (6,11) (5,12) (13,2) (1,14) (2,6) (13,15) (12,6) (7,1) (12,8) (9,7) (1,10) (5,9) (5,13) (5,6) (8,13) (3,12) (11,3) (15,3) (8,15) (11,10) (13,4) (14,2) (2,1) (1,13) (8,2) (10,5) (3,13) (7,11) (13,10) (12,4) (5,0) (7,14) (10,8) (0,15) (0,6) (14,5) (3,7) (4,11) (3,9)\nQ: Is there a path in this graph that visits every 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->5->15->7->13->2->3->14->10->6->11->12->1->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph553",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,7) (8,1) (2,15) (3,2) (9,2) (18,1) (11,0) (17,15) (4,15) (16,8) (18,19) (14,16) (15,14) (14,0) (2,14) (7,19) (2,16) (2,1) (7,5) (3,1) (17,13) (11,8) (16,1) (12,13) (10,1) (12,9) (12,4) (14,3) (5,4) (18,7) (11,6) (5,6) (8,7) (7,12) (4,18) (15,1) (2,10) (6,14) (7,6) (17,16) (5,3) (10,16) (5,10) (0,18) (9,16) (10,4) (9,4) (7,1) (14,8) (0,9) (18,6) (19,8) (9,6) (15,18) (14,17) (3,7) (15,19) (9,5) (15,13) (11,16) (16,4) (13,19) (4,0) (6,2) (17,2) (6,15) (2,5)\nQ: Is there a path in this graph that visits every 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->8->1->18->19->7->15->2->3->14->16->17->13->12->9->4->10->5->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph198",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,13) (13,1) (12,5) (2,4) (4,1) (11,5) (5,0) (13,2) (11,3) (8,3) (3,0) (1,6) (9,3) (5,4) (9,10) (2,7) (2,0) (0,6) (4,11) (2,6) (7,3) (9,6) (10,1) (10,8) (4,8) (0,1) (9,5) (0,13) (8,13) (2,5) (9,7) (4,0) (11,8) (8,5) (12,0) (1,5) (13,12) (5,10) (6,3)\nQ: Is there a path in this graph that visits every 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->13->7->2->4->1->6->9->3->11->8->10."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph227",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (1,3) (3,12) (2,9) (7,4) (6,5) (7,0) (6,8) (4,5) (12,6) (3,10) (4,3) (11,8) (10,12) (7,2) (9,12) (11,12) (0,3) (6,1) (7,5) (2,13) (5,12) (3,11) (4,11) (13,7) (13,0) (6,13) (2,0) (8,7) (6,2) (4,0) (9,13) (1,2) (7,1) (10,2) (10,13) (0,10) (2,3) (10,1) (9,4) (0,1) (8,13) (11,1) (8,5) (5,9) (10,5) (4,8) (0,11) (7,9) (4,2) (9,3) (8,0) (7,3) (0,6) (1,12) (0,12) (12,13) (13,5) (13,4) (10,7) (5,0) (6,7) (4,12) (13,11)\nQ: Is there a path in this graph that visits every 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->5->6->8->11->12->3->1->2->9->13->10."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph25",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,8) (3,2) (6,10) (7,9) (6,2) (0,4) (5,9) (3,4) (9,8) (7,1) (1,2) (8,3) (7,4) (2,5) (10,4) (10,3) (6,4) (4,9)\nQ: Is there a path in this graph that visits every 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->10->6->2->1->7->8->9->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph113",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,9) (4,8) (7,4) (2,9) (11,4) (0,9) (6,10) (3,10) (9,8) (11,2) (7,9) (11,7) (0,6) (2,3) (6,1) (5,8) (2,10) (8,0) (4,0) (6,4) (5,10) (0,7) (2,6) (1,3) (11,1) (8,11) (3,7) (5,6) (4,3) (7,1) (9,4) (0,2)\nQ: Is there a path in this graph that visits every 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->10->3->2->11->1->7->4->8->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph195",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (5,6) (0,8) (7,13) (8,9) (13,6) (3,7) (13,3) (3,5) (9,12) (12,10) (5,13) (1,7) (8,4) (9,1) (7,0) (11,0) (1,11) (3,10) (11,4) (9,11) (5,8) (12,13) (10,6) (9,6) (7,6) (7,11) (0,2) (1,0) (8,1) (3,12) (4,3) (10,2) (10,8) (7,10) (12,0) (2,7) (6,11) (5,1) (12,5) (10,9) (4,13) (8,12) (11,2) (2,13) (4,10) (11,8)\nQ: Is there a path in this graph that visits every 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->12->10->3->7->1->5->6->13->4->11->2."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph175",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,12) (5,12) (4,6) (3,1) (9,4) (1,2) (1,7) (12,3) (2,5) (3,2) (6,0) (10,9) (11,3) (9,2) (1,8) (7,11) (2,11) (0,3) (12,9) (5,0) (11,0) (6,5) (11,12) (10,7) (4,11) (11,5) (1,9) (0,12) (2,7) (9,3) (11,9) (0,9) (12,8) (6,3) (0,10) (8,4) (12,7) (5,8) (8,3) (5,4) (3,7) (0,8) (8,9) (4,2) (11,6) (4,3) (10,1)\nQ: Is there a path in this graph that visits every 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->9->10->7->1->12->5->2->11->3->8."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph118",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (6,2) (7,0) (6,8) (7,11) (9,4) (11,5) (4,11) (8,0) (10,2) (2,9) (1,11) (5,4) (7,2) (8,11) (4,3) (9,6) (7,10) (11,10) (8,2) (10,5) (7,5) (9,0) (2,4) (7,1) (4,1) (6,1) (8,1) (7,3) (4,10) (10,0) (2,5) (0,1) (10,1) (11,6) (4,0) (0,11)\nQ: Is there a path in this graph that visits every 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->5->10->2->9->6->8->1->4->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph54",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (1,5) (1,2) (7,4) (6,8) (3,4) (7,2) (0,3) (9,6) (9,8) (7,5) (1,9) (2,6) (3,5) (9,10) (5,6) (9,3) (1,0) (3,1) (9,7) (6,4) (4,2) (1,7) (0,4)\nQ: Is there a path in this graph that visits every 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->7->2->1->5->6->8->9->10."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph0",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,10) (3,5) (2,9) (2,3) (8,7) (0,2) (6,10) (3,1) (5,8) (10,5) (8,2) (9,4) (2,10) (10,3) (0,9) (5,4) (9,5) (2,7) (5,2) (1,10) (6,2)\nQ: Is there a path in this graph that visits every 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->5->3->1->10->6->2->8->7."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph320",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (4,12) (6,13) (14,13) (7,2) (12,7) (13,7) (6,10) (4,6) (1,3) (14,2) (1,5) (11,0) (5,13) (12,3) (14,15) (1,6) (14,10) (14,1) (5,8) (1,2) (12,11) (15,9) (5,7) (14,9) (7,15) (14,5) (10,4) (5,3) (6,3) (0,3) (11,6) (1,11) (8,9) (15,2) (9,2) (9,12) (7,8) (15,0) (3,4) (0,13) (9,6) (8,3) (6,12) (12,0) (9,5) (11,14) (13,4) (1,8) (10,7) (0,14) (14,6) (5,15)\nQ: Is there a path in this graph that visits every 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->4->6->13->14->2->1->3->5->8->9->15->7->10."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph295",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (11,5) (9,8) (7,0) (1,3) (6,5) (5,10) (1,5) (5,3) (9,0) (3,14) (4,9) (13,7) (2,9) (13,14) (8,3) (9,13) (2,8) (8,13) (5,14) (5,2) (11,14) (9,12) (5,13) (4,3) (1,10) (14,12) (10,9) (2,4) (6,11) (13,1) (8,0) (1,7) (4,7) (6,4) (0,1) (9,14) (4,8) (10,0) (12,4) (7,2) (12,10) (7,8) (1,14) (12,7) (4,0) (8,6) (4,10) (5,9) (6,9) (6,12) (7,6) (4,11) (2,11) (13,3) (10,3) (8,12) (11,12) (11,3) (2,1) (12,2) (10,11)\nQ: Is there a path in this graph that visits every 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->14->3->1->5->11->6->4->9->8->2->12->10."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph85",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (10,11) (4,0) (5,4) (8,3) (6,1) (6,7) (5,7) (4,9) (1,7) (5,9) (1,0) (9,11) (2,3) (8,10) (9,0) (9,6) (8,0) (1,4)\nQ: Is there a path in this graph that visits every 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->1->6->9->11->10->8->3->2."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph179",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,10) (2,5) (10,0) (0,4) (12,7) (11,4) (5,4) (7,0) (4,8) (8,9) (7,6) (5,0) (11,7) (12,2) (12,10) (0,8) (11,0) (8,10) (3,9) (2,11) (10,11) (2,4) (2,10) (5,12) (4,9) (1,8) (1,12) (7,3) (8,2) (10,7) (1,10) (12,0) (5,10) (5,7) (4,6) (3,10) (11,8) (1,5) (8,7) (9,5) (1,4) (5,8)\nQ: Is there a path in this graph that visits every 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->6->7->12->2->5->1->8->11->4->9->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph538",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (0,8) (17,9) (1,2) (10,14) (0,15) (18,9) (13,16) (0,14) (4,18) (12,3) (12,4) (1,7) (8,16) (0,3) (16,11) (12,14) (3,15) (4,3) (16,7) (0,2) (12,0) (12,2) (12,1) (10,4) (2,16) (12,10) (7,17) (16,3) (1,6) (14,16) (9,3) (13,0) (17,12) (9,0) (12,16) (5,1) (1,18) (3,11) (1,11) (6,11) (3,14) (14,4) (4,6) (2,8) (4,17) (11,10) (10,5) (14,11) (8,7) (9,7) (14,1) (18,14) (7,3) (10,6) (12,13) (8,12) (7,4) (5,4) (10,17) (6,7) (10,1) (17,8) (11,8) (18,0) (2,4) (6,14) (11,13) (18,15) (14,15) (6,15) (13,14) (0,4) (8,15) (9,15) (9,1) (13,1) (18,10) (11,0) (18,5) (4,11) (16,10) (8,3) (6,5) (17,14) (2,3) (2,17) (9,16) (15,12) (7,13) (11,17) (18,17) (17,3) (7,14) (11,12) (13,15) (10,2) (17,15) (5,3)\nQ: Is there a path in this graph that visits every 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->16->13->12->3->15->18->9->17->7->1->2->4->10->14->11->6->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph181",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (12,11) (10,5) (6,10) (11,10) (8,5) (4,10) (7,0) (2,10) (1,7) (5,4) (7,5) (2,9) (13,7) (10,13) (7,12) (6,2) (7,6) (13,5) (3,10) (11,0) (0,4) (6,0) (11,5) (9,8) (8,2) (12,4) (4,3) (0,2) (11,4) (12,13) (9,12) (6,13) (9,0) (1,2) (13,11) (2,3) (5,6) (3,9) (11,7) (13,3) (8,12)\nQ: Is there a path in this graph that visits every 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->10->5->8->9->12->11->4->3->13->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph387",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (1,14) (9,2) (4,8) (10,6) (13,9) (14,13) (15,1) (5,14) (14,9) (2,0) (13,15) (13,8) (3,0) (10,12) (13,16) (6,13) (4,14) (12,5) (1,10) (13,3) (5,7) (5,15) (0,13) (1,2) (13,7) (2,11) (6,7) (13,1) (3,8) (16,10) (4,15) (8,1) (7,12) (1,4) (12,3) (5,1) (12,1) (6,9) (9,10) (7,8) (2,10) (5,8) (2,16) (2,3) (8,10) (4,2) (7,2) (15,8) (4,13) (14,8) (0,6)\nQ: Is there a path in this graph that visits every 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->9->14->1->15->4->8->5->12->7->6->10->16->2->11."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph517",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (0,16) (2,16) (10,13) (12,0) (13,1) (8,11) (12,4) (6,7) (15,1) (7,9) (4,7) (17,6) (13,7) (14,12) (11,18) (5,13) (16,17) (12,15) (4,18) (0,4) (17,5) (8,16) (4,5) (16,7) (18,9) (14,15) (6,16) (11,16) (15,13) (17,9) (14,5) (15,2) (6,2) (18,10) (12,7) (16,10) (2,11) (9,2) (11,7) (17,11) (15,6) (12,3) (3,4) (11,12) (18,8) (18,13) (10,17) (14,4) (17,12) (0,13) (9,10) (13,9) (2,12) (0,6) (0,17) (10,8) (12,5) (3,13) (8,4) (8,1) (16,3) (4,13) (15,3) (3,17) (2,8) (18,15) (8,17) (11,3) (13,17) (14,6) (8,0) (4,10) (3,1) (7,5) (2,0) (5,10) (16,14) (9,8) (15,16) (9,12) (1,10) (10,7) (2,14) (2,17) (16,9) (10,11) (0,15) (4,9) (13,2) (17,1) (2,18) (3,10) (2,3) (6,13) (9,6) (18,5) (14,9) (3,9)\nQ: Is there a path in this graph that visits every 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->2->15->1->13->8->11->18->4->12->14->5->17->6->7->9->10->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph276",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,14) (1,3) (8,4) (10,7) (14,6) (9,12) (6,7) (10,3) (12,2) (5,11) (0,11) (13,0) (14,0) (14,3) (4,14) (0,5) (7,4) (8,0) (13,5) (3,0) (9,2) (11,13) (14,10) (12,10) (13,6) (10,11) (1,4) (11,4) (11,6) (9,8) (1,2) (6,8) (3,7) (14,1) (4,5) (4,2) (3,11) (8,13) (10,5) (11,8) (12,11) (9,13) (11,9) (13,1) (13,3) (13,14) (10,9) (5,9) (14,8) (8,5) (9,0) (1,5) (4,10) (0,7)\nQ: Is there a path in this graph that visits every 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->13->6->14->9->12->2->1->3->10->7->4->8."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph548",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (4,18) (13,18) (18,17) (17,5) (11,8) (0,11) (13,5) (9,0) (17,4) (19,2) (7,12) (16,3) (10,16) (7,15) (14,11) (17,2) (9,4) (6,13) (19,16) (7,11) (14,2) (12,3) (19,3) (16,15) (17,7) (10,3) (6,11) (19,4) (19,9) (0,15) (15,3) (5,18) (0,13) (6,3) (4,7) (7,16) (2,8) (7,5) (9,6) (5,16) (16,0) (8,9) (11,17) (5,15) (17,6) (13,9) (12,10) (13,4) (18,2) (14,13) (13,8) (7,19) (5,8) (13,2) (14,4) (12,17) (15,14) (18,12) (6,0) (9,15) (0,2) (8,1) (7,10) (9,14) (14,1) (9,2) (18,15) (7,2) (16,2) (13,3) (13,15) (14,17) (7,6) (7,14) (15,8) (3,14) (12,11) (5,11) (14,19)\nQ: Is there a path in this graph that visits every 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->8->2->19->16->3->12->10->7->15->5->17->18->4->9->6->13->14->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph205",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (2,3) (3,0) (6,5) (0,8) (6,2) (3,13) (2,12) (2,0) (2,8) (10,9) (12,10) (9,8) (9,7) (8,4) (3,9) (1,8) (12,5) (9,4) (8,5) (7,5) (1,10) (11,9) (0,5) (7,13) (5,2) (1,9) (3,6) (2,9) (13,1) (0,11) (13,6) (6,1) (5,4) (11,10) (13,0) (10,2) (10,6) (7,1) (8,3) (5,10) (13,12) (9,12) (12,7) (11,13) (11,12)\nQ: Is there a path in this graph that visits every 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->5->12->10->9->4->8->1->7->13->11."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph265",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (9,1) (8,5) (3,4) (13,12) (6,1) (10,5) (11,10) (8,12) (3,13) (2,6) (1,13) (1,2) (7,9) (8,0) (2,11) (0,4) (8,10) (4,8) (3,1) (4,9) (6,13) (11,6) (3,10) (4,6) (1,14) (9,12) (13,8) (9,14) (3,8) (13,14) (10,9) (13,5) (1,12) (6,5) (13,9) (13,10) (10,2) (6,0) (14,4) (10,7) (2,14) (5,2)\nQ: Is there a path in this graph that visits every 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->5->10->11->2->6->1->3->4->14->13->12->9->7."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph475",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (16,12) (6,10) (3,15) (13,5) (8,6) (13,0) (7,14) (12,13) (2,7) (11,2) (16,9) (0,16) (2,4) (1,2) (2,14) (9,17) (1,14) (13,17) (3,5) (9,2) (13,14) (14,0) (14,17) (8,0) (7,15) (8,1) (6,13) (4,3) (8,15) (0,7) (11,5) (2,12) (0,4) (11,7) (10,17) (13,11) (0,17) (5,14) (10,9) (12,6) (17,11) (15,12) (8,2) (8,14) (8,5) (10,7) (4,15) (7,6) (4,8) (16,4) (15,17) (3,17) (12,10) (17,8) (5,2) (9,1) (7,1) (6,5) (16,7) (7,3) (7,13) (6,9) (6,3) (0,5) (4,6) (8,9) (13,3) (1,17) (0,1) (0,6) (8,3) (9,15) (10,4) (3,2) (17,4) (4,12) (4,7) (6,16) (1,13) (5,17) (12,9) (16,14) (13,16)\nQ: Is there a path in this graph that visits every 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->3->15->7->14->2->11->17->9->16->12->6->10->4->8->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph253",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (10,7) (2,3) (2,13) (9,0) (8,0) (11,8) (1,5) (8,5) (14,10) (7,6) (4,12) (2,12) (9,12) (7,4) (11,1) (5,4) (0,10) (10,13) (6,9) (11,2) (8,7) (7,5) (12,14) (2,6) (8,4) (7,3) (1,3) (13,4) (13,14) (3,9) (11,5) (6,11) (11,4) (11,0)\nQ: Is there a path in this graph that visits every 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->4->7->10->14->13->2->3->1->5->8->11->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph502",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (11,17) (5,0) (8,12) (8,17) (4,0) (8,14) (9,11) (7,1) (4,2) (5,14) (2,6) (11,16) (8,1) (16,12) (11,10) (17,18) (0,17) (1,11) (15,12) (1,4) (0,2) (11,7) (13,8) (1,17) (12,2) (17,13) (6,3) (10,6) (3,7) (17,2) (17,14) (16,9) (9,8) (15,1) (5,4) (15,4) (2,11) (10,15) (18,0) (15,9) (8,5) (6,15) (12,9) (3,1) (4,6) (12,10) (5,13) (11,14) (1,2) (8,10) (7,6) (6,8) (18,10)\nQ: Is there a path in this graph that visits every 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->8->12->16->11->9->15->4->2->1->7->3->6->10->18->17->13."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph142",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (7,8) (6,4) (11,3) (3,6) (7,12) (7,10) (2,8) (5,7) (8,3) (0,4) (2,0) (6,8) (11,2) (2,6) (2,12) (10,5) (3,4) (3,1) (9,0) (1,6) (12,4) (9,1) (3,9) (10,9) (9,7) (12,11) (2,10) (6,5) (7,6) (11,8) (12,3)\nQ: Is there a path in this graph that visits every 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->3->11->12->2->8->7->5->10->9->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph578",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (16,15) (19,2) (7,17) (2,7) (9,2) (5,15) (14,19) (2,0) (14,9) (17,13) (7,9) (7,4) (4,14) (2,14) (12,17) (12,11) (10,16) (17,16) (1,18) (5,11) (9,18) (19,4) (12,4) (19,11) (19,6) (5,13) (11,18) (0,3) (4,9) (6,10) (14,6) (17,0) (5,4) (1,10) (17,19) (3,18) (18,12) (5,6) (2,6) (12,2) (4,2) (3,8) (18,10) (8,9) (0,18) (12,14) (5,7) (10,2) (8,17) (9,16) (7,10) (14,18) (17,1) (12,15) (13,19) (2,18) (1,15) (10,19) (3,5) (12,6) (12,1) (8,11) (14,7) (8,1) (11,0) (2,5) (0,1) (6,4) (4,1) (10,4) (14,0) (8,6) (1,2) (18,6) (3,2) (13,6) (17,18) (5,12) (15,2) (16,4) (17,14) (13,7) (7,11) (15,9) (6,1) (7,19) (8,0) (10,15) (1,7) (15,17) (7,15) (11,4) (11,3) (2,11) (13,15) (15,18) (8,18) (18,4) (19,1) (8,13) (4,17) (16,19) (11,14) (5,17) (3,12) (13,18) (18,7) (8,12) (3,1) (2,17) (8,5) (6,3) (16,18) (13,3) (0,5) (5,14)\nQ: Is there a path in this graph that visits every 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->19->14->9->7->17->13->5->15->16->10->6->12->11->18->3->8->1->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph439",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (11,15) (11,17) (5,7) (17,15) (0,17) (12,0) (10,4) (15,10) (13,15) (17,3) (3,0) (12,16) (8,17) (14,6) (11,16) (11,3) (1,11) (6,5) (13,0) (6,7) (2,3) (11,14) (0,9) (13,9) (4,3) (2,12) (16,10) (0,1) (12,17) (14,9) (7,4) (8,4) (4,14) (15,12) (12,6) (3,15) (7,15) (2,11) (10,3) (8,15) (12,13) (5,11) (10,7) (2,17)\nQ: Is there a path in this graph that visits every 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->6->14->9->13->15->8->4->3->2->12->16->10->7->5->11->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph102",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (2,4) (5,4) (8,6) (11,1) (2,8) (3,2) (3,6) (9,10) (10,5) (9,6) (2,5) (10,8) (5,3) (10,0) (4,6) (6,1) (1,10) (7,6) (8,1) (10,6) (7,11) (2,10) (3,1) (8,9) (1,7) (4,11) (2,7) (2,6) (7,5) (8,7) (3,0) (7,10) (11,2) (8,4) (11,5) (2,1) (4,9) (0,1) (11,8) (10,4) (5,0) (4,0) (9,11) (8,5) (8,0) (11,10) (4,3) (1,9)\nQ: Is there a path in this graph that visits every 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->8->2->4->5->3->1->11->7."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph516",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (10,2) (9,17) (6,4) (8,6) (3,12) (8,3) (9,13) (12,14) (13,17) (3,16) (3,14) (7,15) (18,7) (12,17) (14,11) (4,5) (2,11) (2,5) (10,5) (12,2) (10,12) (18,1) (14,2) (15,9) (12,18) (11,16) (18,6) (12,5) (11,18) (2,18) (9,0) (16,14) (10,0) (5,14) (3,6) (13,15) (3,7) (11,12) (4,2) (9,5) (1,10) (9,12) (5,3) (18,3) (4,17) (15,12) (2,6) (11,5) (4,9) (4,11) (3,1) (15,18) (12,1) (0,2) (9,2) (3,4) (16,5) (17,7) (13,16) (16,8) (0,16) (6,7) (5,7) (17,14) (10,3) (0,4) (11,15) (8,9) (10,6) (15,17) (10,16) (8,2) (11,1) (7,0) (11,0) (16,15) (3,15) (8,4) (4,16) (5,17) (5,18) (6,12) (0,18) (6,13) (4,13) (0,5) (10,7) (18,17) (7,9) (8,10) (5,8) (15,10) (4,15) (3,0) (10,14) (8,14) (13,7) (18,16) (12,0) (6,9) (1,9) (13,18) (3,17) (8,15) (7,4) (15,0) (18,9) (12,13) (2,1) (14,4) (16,1) (6,1) (1,5)\nQ: Is there a path in this graph that visits every 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->17->13->15->7->18->1->10->2->11->14->12->3->8->6->4->5->16."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph408",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (15,5) (5,10) (1,8) (4,10) (4,3) (13,9) (3,10) (2,3) (15,9) (5,16) (2,15) (8,14) (15,8) (8,9) (13,7) (9,2) (4,14) (12,13) (9,11) (0,8) (14,5) (1,13) (1,15) (6,10) (11,14) (11,6) (12,9) (8,7) (7,5) (5,11) (11,3) (15,0) (9,3) (15,16) (6,1) (2,0) (0,9) (3,13) (1,9) (6,2) (0,11) (6,3) (15,3) (6,16) (10,7) (11,10) (13,11) (10,15) (0,4) (3,7) (13,14) (1,16) (0,12) (14,6) (4,8) (10,0) (5,4) (6,12) (15,7) (10,13) (16,7) (5,12) (16,3) (0,14) (9,4) (5,8) (2,5) (2,1) (6,7) (15,13) (8,10) (6,9) (0,16) (13,6) (16,2) (16,8) (4,13) (16,13) (2,4) (16,10) (11,7) (11,16) (3,8) (5,1) (10,9) (6,8) (5,0) (3,14) (2,7) (12,10) (11,2) (13,0) (1,0) (1,14) (5,9) (13,8) (4,15) (12,2)\nQ: Is there a path in this graph that visits every 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->13->9->15->5->10->4->3->2->16->7->11->14->6->12."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph275",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (0,3) (3,1) (4,0) (4,3) (12,3) (1,9) (14,0) (6,10) (1,8) (0,7) (8,3) (1,0) (3,9) (1,10) (8,0) (8,13) (6,8) (9,10) (11,4) (14,12) (13,9) (9,2) (6,7) (2,11) (10,4) (9,6) (5,12) (13,14) (7,14) (1,12) (1,7) (0,13) (9,8) (2,12) (11,12) (5,6) (10,3) (5,14) (11,13) (10,8) (6,0) (6,1) (1,14) (6,2) (0,11) (4,6) (4,2) (4,5) (1,5) (3,2) (6,11) (7,2) (12,7) (8,14) (13,12) (2,14) (5,8) (6,12) (12,0) (2,0) (1,13) (8,11) (13,6) (4,14) (10,7) (7,8) (9,0) (7,5)\nQ: Is there a path in this graph that visits every 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->9->10->6->8->13->14->12->5->4->11->2->7."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph77",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,4) (4,2) (9,6) (7,10) (5,3) (6,10) (11,1) (2,9) (6,4) (5,11) (8,6) (10,5) (3,10) (9,7) (9,10) (1,7) (2,10) (1,5) (0,3) (11,7) (4,3) (4,5) (7,3) (2,1) (1,4) (6,11) (11,10) (9,1)\nQ: Is there a path in this graph that visits every 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->11->1->7->10->9->2->4->6->8."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph447",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (8,16) (5,4) (11,1) (12,1) (9,3) (0,10) (17,5) (14,15) (14,4) (1,17) (15,16) (0,4) (11,16) (15,10) (8,1) (10,13) (11,14) (17,16) (9,6) (3,17) (15,5) (13,14) (3,1) (9,8) (8,11) (13,6) (2,6) (14,16) (17,8) (7,9) (10,4) (4,11) (6,3) (3,11) (1,0) (10,6) (5,6) (4,1) (11,2) (8,14) (17,12) (11,7) (15,2) (10,2) (7,2) (3,8) (6,8) (5,3) (0,12) (0,7) (2,0) (6,14) (13,17) (17,2) (4,9)\nQ: Is there a path in this graph that visits every 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->14->4->5->17->12->1->11->16->8->3->9->7->2->6->13."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph333",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (14,10) (12,10) (8,9) (7,10) (13,1) (11,10) (9,13) (0,1) (1,8) (0,13) (9,7) (8,2) (1,6) (2,15) (4,13) (14,4) (12,7) (13,8) (8,0) (15,11) (10,1) (14,8) (9,6) (6,3) (3,8) (6,0) (6,4) (14,2) (4,11) (5,3) (1,4) (1,7) (4,3) (14,7) (7,15) (7,5) (1,2) (5,0) (13,10) (1,11) (10,6) (13,11) (14,1) (10,9) (11,2) (0,3) (15,12) (8,6) (13,12) (14,0) (12,1) (0,4) (11,14) (1,5) (4,7) (0,15) (7,3) (12,4) (2,13) (12,8) (0,2) (11,12) (11,8) (0,12) (9,4) (15,10) (3,12) (11,3) (12,6) (13,6) (3,13) (14,9) (3,15)\nQ: Is there a path in this graph that visits every 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->9->8->2->15->11->10->14->4->6->3->5->7->12."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph571",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (8,2) (5,6) (8,0) (14,19) (18,6) (16,0) (2,10) (9,6) (14,6) (16,19) (17,14) (2,18) (9,14) (9,1) (15,0) (13,1) (15,7) (19,4) (13,14) (9,8) (5,8) (17,2) (2,15) (18,1) (5,19) (3,6) (12,17) (12,8) (9,13) (14,10) (5,15) (13,7) (13,5) (4,17) (2,6) (11,10) (1,6) (0,19) (4,14) (2,19) (12,10) (4,18) (19,17) (15,13) (14,15) (11,16) (19,10) (18,12) (10,4) (2,12) (19,8) (6,19) (11,9) (19,9) (17,1) (15,12) (3,11) (7,9) (12,1) (7,11) (6,11) (18,0) (0,5) (16,5) (13,4) (7,12) (13,8) (10,16) (11,14) (4,8) (4,3) (13,17) (7,2) (13,3) (16,3) (18,17) (10,17) (3,19) (16,17) (8,7) (15,1) (7,0) (10,15) (3,15) (4,6) (12,13) (19,11) (16,9) (1,2) (3,17) (1,10) (8,14) (0,14) (12,16) (16,2) (18,8) (1,4) (2,9) (0,1) (10,13) (7,4) (19,12) (10,18) (14,12) (13,18) (17,0) (11,8) (16,15) (5,14) (11,18) (5,2) (12,11) (2,0) (5,7) (9,18) (4,5) (16,1)\nQ: Is there a path in this graph that visits every 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->10->14->19->16->11->9->6->5->15->7->13->1->18->4->3->17->12."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph266",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (2,8) (3,2) (4,9) (7,2) (9,12) (14,5) (7,4) (10,7) (14,7) (9,6) (11,7) (7,3) (14,8) (6,10) (9,1) (8,11) (6,8) (9,11) (3,0) (2,12) (5,8) (1,13) (1,11) (6,4) (8,13) (3,5) (3,13) (5,1) (3,6) (5,11) (0,1) (4,8) (3,10) (13,5) (0,12) (12,5) (5,9) (6,11) (11,2) (2,10) (3,4) (5,2) (0,2) (0,14)\nQ: Is there a path in this graph that visits every 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->14->5->13->1->11->7->10->6->4->9->12."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph61",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,0) (8,1) (4,0) (5,4) (2,3) (9,4) (10,7) (6,0) (7,0) (4,1) (2,11) (8,7) (7,1) (8,9) (11,6) (11,3) (1,10) (5,10) (3,1) (11,10) (0,2) (0,1) (11,8) (6,4) (3,6) (0,5) (0,3) (1,5)\nQ: Is there a path in this graph that visits every 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->3->1->5->10->7->8->9->4->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph437",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (12,5) (3,15) (8,17) (14,16) (1,0) (17,0) (2,1) (8,1) (15,2) (16,5) (4,5) (14,7) (16,15) (16,8) (6,2) (3,14) (17,3) (15,13) (10,12) (14,4) (10,5) (3,13) (0,10) (8,0) (16,7) (15,5) (4,2) (12,8) (14,5) (7,11) (9,7) (16,13) (5,13) (7,15) (9,3) (13,6) (1,13) (14,13) (17,16) (6,12) (10,9) (2,3) (7,1) (0,11) (7,4) (16,6) (13,9) (10,15) (17,9) (11,14) (2,8) (16,0) (11,17) (7,0) (4,6) (10,4) (4,0) (10,11) (17,13) (10,7)\nQ: Is there a path in this graph that visits every 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->15->3->14->16->5->12->10->9->13->6->4->7->11->17->8."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph73",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (0,11) (11,7) (10,8) (6,2) (8,4) (10,0) (10,2) (9,6) (2,11) (11,10) (3,11) (8,3) (8,2) (8,5) (10,4) (2,4) (11,8) (2,3) (2,1) (9,1) (9,11) (6,1) (6,5) (0,5) (7,0) (0,1) (4,5) (2,7) (6,4) (5,1) (6,8)\nQ: Is there a path in this graph that visits every 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->2->6->9->1->5->4->10->8->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph36",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (9,10) (2,7) (8,7) (6,5) (0,3) (2,4) (10,4) (3,10) (10,0) (2,0) (3,9) (6,2) (10,1) (3,6) (9,2) (0,5) (5,9) (3,5) (7,3) (8,6) (10,5) (8,4) (1,3) (1,6) (5,1) (7,6) (1,7) (8,9) (3,4) (7,4) (4,5) (6,9) (2,10) (2,8)\nQ: Is there a path in this graph that visits every 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->2->7->8->6->1->5->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph568",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,0) (7,0) (15,8) (0,9) (4,11) (13,17) (7,10) (5,7) (8,14) (0,12) (9,3) (10,12) (14,9) (3,13) (17,15) (3,7) (19,1) (4,0) (3,18) (12,9) (19,5) (3,15) (10,8) (19,11) (11,13) (8,2) (9,18) (7,2) (0,5) (1,8) (13,18) (11,6) (9,8) (4,6) (17,4) (1,18) (11,7) (17,8) (11,10) (4,1) (12,15) (10,19) (12,7) (17,5) (8,4) (13,10) (16,6) (13,4) (9,4) (5,10) (14,10) (12,11) (3,6) (3,4) (13,0) (16,12) (15,2) (9,16) (1,7) (0,8) (17,7) (18,6) (2,6) (1,12) (18,4) (3,19) (3,17) (1,16) (3,11) (11,18) (14,18) (19,6) (11,5) (17,12) (13,5) (12,19) (15,6) (10,6) (9,5) (19,7) (18,17) (2,9) (15,7) (10,18) (10,9) (12,8) (14,13) (1,17) (7,4) (8,6) (13,7) (1,13) (1,3)\nQ: Is there a path in this graph that visits every 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->14->9->3->13->17->4->11->19->1->18->6->16->12->10->5->7->2."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph121",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (8,5) (2,5) (10,11) (7,2) (5,4) (5,1) (8,2) (4,8) (4,10) (1,10) (9,10) (11,2) (6,2) (7,5) (7,12) (7,8) (1,3) (8,11) (5,11) (9,0) (6,12) (9,11) (4,9) (8,3) (2,12) (8,6) (1,2) (4,12) (2,10) (11,3)\nQ: Is there a path in this graph that visits every 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->11->2->7->5->4->12->6->8->3->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph191",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (11,10) (2,3) (5,8) (1,11) (13,9) (3,13) (12,10) (11,12) (6,12) (2,10) (5,1) (0,4) (3,9) (0,1) (8,4) (0,10) (1,3) (13,11) (10,4) (7,3) (10,6) (13,1) (8,3) (11,5) (7,11) (4,13) (10,1) (7,2) (8,7) (11,4) (10,13) (12,4) (12,2) (6,5) (0,2) (13,7) (10,9) (13,5) (4,2) (9,2) (5,4) (1,6) (2,6) (7,9)\nQ: Is there a path in this graph that visits every 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->5->1->11->10->12->6->2->3->13->9->7."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph37",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,2) (9,4) (4,8) (7,0) (5,0) (10,2) (6,2) (1,2) (4,1) (2,7) (6,7) (3,1) (10,0) (8,9) (10,6) (7,10) (0,9) (4,6) (10,1) (2,5) (3,4) (9,10) (3,0) (2,0) (0,1) (6,9) (7,4) (3,9) (6,1) (9,7) (7,1) (3,5) (5,4)\nQ: Is there a path in this graph that visits every 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->8->9->10->6->1->3->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph554",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,7) (10,9) (16,10) (4,15) (10,13) (10,5) (8,10) (19,15) (4,18) (3,2) (12,19) (10,18) (3,7) (3,1) (5,7) (14,19) (0,3) (18,14) (19,6) (1,9) (11,8) (14,15) (2,5) (4,0) (19,9) (7,4) (3,18) (9,3) (10,19) (4,11) (9,0) (4,19) (8,6) (7,12) (11,13) (15,7) (2,6) (15,5) (19,5) (10,7) (14,3) (8,12) (8,13) (16,19) (6,0) (6,18) (17,3) (4,14) (14,6) (17,4) (12,9) (18,19) (3,6) (11,1) (2,7) (16,11) (14,2) (18,1) (5,6) (16,15) (6,9) (4,12) (11,3) (16,8) (5,3) (2,13) (15,18) (12,11) (12,14) (5,12) (5,14) (5,8) (4,9) (5,13) (17,1) (2,18) (14,7) (2,16) (5,18) (19,13) (15,12)\nQ: Is there a path in this graph that visits every 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->2->5->10->9->1->11->8->13->19->16->15->18->6->14->12->4->17."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph208",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,3) (1,10) (10,9) (7,0) (4,8) (0,10) (13,7) (8,1) (12,2) (13,5) (12,1) (13,10) (2,7) (5,9) (8,13) (8,12) (9,3) (3,6) (5,12) (11,7) (8,10) (7,3) (13,9) (6,11) (0,11) (6,4) (2,6) (8,3) (8,7) (12,4) (10,5) (0,1) (1,4) (9,11)\nQ: Is there a path in this graph that visits every 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->10->1->8->4->6->11->7->13->5->12->2."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph574",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (2,18) (1,4) (11,18) (0,12) (18,17) (14,15) (17,12) (2,16) (5,9) (5,4) (16,6) (2,14) (3,2) (6,15) (18,16) (10,11) (16,8) (15,8) (7,3) (14,8) (11,17) (6,1) (9,8) (12,16) (18,8) (16,4) (16,17) (0,15) (7,2) (2,8) (14,11) (19,10) (10,3) (10,0) (6,14) (11,12) (0,1) (1,3) (15,9) (5,16) (0,5) (10,4) (1,9) (11,9) (14,5) (10,6) (8,0) (12,4) (6,8) (2,11) (0,2) (14,12) (8,4) (4,11) (13,9) (2,5) (9,18) (4,6) (13,7) (7,11) (17,7) (12,3) (1,11) (0,11) (9,3) (15,12) (1,18) (4,18) (3,4) (0,13) (15,11) (15,18) (0,3) (16,3) (7,0) (5,15) (2,6) (11,3) (2,1) (3,14) (9,6) (13,8) (14,19) (14,18) (6,17) (19,2) (10,14) (13,1) (10,16) (9,12) (13,18) (1,19) (5,13) (16,1) (19,0) (14,1) (13,6) (9,0) (17,10) (11,19) (4,7) (9,17) (1,17) (15,4) (5,8) (3,8) (7,12) (10,2) (17,5) (11,8) (9,19) (8,12) (13,12) (19,5) (15,7) (7,1) (11,13) (17,19) (13,17) (10,7) (13,19) (15,2) (19,6) (5,7) (16,14) (5,11) (12,10) (17,14) (6,12) (16,13) (10,15) (1,15)\nQ: Is there a path in this graph that visits every 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->18->2->16->6->15->14->8->9->5->4->1->3->7->13->11->10->19."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph292",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (11,5) (0,3) (13,11) (8,11) (6,4) (1,6) (2,4) (11,12) (4,5) (13,8) (12,1) (6,11) (7,4) (13,9) (13,3) (2,0) (9,5) (0,1) (7,14) (7,8) (3,5) (2,9) (5,1) (6,9) (13,5) (9,14) (8,0) (8,1) (11,4) (10,9) (11,14) (12,10) (6,13) (12,3) (12,9) (14,4) (14,13) (12,7) (10,7) (4,0) (12,13) (11,3) (0,6) (5,0) (14,2) (11,9) (14,0) (0,7) (7,2) (11,2) (4,9) (13,7) (4,8) (5,14) (1,13) (6,14) (6,2) (1,14) (8,5) (8,14)\nQ: Is there a path in this graph that visits every 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->11->5->4->6->1->12->10->9->2->14->7->8."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph280",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (14,7) (9,12) (3,8) (7,10) (2,5) (14,1) (9,14) (5,11) (6,4) (5,3) (8,12) (6,14) (12,4) (7,1) (13,0) (14,11) (1,9) (0,11) (3,11) (9,5) (5,8) (7,13) (7,9) (10,9) (10,5) (10,6) (7,8) (6,11) (11,8) (2,12) (7,6) (2,6) (7,0) (4,10) (0,9) (12,5) (1,2) (2,3) (13,2) (12,13) (11,9) (2,11) (14,13) (10,0) (10,1) (2,14) (0,2) (14,10) (8,13) (6,1) (11,13) (0,4) (0,5) (9,3) (8,14) (1,11) (12,3) (1,8) (14,0) (2,8) (9,6) (5,6) (7,4) (5,7) (9,2) (10,11)\nQ: Is there a path in this graph that visits every 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->14->1->9->12->8->3->5->2->6->4->10->11."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph466",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (3,16) (1,3) (10,13) (10,14) (2,17) (8,3) (7,8) (9,14) (11,6) (7,0) (14,11) (17,8) (2,9) (3,11) (7,2) (15,17) (10,11) (2,14) (6,13) (3,17) (2,8) (17,12) (7,4) (15,11) (7,13) (0,10) (6,5) (7,1) (8,13) (2,3) (2,5) (2,6) (10,2) (14,12) (6,7) (10,5) (7,9) (7,5) (11,8) (16,6) (10,15) (9,13) (6,8) (11,9) (5,3) (11,7) (0,2) (14,5) (5,13) (17,1) (1,11) (17,13) (9,3) (6,15) (8,14) (2,4) (16,11) (11,2) (14,16) (6,17) (10,1) (14,0) (17,16) (14,13) (4,13) (10,4) (2,1) (17,4) (7,17) (8,12) (4,9) (12,6) (13,1) (6,10) (16,8) (6,14) (14,7) (3,6) (8,4) (11,12) (12,15) (15,0) (16,13) (0,4) (6,1) (17,9) (1,9) (12,10) (16,9) (9,12) (16,10) (5,11) (0,16) (9,0) (6,9) (2,16) (13,3) (15,13) (16,7) (11,13) (0,13) (4,6) (9,15) (14,3) (11,0) (14,1)\nQ: Is there a path in this graph that visits every 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->16->6->11->14->10->13->5->2->4->17->15->12->9->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph375",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (1,3) (0,1) (6,7) (10,3) (10,4) (14,10) (5,14) (11,8) (11,1) (11,16) (9,10) (4,12) (10,5) (4,15) (12,16) (10,6) (1,7) (7,10) (0,11) (13,3) (12,13) (4,11) (5,8) (16,10) (16,3) (5,2) (16,9) (0,3) (11,14) (12,9) (6,3) (1,5) (13,7) (5,9) (5,7) (2,1) (0,6) (15,2) (9,11) (6,13) (13,16) (12,8) (11,13) (3,2) (10,12) (1,10) (3,8) (0,15) (5,13) (3,5) (0,16) (8,16) (12,1) (8,13) (11,7) (9,2) (4,5) (4,3) (0,4) (14,6) (9,0) (15,6)\nQ: Is there a path in this graph that visits every 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->10->4->12->16->11->8->13->7->6->14->5->9->2->15."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph458",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (15,13) (10,5) (10,13) (7,4) (0,15) (14,4) (9,5) (10,9) (4,10) (1,7) (14,5) (11,17) (6,5) (4,16) (12,4) (9,11) (7,8) (11,13) (3,16) (7,9) (14,0) (10,12) (15,12) (2,8) (14,17) (16,15) (11,16) (7,6) (11,1) (8,1) (17,1) (0,5) (5,2) (2,14) (3,13) (8,15) (4,17) (8,17) (6,2) (13,12) (17,5) (16,12) (5,16) (4,13) (15,1) (0,7) (16,9) (4,0) (13,1) (1,0) (2,13) (9,8) (3,6) (15,9) (6,4) (0,12) (16,8) (4,2) (10,8) (13,9) (6,13) (12,7) (17,3) (12,2) (15,11) (12,5) (4,15) (0,10) (11,6) (15,2) (4,11) (10,6) (1,9) (11,3) (10,3) (15,7) (3,12) (14,7) (1,10) (15,3) (13,17) (2,7) (14,6) (2,9) (2,10) (11,0) (13,8) (2,1) (5,3) (7,10) (11,2) (1,4) (17,16) (3,0) (14,13) (7,5) (3,8) (11,12) (14,10) (2,17) (14,3) (4,5) (6,8) (15,6) (0,8) (11,8)\nQ: Is there a path in this graph that visits every 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->10->5->9->11->17->14->16->4->7->1->8->2->6->3->12."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph130",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (9,4) (8,1) (2,3) (5,7) (8,9) (3,12) (6,2) (4,10) (12,7) (0,4) (9,7) (9,10) (7,11) (8,10) (9,1) (6,12) (9,12) (3,0) (11,2) (4,1) (11,0) (6,3) (0,6) (7,0) (7,8) (0,9) (5,9) (3,5) (1,11) (10,0) (1,6)\nQ: Is there a path in this graph that visits every 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->7->5->3->12->6->2->11->1->8->10."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph220",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,0) (3,10) (5,11) (9,10) (3,6) (13,7) (5,12) (8,6) (11,4) (5,3) (0,6) (3,8) (7,0) (2,12) (9,6) (4,1) (6,13) (2,3) (13,10) (10,2) (4,9) (8,5) (8,12) (9,3) (13,0) (5,6) (0,4) (4,8) (10,6) (10,8) (7,12) (2,8) (3,7) (11,7) (11,8) (10,4) (9,0) (13,9) (12,11) (11,9) (13,5) (7,2) (0,8) (13,4) (12,1) (2,4) (5,2) (12,9) (7,8) (9,7) (11,6) (2,11) (5,10) (7,1) (6,2) (12,0) (9,2) (12,13)\nQ: Is there a path in this graph that visits every 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->6->8->5->11->4->1->12->2->7->13."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph20",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (10,1) (4,1) (7,6) (9,6) (1,7) (7,5) (2,4) (3,6) (5,1) (0,7) (1,0) (0,9) (2,3) (10,3) (8,2) (0,8) (2,9) (0,4) (1,8) (9,8) (6,5)\nQ: Is there a path in this graph that visits every 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->10->3->6->9->8->2->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph82",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (5,0) (4,9) (1,5) (0,7) (11,0) (9,2) (1,7) (11,2) (2,6) (8,3) (6,10) (7,10) (5,2) (4,6) (8,5) (5,11) (5,10) (2,3) (10,8) (2,7) (11,6) (3,7) (8,6) (1,10) (3,1) (0,3)\nQ: Is there a path in this graph that visits every 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->7->10->8->3->2->9->4->6->11."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph591",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (0,18) (0,7) (1,6) (0,5) (1,0) (19,4) (0,15) (1,12) (17,15) (13,9) (9,16) (16,14) (18,19) (14,6) (18,5) (3,6) (8,16) (1,18) (2,13) (8,5) (17,10) (6,18) (13,6) (19,16) (5,19) (18,4) (7,18) (5,15) (11,16) (12,15) (12,5) (9,5) (0,10) (8,14) (15,13) (7,9) (19,11) (16,1) (3,13) (2,15) (12,19) (11,9) (11,8) (14,9) (4,13) (12,7) (15,9) (5,10) (12,4) (8,19) (17,3) (17,0) (8,7) (19,9) (0,9) (1,5) (8,6) (0,16) (10,2) (5,4) (13,14) (2,4) (3,8) (1,8) (6,11) (3,1) (7,13) (13,0) (12,2) (17,12) (10,13) (16,2) (4,15) (6,5) (11,2) (12,11) (13,5) (11,4) (6,0) (7,16) (10,11) (4,16) (17,18) (8,4) (12,13) (17,9) (11,15) (12,9) (14,5) (10,1) (12,8) (14,17) (13,1) (18,14) (2,5) (3,0) (13,11) (8,10) (1,14) (18,13) (5,11) (6,15) (18,9) (10,18) (3,5) (19,0) (2,18) (7,19) (2,14) (11,0) (13,19) (16,18) (14,12) (12,16) (18,3) (6,2) (7,14) (12,6) (10,14) (15,18)\nQ: Is there a path in this graph that visits every 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->19->4->13->9->16->14->6->1->12->15->17->10->2->11->5->3->8->7."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph126",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (4,7) (3,12) (6,2) (2,10) (0,8) (7,11) (9,6) (12,5) (4,9) (7,2) (4,3) (3,8) (10,12) (8,10) (11,9) (11,2) (9,3) (10,7) (11,12) (1,2) (4,0) (1,3) (9,5) (1,11) (11,8) (0,2) (0,11) (4,1) (6,8) (12,6) (3,10) (12,1) (5,6) (10,9) (7,0) (8,4)\nQ: Is there a path in this graph that visits every 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->12->5->10->2->6->9->4->7->11->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph402",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (11,12) (6,13) (9,13) (8,2) (7,15) (16,13) (12,10) (13,7) (9,6) (2,10) (10,1) (8,13) (8,6) (0,11) (13,4) (14,0) (3,4) (8,11) (3,1) (4,10) (2,11) (9,5) (9,15) (1,8) (7,8) (4,11) (3,0) (5,4) (1,0) (15,10) (15,11) (7,2) (0,13) (13,15) (5,6) (0,10) (12,16) (6,12) (5,0) (10,9) (5,1) (5,8) (16,3) (9,16) (1,15) (5,7) (7,16) (0,16) (7,12) (13,12) (15,0) (1,16) (4,14) (16,11) (14,13) (15,5) (5,13) (14,15) (15,16) (8,15) (3,10) (12,15) (8,4) (16,10) (9,11) (12,3) (7,11) (6,15) (9,1) (9,12) (3,13) (3,9) (3,14) (12,0) (15,2) (1,6) (11,1) (1,2) (5,2) (10,5)\nQ: Is there a path in this graph that visits every 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->13->6->9->5->4->3->1->10->12->16->7->8->2->15->14."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph95",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (4,0) (7,9) (8,5) (4,6) (11,7) (6,10) (0,6) (4,3) (8,0) (11,5) (7,0) (10,9) (7,4) (0,3) (1,9) (1,5) (10,3) (9,0) (3,2) (6,8) (1,8) (1,6) (2,5) (0,2) (11,6) (5,4) (3,9) (2,11) (8,7) (8,2) (11,9) (11,3) (7,5) (4,8) (0,11)\nQ: Is there a path in this graph that visits every 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->10->9->7->11->5->1->8->2->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph35",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,3) (4,1) (9,1) (6,10) (4,8) (7,3) (7,2) (4,9) (9,3) (5,0) (6,9) (10,4) (0,1) (1,5) (3,1) (3,2) (6,7) (8,6) (2,5) (7,9) (6,1) (2,4) (5,3) (2,9) (10,7) (8,7) (8,0)\nQ: Is there a path in this graph that visits every 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->3->9->2->7->10->6->8."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph481",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (4,12) (10,17) (6,16) (15,10) (17,8) (3,11) (14,17) (16,13) (2,12) (11,2) (12,5) (8,9) (17,12) (6,0) (1,0) (2,0) (9,1) (2,17) (7,6) (9,7) (13,0) (1,11) (0,3) (0,9) (11,6) (5,10) (7,17) (3,8) (3,12) (7,8) (18,4) (5,16) (14,1) (4,7) (1,10) (15,7) (6,3) (3,13) (13,15) (1,8) (3,15) (13,1) (15,11) (1,12) (14,13) (3,14) (11,12) (18,11) (9,4) (16,2) (2,13) (13,8) (11,9) (0,5) (15,12) (0,18) (17,5) (3,10) (13,5)\nQ: Is there a path in this graph that visits every 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->13->3->11->2->12->5->10->15->7->17->14->1->8->9->4->18."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph323",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (15,1) (13,8) (11,4) (3,6) (1,13) (1,2) (9,3) (3,1) (10,7) (11,7) (6,4) (0,8) (14,9) (15,9) (9,5) (8,6) (9,1) (5,4) (9,0) (5,13) (11,0) (4,7) (14,3) (15,4) (5,12) (4,13) (5,10) (14,15) (15,0) (10,1) (9,10) (13,2) (8,2) (10,6) (7,15) (6,7) (7,14) (8,11) (5,14) (9,12) (0,12) (3,10) (4,3) (14,8) (9,11) (3,15) (4,8) (13,9) (6,14) (2,11) (9,6) (7,13) (15,12) (2,5) (15,6)\nQ: Is there a path in this graph that visits every 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->13->1->15->9->3->14->7->10->6->4->11->2->5->12."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph470",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,2) (9,1) (11,13) (17,4) (5,2) (6,4) (3,11) (1,0) (3,4) (9,16) (10,1) (7,4) (4,8) (16,13) (15,12) (8,1) (11,17) (13,14) (2,8) (10,6) (14,11) (11,12) (15,13) (3,0) (8,9) (14,12) (16,5) (7,1) (14,15) (8,14) (2,1) (14,6) (5,10) (7,12) (16,15) (13,7) (13,8) (4,10) (10,9) (1,11) (13,1) (13,6) (9,17) (8,11) (6,8) (6,3) (10,2) (6,11) (3,15) (13,12) (0,14) (1,16) (11,7) (16,14) (4,9) (0,8) (2,17) (1,6) (12,2) (10,7) (7,15) (9,13) (6,0) (14,5) (17,16) (8,3) (1,12) (2,4) (0,2) (9,5) (6,12) (13,5) (15,17) (12,10) (4,14) (3,7) (10,11) (16,11) (0,5) (17,6) (15,4) (11,9) (5,12) (16,4) (11,5) (9,0)\nQ: Is there a path in this graph that visits every 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->2->5->16->13->11->3->4->17->15->12->14->8->6->10->7."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph420",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (1,3) (15,3) (2,3) (14,2) (16,3) (7,16) (14,10) (9,10) (8,1) (9,12) (17,7) (8,3) (12,15) (1,14) (16,0) (11,15) (4,17) (2,15) (16,2) (4,10) (12,8) (10,6) (0,8) (10,5) (14,17) (3,17) (11,5) (0,4) (11,12) (16,8) (12,13) (16,6) (10,13) (6,1) (16,1) (7,10) (6,0) (9,11) (1,13) (7,3) (0,9) (2,10) (7,1) (15,13) (15,14) (2,7) (6,17) (5,2) (14,8) (13,4) (3,5) (9,5) (8,11) (0,1) (10,12) (0,14) (14,7) (9,17) (14,16) (16,12)\nQ: Is there a path in this graph that visits every 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->1->8->12->9->10->14->7->2->5->11->15->13->4->17->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph120",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,0) (12,3) (3,9) (6,1) (7,12) (11,7) (8,7) (5,10) (5,2) (3,6) (1,3) (1,11) (11,6) (2,12) (0,4) (9,0) (8,12) (11,3) (5,3) (4,12) (5,4) (9,11) (7,5) (8,5) (6,5) (0,2) (1,4) (5,0) (11,2)\nQ: Is there a path in this graph that visits every 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->3->9->11->7->8->12->2->5->10."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph131",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,5) (2,11) (8,4) (5,0) (1,11) (1,5) (12,3) (8,10) (9,7) (1,7) (7,3) (12,1) (5,9) (12,11) (1,6) (9,3) (1,8) (2,6) (8,0) (11,9) (9,8) (5,6) (6,3) (0,2) (2,7) (10,11) (0,10) (10,2) (8,11) (10,4) (12,2) (5,11) (0,4) (2,3) (5,10)\nQ: Is there a path in this graph that visits every 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->3->6->1->7->9->8->4->10."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph537",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (3,11) (15,8) (18,12) (7,9) (10,15) (2,1) (14,11) (18,16) (10,12) (8,7) (3,2) (3,6) (7,12) (5,4) (15,16) (16,5) (14,0) (0,1) (1,18) (7,10) (2,6) (4,6) (2,4) (10,0) (2,13) (11,9) (3,7) (18,5) (18,11) (13,0) (11,5) (15,9) (10,16) (8,5) (3,18) (6,0) (1,14) (4,18) (2,11) (4,3) (17,1) (4,12) (10,3) (1,16) (18,9) (17,3) (0,9) (14,10) (14,3) (5,12) (12,13) (1,3) (8,16) (6,12) (13,14) (10,9) (17,11) (5,2) (13,5) (4,8) (5,15) (2,8) (17,10) (14,9) (6,7) (15,14) (17,16) (1,13) (6,13) (0,12) (18,7) (18,2) (10,5) (13,17) (14,16) (12,3) (2,7) (11,12) (5,17) (14,2) (6,18) (1,7) (9,4) (9,3) (0,2) (13,4) (1,11) (1,4) (15,3) (15,1) (1,12) (4,17) (14,7) (6,14) (10,11) (4,15) (13,3) (18,0) (9,2) (17,15)\nQ: Is there a path in this graph that visits every 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->11->3->2->1->18->12->10->15->8->7->9->4->5->16->17->13->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph306",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (14,4) (2,11) (11,7) (12,4) (12,9) (2,15) (14,7) (9,7) (9,6) (8,0) (10,13) (5,14) (14,10) (12,0) (9,8) (10,4) (12,15) (12,14) (3,1) (4,6) (14,6) (10,8) (12,11) (11,1) (3,6) (10,11) (7,12) (9,0) (6,2) (1,0) (13,3) (3,2) (6,7) (1,7) (13,12) (8,6) (9,13) (4,9) (8,4) (5,9) (6,11) (1,14) (12,5) (7,13) (2,13) (7,0) (2,1) (10,5) (11,0) (7,10) (3,5) (8,11) (8,7) (9,3)\nQ: Is there a path in this graph that visits every 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->12->4->14->7->6->11->1->3->5->10->13->2->15."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph287",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (6,0) (3,5) (6,4) (6,10) (2,6) (3,2) (2,12) (8,14) (10,9) (8,1) (3,14) (6,13) (2,7) (13,11) (1,10) (12,9) (3,9) (7,5) (1,4) (14,4) (1,7) (7,13) (2,10) (12,13) (11,7) (13,1) (8,0) (14,6) (14,0) (11,6) (3,4) (2,11) (12,1) (4,13) (12,5) (14,1) (13,0) (14,11) (4,7) (8,5) (7,12) (0,4) (8,7) (1,5) (12,0) (12,14) (11,0) (13,5) (13,9) (14,2) (4,5) (12,11) (8,12) (6,5) (12,10) (7,9) (0,9) (11,3) (5,2) (0,3) (3,13) (3,8) (2,13) (1,9)\nQ: Is there a path in this graph that visits every 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->1->8->14->3->5->7->2->12->11->13->9->10."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph545",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (15,16) (8,4) (1,13) (13,11) (10,2) (8,19) (5,7) (11,1) (8,0) (19,15) (1,15) (14,13) (10,16) (19,17) (6,12) (11,4) (13,18) (9,5) (2,6) (19,1) (9,4) (9,12) (2,1) (2,12) (12,19) (2,4) (4,18) (7,6) (13,4) (9,0) (16,17) (7,8) (15,17) (8,14) (2,13) (11,15) (0,18) (3,13) (1,12) (11,0) (6,18) (3,11) (1,4) (16,9) (2,8) (17,8) (16,7) (7,10) (19,11) (15,0) (10,13) (13,9) (15,4) (16,8) (5,12) (6,1) (6,14) (5,3) (17,6) (10,6) (18,10) (15,6) (1,9) (3,7) (15,14) (7,11) (11,8) (16,5) (2,5) (8,12) (17,1) (12,4) (14,5) (19,9) (3,18) (3,0) (3,10) (16,19) (14,7) (19,18) (19,0) (1,0) (8,6) (18,14) (5,18) (15,2)\nQ: Is there a path in this graph that visits every 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->11->13->1->15->16->10->2->6->12->9->5->3->7->14->18->19->17."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph587",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (5,13) (13,1) (12,9) (1,6) (9,7) (16,7) (19,12) (8,19) (4,17) (11,10) (2,14) (12,16) (17,1) (16,10) (10,3) (13,6) (15,0) (4,11) (8,1) (18,14) (4,16) (19,6) (5,12) (5,16) (7,14) (12,4) (3,5) (13,17) (0,8) (12,8) (1,10) (7,3) (3,18) (8,6) (5,9) (4,19) (4,2) (15,17) (18,15) (0,10) (14,16) (3,9) (8,10) (8,9) (5,7) (13,3) (16,13) (2,8) (19,3) (7,18) (14,9) (7,13) (0,4) (15,14) (16,18) (11,6) (2,6) (2,13) (18,1) (8,11) (15,12) (5,10) (5,15) (2,12) (5,1) (8,17) (9,13) (11,14) (2,9) (9,6) (13,4) (9,18) (17,12) (19,2) (4,10) (15,16) (4,9) (13,14) (2,0) (14,4) (10,2) (2,7) (3,15) (15,19) (13,12) (13,0) (0,16) (18,11) (6,4) (3,12) (3,17) (11,0) (7,6) (14,8) (11,5) (18,13) (12,6) (6,10) (3,1) (6,15) (19,10) (18,2) (10,9) (18,12) (5,8) (11,12) (11,13) (0,19) (7,17) (14,6) (4,7) (17,10) (11,7)\nQ: Is there a path in this graph that visits every 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->4->11->10->16->7->9->12->19->8->1->13->5->3->18->14->2->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph596",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (10,5) (15,5) (6,3) (9,4) (16,19) (1,19) (1,3) (7,14) (18,16) (7,15) (13,3) (1,16) (5,2) (5,17) (15,11) (0,10) (6,7) (16,10) (3,16) (13,12) (3,11) (5,18) (12,14) (19,14) (17,13) (14,0) (3,12) (1,18) (1,17) (19,4) (18,2) (13,1) (15,13) (14,1) (1,5) (14,15) (3,8) (17,7) (6,9) (4,16) (6,17) (3,7) (8,17) (3,5) (8,19) (6,13) (10,13) (5,19) (1,0) (9,11) (6,10) (6,12) (13,16) (8,13) (7,0) (17,4) (7,19) (19,2) (15,4) (5,12) (15,16) (14,18) (3,4) (11,8) (17,3) (19,3) (5,9) (13,5) (10,2) (7,13) (0,8) (7,1) (13,2) (11,14) (18,9) (12,7) (16,5) (4,7) (8,16) (7,18) (3,18) (12,8) (8,1) (4,6) (16,9) (14,10) (8,14) (11,6) (19,13) (9,14) (14,5) (9,0) (0,13) (7,2) (15,1) (4,18) (5,11) (2,14) (18,11) (15,12) (13,9) (18,13) (6,19) (18,19) (1,2) (10,19) (18,10) (16,2) (18,12) (9,17) (0,5) (12,10) (18,8) (0,3) (8,2) (8,5) (15,10) (12,2) (6,14)\nQ: Is there a path in this graph that visits every 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->15->7->14->12->13->3->6->9->4->19->16->18->2->1->17->8->11."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph552",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (4,8) (11,4) (6,1) (15,14) (8,3) (18,4) (5,3) (16,9) (8,1) (8,13) (0,10) (9,12) (15,17) (6,9) (19,14) (10,16) (3,15) (2,1) (5,10) (12,0) (18,3) (19,0) (11,17) (13,0) (6,11) (19,10) (5,13) (9,4) (11,16) (14,18) (7,5) (4,19) (6,14) (16,13) (18,1) (5,18) (7,8) (10,7) (12,16) (17,6) (9,7) (7,18) (11,8) (11,7) (13,19) (19,12) (17,2) (18,17) (18,10) (4,0) (0,18) (4,16) (2,6) (10,6) (13,11) (2,11) (15,1) (7,12) (17,14) (7,3) (14,12) (12,5) (14,5) (9,13) (3,19) (8,16) (18,8) (5,17) (4,12) (13,18) (16,6) (2,18) (19,9) (7,19) (8,14) (6,3) (9,11) (6,4) (12,3)\nQ: Is there a path in this graph that visits every 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->9->12->19->14->15->17->11->4->8->3->7->5->13->18->1->6->2."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph56",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (8,10) (9,2) (6,3) (6,9) (3,5) (7,6) (4,3) (3,7) (5,7) (7,10) (4,1) (10,9) (10,3) (7,4) (9,7) (6,10) (0,9) (10,2) (0,3) (9,4) (1,2) (5,0) (9,1) (0,4) (0,2) (10,1) (8,3) (2,8) (1,8) (8,0) (1,0) (5,9) (8,6) (2,3) (7,8) (4,10) (7,1) (8,5)\nQ: Is there a path in this graph that visits every 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->10->8->1->4->3->6->7->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph255",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (8,0) (12,3) (11,2) (10,13) (14,2) (8,9) (8,1) (5,4) (7,3) (12,13) (7,2) (10,9) (1,5) (11,5) (0,4) (11,8) (4,11) (7,10) (13,1) (0,13) (9,12) (10,14) (4,7) (5,2) (14,5) (7,0) (9,1) (0,5) (5,3) (12,4) (5,13) (12,10) (2,0) (3,4) (4,8) (6,8) (14,9) (8,14) (13,4) (1,11) (12,2) (0,9) (13,6)\nQ: Is there a path in this graph that visits every 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->10->7->3->12->4->5->14->2->11->1->13->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph471",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (6,0) (15,10) (11,10) (16,12) (5,2) (11,2) (2,7) (7,8) (5,3) (6,12) (17,2) (5,0) (10,13) (4,11) (16,6) (1,4) (9,6) (13,9) (0,14) (5,9) (5,13) (6,10) (13,2) (16,8) (0,4) (16,13) (17,13) (13,6) (0,15) (16,1) (12,11) (4,7) (8,0) (15,11) (9,3) (7,13) (5,11) (12,14) (5,15) (17,16) (10,5) (16,10) (8,17) (11,16) (1,2) (2,15) (3,4) (10,2) (17,5) (17,15) (1,5) (3,14) (0,1) (12,5) (7,17) (9,11) (8,5) (8,10) (14,10) (5,14) (6,8) (17,10) (4,9) (16,0) (4,8) (6,7) (14,6) (7,10) (3,6) (10,9) (8,11) (9,2) (5,16) (8,1) (17,4) (9,0) (13,1) (15,4) (17,9) (6,1) (6,2) (4,5) (2,12) (0,7) (16,14) (9,7) (3,12) (16,4) (15,16) (8,15) (2,16) (1,12) (13,0) (17,0) (16,3) (6,5) (13,11) (17,3) (14,1) (11,17) (13,14)\nQ: Is there a path in this graph that visits every 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->16->8->7->2->5->3->9->13->10->15->11->17->4->1->14."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph360",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (10,0) (9,7) (12,1) (4,15) (14,7) (5,7) (7,16) (11,2) (13,8) (11,9) (5,1) (5,9) (0,5) (4,11) (16,4) (6,11) (9,13) (15,11) (4,10) (5,14) (2,15) (0,2) (4,14) (9,1) (16,6) (16,12) (14,16) (8,0) (15,14) (0,1) (6,15) (16,0) (7,4) (3,9) (5,13) (8,10) (13,0) (15,3) (1,6) (12,10) (12,14) (6,3) (13,12) (16,2) (4,13) (16,11) (9,8) (16,8) (2,8) (8,6) (14,2)\nQ: Is there a path in this graph that visits every 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->11->2->16->7->9->1->12->14->5->13->8->6->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph127",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (2,4) (12,4) (12,6) (2,6) (6,4) (7,6) (4,11) (5,2) (3,0) (4,9) (8,9) (1,11) (12,7) (11,3) (9,3) (5,6) (12,2) (12,0) (2,7) (7,0) (1,10) (6,3) (4,0) (10,5) (8,2) (5,9) (0,5) (11,2) (2,1) (0,6)\nQ: Is there a path in this graph that visits every 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->12->6->7->2->8->9->5->10->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph492",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (6,0) (10,12) (2,3) (18,1) (11,9) (5,17) (17,0) (1,5) (16,14) (3,14) (4,8) (17,13) (15,10) (17,10) (18,7) (14,4) (8,2) (16,2) (6,17) (15,16) (1,16) (13,11) (3,4) (8,14) (10,7) (15,1) (5,16) (10,8) (3,0) (10,11) (11,8) (10,9) (17,3) (18,11) (10,14) (8,1) (13,7) (15,9) (1,9) (6,9) (9,7) (7,5) (18,10) (4,5) (2,4) (15,0) (4,13) (4,18) (15,4) (1,2) (13,3) (5,10) (12,15) (17,15) (3,6) (13,15) (3,9) (17,11) (2,13) (5,2) (5,12) (16,11) (11,12) (14,13) (5,6) (11,7) (2,12) (14,12) (6,2) (1,0) (7,14) (12,1)\nQ: Is there a path in this graph that visits every 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->5->1->18->7->10->12->15->16->14->3->2->8->4->13->11->9."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph501",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (17,1) (4,3) (14,6) (3,5) (14,13) (8,16) (15,17) (15,5) (15,4) (7,9) (18,2) (18,17) (13,2) (6,16) (17,8) (3,8) (11,10) (3,15) (0,6) (16,14) (2,8) (2,10) (4,18) (9,8) (16,4) (16,17) (10,6) (2,15) (14,17) (9,2) (3,12) (5,12) (6,18) (13,3) (11,2) (0,14) (11,5) (12,8) (14,5) (5,1) (7,10) (1,10) (7,18) (10,18) (9,14) (6,13) (1,8) (8,10) (16,5) (0,12) (12,9) (18,5) (1,2) (18,1) (1,13) (10,0) (14,3) (13,16) (16,18) (17,0) (17,7) (1,4) (2,17) (10,13) (11,8) (2,0) (0,5) (7,15) (18,11) (0,11) (10,12) (1,3)\nQ: Is there a path in this graph that visits every 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->14->13->2->18->17->1->5->3->4->15->7->9->12->10->11->8->16."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph34",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (4,1) (6,7) (0,10) (1,10) (9,1) (4,2) (1,8) (7,5) (9,3) (2,0) (7,4) (0,4) (3,8) (4,9) (6,3) (0,6) (5,1) (10,2) (2,8) (9,8) (10,3) (9,7) (1,7) (4,5) (5,2)\nQ: Is there a path in this graph that visits every 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->2->8->9->3->6->7->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph143",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (8,7) (9,1) (4,8) (6,12) (2,7) (4,11) (11,0) (11,7) (12,7) (1,7) (8,10) (3,0) (1,11) (5,0) (11,5) (7,6) (11,3) (3,7) (3,8) (9,7) (6,9) (12,3) (1,10) (7,5) (4,5) (12,8) (10,9) (3,9) (6,0) (2,6) (4,7) (11,6) (6,8) (12,11) (2,9) (10,2)\nQ: Is there a path in this graph that visits every 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->8->9->1->10->2->6->12->3->7->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph109",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (0,2) (5,1) (8,11) (2,4) (4,3) (9,11) (9,7) (0,3) (9,8) (0,6) (11,4) (3,10) (2,7) (1,10) (2,8) (11,3) (10,7) (9,3) (1,8) (6,3) (5,3) (1,0) (7,1) (10,2) (4,8) (0,7) (8,6) (4,0) (11,7) (10,6) (10,9) (8,3) (5,0) (5,11) (10,11) (1,11) (1,3) (10,4) (6,1) (7,8) (0,9) (5,2)\nQ: Is there a path in this graph that visits every 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->3->10->1->5->11->9->7->8->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph525",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (13,3) (8,4) (1,4) (18,6) (17,12) (18,17) (17,11) (16,9) (5,17) (16,15) (16,0) (14,15) (15,1) (15,11) (6,9) (3,18) (5,15) (7,17) (1,14) (0,11) (14,6) (4,11) (15,0) (3,17) (18,1) (0,9) (16,1) (7,16) (6,11) (6,0) (10,13) (12,14) (13,2) (7,3) (8,6) (13,5) (13,9) (12,5) (11,7) (18,10) (15,8) (14,2) (9,17) (14,0) (8,5) (2,12) (15,13) (7,8) (1,3) (5,6) (6,7) (5,7) (5,2) (18,13) (11,14) (8,16) (1,0) (17,13) (2,9) (16,5) (4,15) (9,11) (9,12) (2,11) (9,7) (11,18) (9,8) (5,4) (17,8) (12,10) (6,16) (18,9) (6,17) (1,12) (10,2) (13,8) (5,0) (8,0) (16,14) (11,5) (16,4) (10,15) (15,12) (16,13) (13,7) (15,7) (8,14) (0,10) (18,5) (1,8) (15,17) (12,6) (11,16) (18,7) (3,16) (10,3) (9,10) (13,12) (10,14) (18,14) (8,10) (3,15) (13,11)\nQ: Is there a path in this graph that visits every 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->6->18->17->12->14->15->1->4->8->5->13->3->7->11->2->10."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph58",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (0,6) (1,9) (8,6) (1,8) (10,4) (9,7) (2,0) (4,6) (9,6) (9,0) (9,2) (3,1) (9,10) (3,0) (0,7) (5,3) (2,6) (8,10) (4,2) (1,2) (3,10) (7,10) (5,2) (5,1) (4,8) (5,4) (1,6) (5,8)\nQ: Is there a path in this graph that visits every 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->1->9->7->10->4->2->5->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph410",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (7,16) (10,1) (4,1) (9,13) (7,14) (10,9) (5,14) (0,9) (15,6) (8,7) (9,15) (12,0) (13,2) (1,0) (8,16) (11,2) (1,8) (9,5) (16,5) (16,2) (12,16) (0,14) (13,5) (13,11) (4,8) (3,10) (3,16) (6,4) (10,16) (7,3) (16,14) (9,3) (4,9) (4,7) (3,0) (14,2) (11,0) (2,5) (13,4) (8,2) (16,4) (9,11) (12,15) (2,1) (7,9) (14,12) (1,15) (10,0) (1,9) (6,16) (5,6) (5,12) (11,8) (8,12) (1,14) (11,5) (10,15) (13,7) (15,13) (2,15) (4,10) (4,0) (16,15) (5,3) (7,0) (6,2) (3,8) (15,7) (5,8) (14,3) (2,10) (7,1) (11,10) (2,4) (8,15) (14,8) (7,10) (1,16) (9,6) (14,10) (1,6) (14,6)\nQ: Is there a path in this graph that visits every 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->13->2->11->8->7->16->5->14->12->15->6->4->1->10->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph539",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (2,9) (2,16) (7,1) (18,12) (1,3) (10,15) (0,17) (3,0) (17,4) (5,10) (2,6) (7,10) (0,18) (4,10) (8,14) (7,14) (1,18) (4,12) (18,4) (17,12) (5,14) (16,6) (18,8) (1,9) (13,10) (0,8) (8,13) (16,9) (7,9) (15,13) (7,2) (0,4) (16,15) (12,5) (3,4) (10,8) (15,18) (8,2) (17,2) (4,9) (18,10) (8,6) (13,12) (10,14) (17,5) (12,1) (12,14) (1,5) (12,0) (7,17) (5,3) (10,17) (16,5) (12,2) (0,13) (2,15) (17,15) (4,2) (12,15) (9,5) (0,2) (15,14) (13,2) (2,14) (11,1) (8,3) (9,12) (11,9) (11,3) (10,3) (7,5) (2,10) (2,1) (9,14) (4,1) (9,18) (17,16) (3,15) (4,15) (10,11) (1,8) (13,7) (0,14) (17,14) (4,11) (9,6) (12,8) (7,11) (15,7) (16,11) (11,14) (1,17) (16,13) (7,12) (7,8) (8,4) (7,6) (9,0) (3,9) (4,6) (12,6) (9,15) (4,5) (0,10) (18,5) (0,16) (2,18) (14,6) (13,3) (11,8) (6,5)\nQ: Is there a path in this graph that visits every 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->4->10->15->13->8->14->7->1->3->5->12->18->9->2->6->16->11."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph202",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (7,1) (6,10) (11,12) (3,9) (1,0) (9,12) (11,13) (7,3) (12,1) (12,10) (9,8) (2,5) (1,8) (0,8) (6,9) (12,0) (11,8) (3,4) (12,8) (5,13) (10,5) (7,6) (2,13) (11,2) (11,5) (4,1) (7,8) (8,5) (1,5) (12,4) (7,9) (2,8) (6,13) (7,5) (3,8) (3,1) (11,1)\nQ: Is there a path in this graph that visits every 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->3->9->8->11->2->5->13->6->10->12->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph267",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,7) (13,3) (10,8) (5,4) (0,4) (4,12) (9,5) (6,2) (10,6) (14,1) (5,2) (2,8) (6,4) (9,6) (1,3) (8,3) (1,5) (1,12) (2,11) (7,9) (1,8) (10,7) (1,10) (13,11) (10,11) (10,2) (14,0) (2,12) (6,0) (0,2) (3,5) (3,6) (7,6) (11,4) (14,5) (11,9) (10,5) (1,6)\nQ: Is there a path in this graph that visits every 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->6->7->10->8->3->13->11->2->12->1->14."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph559",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (7,15) (15,3) (7,17) (6,19) (6,12) (16,1) (10,3) (6,4) (10,8) (18,14) (12,19) (0,9) (9,13) (7,8) (7,1) (2,10) (19,13) (14,5) (7,3) (6,9) (3,5) (11,17) (17,9) (8,6) (0,16) (1,12) (9,19) (19,7) (18,8) (16,5) (4,15) (10,0) (6,16) (4,16) (17,14) (0,6) (8,16) (14,6) (14,7) (2,17) (0,12) (12,15) (9,15) (16,14) (12,16) (8,15) (7,5) (0,13) (1,8) (2,16) (6,7) (17,18) (9,5) (15,16) (15,18) (12,18) (2,5) (2,4) (5,11) (11,15) (18,0) (11,7) (13,11) (5,17) (1,14) (1,19) (19,8) (15,0) (14,2) (13,6) (17,0) (15,17) (19,11) (17,13) (0,4) (5,13) (5,18) (8,13) (2,19) (0,7) (12,8) (17,12)\nQ: Is there a path in this graph that visits every 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->13->3->15->7->17->11->5->14->18->8->10->2->16->1->12->19->6->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph169",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (9,12) (10,11) (1,0) (2,7) (10,4) (5,8) (4,0) (8,9) (7,6) (8,12) (0,6) (2,3) (4,9) (2,4) (3,7) (7,4) (2,5) (7,8) (9,2) (7,9) (1,10) (4,1) (11,2) (3,1) (0,3) (11,6) (4,5) (9,0) (8,0) (8,3) (3,11) (6,5) (6,9) (8,11) (5,11) (7,0) (8,4) (11,9) (7,11) (5,3) (2,8)\nQ: Is there a path in this graph that visits every 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->11->2->7->6->5->4->9->12->8->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph365",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (3,13) (7,8) (2,11) (9,3) (7,15) (7,10) (5,15) (6,13) (10,13) (9,5) (6,7) (12,2) (0,10) (12,6) (12,0) (15,13) (8,16) (1,10) (6,9) (4,6) (16,11) (5,4) (13,1) (1,5) (0,11) (3,2) (9,14) (7,2) (9,13) (7,0) (5,16) (12,11) (8,14) (14,4) (4,16) (14,12) (15,12) (5,6) (5,0) (0,16) (5,13) (14,16) (4,3) (2,14) (14,5) (1,16) (5,12) (11,5) (6,0) (6,3) (10,4) (8,12) (3,0) (11,7) (2,10) (8,5)\nQ: Is there a path in this graph that visits every 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->16->11->2->12->6->9->3->4->14->5->15->13->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph41",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (10,3) (1,10) (1,3) (8,2) (8,10) (8,7) (10,9) (8,4) (0,10) (2,10) (9,8) (6,5) (7,4) (2,9) (0,9) (5,1) (3,2) (10,6) (4,2) (2,0) (9,5) (1,6) (1,4) (1,0) (4,0) (7,1)\nQ: Is there a path in this graph that visits every 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->1->6->5->9->8->2->4->7."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph210",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,12) (3,0) (7,5) (13,9) (3,7) (5,6) (11,9) (4,0) (6,1) (10,13) (5,11) (13,3) (1,0) (5,10) (1,10) (5,0) (0,13) (9,0) (12,6) (6,2) (10,8) (6,3) (9,12) (0,2) (7,9) (11,8) (2,4) (0,6) (13,8) (11,13) (3,4) (11,7) (8,9) (4,13) (7,4) (4,11) (3,10) (8,2) (7,6) (2,9) (9,4) (6,13) (12,11) (4,6) (7,12) (10,9) (10,12) (3,8) (0,10) (3,5) (7,0) (8,5) (1,8) (5,4) (2,3)\nQ: Is there a path in this graph that visits every 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->6->1->10->13->12->9->11->8->2->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph401",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (12,14) (7,15) (6,9) (2,16) (7,4) (7,2) (5,13) (2,8) (10,9) (2,11) (1,8) (5,16) (8,14) (8,11) (11,3) (9,7) (16,15) (7,11) (5,12) (2,12) (0,12) (10,11) (9,1) (0,11) (4,16) (15,1) (6,2) (1,3) (9,0) (4,1) (3,14) (0,7) (13,2) (6,0) (1,0) (9,16) (9,3) (8,3) (6,15) (0,15) (14,15) (7,5) (2,1) (6,14) (5,11) (2,15) (12,6) (13,14) (8,0) (11,16) (16,13) (4,8) (5,9) (6,7) (7,12) (15,10) (13,7) (16,10) (4,6) (6,5) (13,8) (16,1) (8,10) (11,13) (15,12) (13,1) (4,9) (0,2) (14,9) (3,15) (6,13) (14,0) (2,4) (12,16) (0,3) (8,7) (14,16) (7,14) (6,16)\nQ: Is there a path in this graph that visits every 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->14->8->2->16->5->13->7->15->1->3->11->10->9->6->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph528",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (1,13) (10,12) (4,15) (17,3) (1,14) (5,2) (12,4) (3,4) (11,16) (8,15) (14,3) (16,14) (11,8) (6,9) (16,3) (4,7) (6,17) (17,16) (14,8) (18,0) (8,4) (7,18) (5,17) (13,5) (1,17) (6,13) (16,12) (2,7) (4,13) (10,1) (15,14) (18,14) (16,15) (17,9) (3,0) (2,15) (13,2) (11,10) (9,5) (2,3) (12,9) (7,17) (3,6) (10,3) (9,14) (0,1) (9,2) (5,14) (0,6) (14,7) (18,13) (2,16) (2,0) (5,15) (0,5) (6,5) (17,14) (4,9) (15,9) (5,11) (15,10) (7,3) (10,14) (1,3) (17,10) (3,18) (7,8) (11,17) (8,0) (14,12) (9,18) (7,10) (4,6) (6,16) (16,1) (4,14) (8,10) (18,8) (1,9) (13,7) (9,16) (7,0) (10,9) (2,18) (12,13) (18,11) (1,6) (0,12) (18,1) (18,15) (16,8) (11,6) (7,1) (16,18) (3,9) (18,5) (17,15) (13,11) (4,10) (3,11) (4,18) (10,2) (17,13)\nQ: Is there a path in this graph that visits every 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->7->4->15->8->11->16->14->1->13->5->2->3->17->6->9->12->10."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph89",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (7,11) (10,2) (6,7) (11,10) (4,8) (6,2) (1,3) (3,10) (5,4) (1,11) (11,5) (6,1) (10,5) (4,3) (4,11) (5,2) (9,3) (7,2) (3,6) (2,1) (8,2) (4,1) (11,2) (0,7) (9,4) (0,1)\nQ: Is there a path in this graph that visits every 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->10->5->4->8->2->6->1->3->9."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph322",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (0,4) (11,10) (7,5) (6,1) (2,5) (13,1) (2,4) (9,13) (7,0) (8,3) (10,3) (2,10) (4,1) (2,12) (14,15) (14,12) (5,15) (3,14) (7,9) (13,10) (1,8) (6,0) (6,15) (0,14) (15,4) (1,14) (8,5) (5,9) (0,11) (12,1) (12,6) (12,0) (4,3) (13,11) (12,8) (14,10) (5,13) (2,6) (4,9) (14,8) (8,13) (7,8) (4,12) (6,3) (10,8) (11,3) (6,4) (3,5) (3,7) (15,0) (6,5) (10,5) (2,3) (12,5) (14,6) (7,6)\nQ: Is there a path in this graph that visits every 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->7->9->13->1->6->15->14->12->8->3->10->11."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph550",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (4,12) (3,18) (19,9) (6,5) (6,11) (3,16) (18,5) (8,9) (10,17) (17,5) (18,10) (3,8) (14,12) (7,5) (8,15) (9,11) (17,9) (6,15) (14,10) (17,18) (0,13) (12,8) (18,11) (19,0) (16,0) (16,5) (2,17) (12,9) (7,2) (16,11) (17,8) (13,16) (19,7) (14,6) (19,17) (1,12) (6,12) (14,15) (19,1) (18,14) (4,10) (7,18) (9,3) (19,8) (2,8) (9,14) (13,15) (13,8) (12,2) (13,10) (15,12) (3,17) (19,12) (8,7) (10,8) (12,0) (7,0) (13,12) (16,6) (7,15) (14,5) (16,15) (18,15) (11,12) (15,2) (1,5) (0,18) (11,7) (14,16) (3,15) (17,16) (9,0) (4,0) (3,6) (1,2) (6,1) (5,11) (16,7) (16,9) (13,1) (4,11) (14,19) (10,7) (13,17) (15,0) (8,0)\nQ: Is there a path in this graph that visits every 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->16->3->18->5->6->11->9->19->7->2->17->8->15->14->10->4->12->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph46",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (6,8) (3,7) (6,2) (10,4) (10,3) (5,9) (4,6) (5,6) (7,2) (3,6) (8,10) (2,5) (4,9) (5,3) (1,10) (7,5) (6,1) (6,7) (0,9) (7,1) (7,9) (10,0) (10,5) (7,8) (6,0) (4,8) (8,3) (1,8) (2,8) (3,0) (2,1) (9,3) (8,0)\nQ: Is there a path in this graph that visits every 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->6->8->4->10->3->7->2->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph161",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (4,3) (3,5) (9,4) (7,2) (0,5) (6,11) (3,12) (4,2) (7,11) (7,9) (6,0) (11,3) (3,7) (2,3) (2,11) (8,7) (2,9) (10,3) (6,1) (0,2) (2,10) (7,4) (12,0) (11,4) (9,10) (12,5) (10,12) (10,1) (2,12) (8,12) (1,8) (8,9) (11,9) (1,0) (5,2) (7,10) (7,6) (6,3) (3,1) (1,2) (2,8) (1,5) (11,8) (5,7)\nQ: Is there a path in this graph that visits every 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->9->7->2->11->6->1->10->12->8."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph362",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (16,15) (1,15) (10,12) (12,11) (9,14) (5,2) (2,3) (9,7) (7,10) (16,14) (6,11) (12,7) (8,14) (11,15) (12,13) (11,1) (7,3) (10,14) (15,14) (15,0) (0,16) (12,8) (11,3) (0,1) (5,0) (14,3) (4,11) (16,4) (1,4) (6,0) (3,1) (3,16) (8,2) (9,1) (4,8) (11,5) (8,6) (7,13) (13,2) (12,0) (16,8) (12,16) (10,15) (4,9) (3,9) (0,4) (9,13) (8,10) (12,1) (7,2) (7,14) (1,2) (5,1) (14,0)\nQ: Is there a path in this graph that visits every 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->14->9->7->10->12->13->2->5->11->6->8->4->1->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph122",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (1,2) (7,0) (9,12) (9,7) (9,0) (8,11) (8,10) (11,3) (6,1) (7,5) (4,11) (12,7) (9,6) (3,8) (9,4) (11,1) (0,11) (6,10) (5,4) (6,5) (9,2) (8,7) (5,9) (1,12) (8,1) (2,5) (12,11) (1,5) (3,10) (10,11) (8,4)\nQ: Is there a path in this graph that visits every 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->12->7->5->4->11->8->3->10->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph211",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (0,6) (7,6) (4,1) (9,11) (6,9) (4,7) (9,0) (3,7) (1,6) (4,6) (9,1) (4,8) (0,7) (9,3) (10,3) (0,10) (8,3) (1,12) (10,12) (10,13) (8,7) (8,6) (1,10) (1,7) (4,3) (3,2) (5,13) (5,6) (13,1) (4,5) (0,4) (13,2) (10,7) (2,11) (4,10) (12,3) (12,6) (11,12) (3,0) (5,2) (0,13) (5,7) (0,1) (12,5) (7,13) (9,10) (2,9) (11,13)\nQ: Is there a path in this graph that visits every 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->1->9->11->2->13->5->12->10->3->8."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph563",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (16,6) (15,1) (2,14) (12,8) (10,1) (7,5) (11,19) (19,12) (10,3) (12,2) (7,14) (13,15) (10,18) (14,11) (7,0) (11,13) (10,16) (9,13) (9,7) (9,1) (7,19) (7,1) (1,12) (5,4) (0,10) (2,5) (3,9) (2,16) (3,8) (6,13) (6,17) (7,2) (1,18) (11,7) (7,17) (4,15) (11,9) (4,16) (17,10) (3,7) (17,11) (15,5) (3,15) (18,13) (17,4) (9,14) (13,17) (12,15) (12,0) (13,10) (12,18) (6,10) (13,19) (15,18) (8,13) (3,5) (0,5) (10,7) (7,12) (14,0) (11,3) (6,1) (6,15) (19,16) (8,18) (13,7) (6,7) (8,6) (9,0) (11,0) (12,17) (14,19) (11,5) (19,3) (8,14) (2,3) (16,17) (14,10) (18,11) (12,11) (4,3) (8,11)\nQ: Is there a path in this graph that visits every 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->4->15->1->10->3->9->13->11->19->12->18->8->6->17->16->2->14."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph52",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,5) (5,9) (1,5) (6,4) (3,2) (8,3) (3,5) (10,7) (2,8) (4,3) (9,7) (3,1) (3,9) (2,7) (8,0) (10,9) (8,5) (7,4) (3,7) (5,6) (4,0) (2,4) (2,1) (5,10) (0,7) (10,0) (1,6) (3,6) (4,8) (9,4) (6,8) (0,1) (3,0) (10,1)\nQ: Is there a path in this graph that visits every 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->2->7->5->9->10->1->6->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph500",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (17,0) (1,16) (15,2) (1,14) (2,8) (0,14) (14,15) (17,5) (13,4) (3,15) (4,6) (8,5) (16,7) (8,15) (18,3) (16,6) (6,15) (13,0) (7,2) (10,17) (9,7) (12,4) (4,5) (10,9) (7,11) (4,10) (11,16) (13,16) (13,11) (1,7) (17,13) (18,11) (11,4) (18,17) (18,6) (6,2) (13,10) (6,17) (3,1) (15,9) (7,12) (16,14) (12,15) (11,12) (18,4) (3,0) (10,3) (9,8) (15,5) (8,3) (12,3) (10,14) (2,13) (1,6) (16,15) (7,0) (1,11) (14,18) (5,3) (6,7) (7,15) (7,14) (17,14) (16,10) (5,0) (2,9) (11,6) (10,2) (4,7) (4,9) (10,0) (10,12) (8,16) (7,17) (13,7) (8,17)\nQ: Is there a path in this graph that visits every 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->8->2->15->14->1->16->7->9->10->4->13->11->12->3->18->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph180",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (3,11) (4,7) (9,0) (0,3) (9,11) (0,2) (7,9) (5,12) (1,5) (9,13) (5,6) (9,3) (8,11) (1,4) (10,3) (10,5) (13,11) (12,1) (7,13) (13,0) (2,7) (5,2) (5,8) (7,6) (12,2) (0,8) (13,3) (4,5) (6,11) (0,11) (5,0) (1,11) (10,1) (8,2) (0,10) (10,9) (6,0)\nQ: Is there a path in this graph that visits every 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->8->2->12->5->6->7->4->1->10->3->13."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph76",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (7,2) (10,11) (4,11) (4,5) (8,3) (7,1) (6,8) (1,9) (8,7) (5,6) (3,10) (7,11) (7,0) (7,10) (11,2) (5,8) (5,11) (6,7) (3,6) (7,9) (6,1) (0,2) (9,3) (11,3) (3,5) (4,8) (5,7) (1,3) (4,9)\nQ: Is there a path in this graph that visits every 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->11->10->3->8->6->5->4->9->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph40",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (4,0) (8,10) (2,4) (7,6) (8,0) (3,7) (5,4) (2,7) (7,9) (1,8) (6,8) (2,10) (3,1) (10,5) (9,4) (0,5) (3,4) (3,10) (6,0) (0,1) (2,3) (3,5) (3,0) (6,2) (2,0) (7,0) (6,4) (9,0) (6,3) (6,10) (4,10)\nQ: Is there a path in this graph that visits every 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->10->5->3->1->8->6->7->9."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph88",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (11,9) (7,4) (1,6) (2,6) (1,8) (11,7) (9,8) (11,6) (3,8) (0,10) (8,6) (5,0) (2,0) (4,1) (3,9) (1,5) (3,5) (0,1) (1,10) (0,6) (5,11) (5,6) (2,8) (9,4) (10,8) (6,10) (6,3)\nQ: Is there a path in this graph that visits every 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->6->2->8->9->3->5->11->7->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph413",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (5,6) (7,10) (11,6) (14,0) (5,2) (9,4) (0,2) (3,10) (12,13) (13,11) (12,3) (13,8) (13,7) (7,4) (3,6) (6,1) (2,13) (4,13) (4,3) (8,9) (3,11) (14,4) (11,10) (4,11) (0,5) (15,0) (7,8) (12,6) (15,3) (15,14) (5,12) (2,10) (5,10) (12,0) (3,14) (4,15) (9,15) (2,16) (13,1) (8,1) (7,5) (14,13) (10,8) (12,10) (7,2) (4,1) (2,9) (3,7) (0,6) (7,12) (13,15) (5,13) (1,2) (4,2) (15,5) (16,7) (10,0) (12,9) (3,2) (11,0) (3,1) (12,4) (14,11) (2,15) (5,1) (10,13) (5,8) (11,15) (5,4) (1,14) (9,0) (16,5) (6,15) (11,7) (8,15) (6,8) (0,1) (9,11) (4,0) (13,3) (3,9) (8,3)\nQ: Is there a path in this graph that visits every 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->4->9->8->13->12->3->10->7->5->15->11->6->1->2->16."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph128",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (6,11) (10,7) (11,3) (8,3) (12,0) (2,10) (5,3) (1,2) (8,5) (0,4) (7,11) (5,4) (10,3) (10,11) (11,8) (4,7) (2,9) (12,9) (1,3) (5,7) (4,6) (9,5) (4,11) (3,12) (10,0) (9,0) (6,5) (2,3) (12,1) (4,3) (8,0) (7,12) (5,0) (12,2) (4,2) (4,8) (8,12) (5,2)\nQ: Is there a path in this graph that visits every 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->10->7->11->6->4->5->8->3->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph165",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (11,0) (5,10) (7,3) (9,0) (2,10) (1,9) (11,6) (1,4) (1,11) (1,10) (3,1) (0,1) (8,5) (5,0) (6,0) (8,3) (11,3) (7,10) (12,0) (2,12) (0,10) (2,5) (8,6) (0,4) (10,9) (9,4) (7,12) (10,8) (6,2) (12,6) (11,5) (8,12) (5,3) (1,5) (9,6) (7,9) (12,10) (10,11) (2,11) (3,0) (2,7) (8,7) (9,3) (9,12) (8,2) (5,12)\nQ: Is there a path in this graph that visits every 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->5->8->3->7->12->6->11->1->9->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph100",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (9,8) (5,7) (0,6) (5,1) (3,9) (3,1) (11,8) (11,10) (11,1) (5,6) (7,6) (10,3) (2,11) (1,7) (9,6) (0,1) (8,10) (6,11) (5,4) (10,2) (6,8) (4,8) (5,11) (3,2) (4,10) (7,11) (0,9) (7,0) (3,4) (1,9) (3,6) (9,11) (0,3) (4,1) (2,0) (11,3) (0,11) (0,4) (2,6) (8,5) (8,2) (4,6) (1,6) (3,8) (10,1)\nQ: Is there a path in this graph that visits every 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->1->3->9->8->11->2->10->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph167",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (3,6) (12,8) (9,11) (9,1) (7,5) (0,3) (12,2) (0,5) (7,2) (7,3) (6,11) (5,6) (11,10) (10,3) (7,4) (2,8) (5,12) (9,6) (11,8) (3,5) (2,10) (4,2) (8,4) (7,10) (1,0) (2,6) (0,6) (9,0) (0,12) (0,10) (12,4) (12,1) (8,5) (8,7) (7,9) (3,1) (1,6) (12,9) (5,4) (11,3) (8,1) (2,3) (0,2) (8,10) (5,1) (7,0)\nQ: Is there a path in this graph that visits every 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->11->9->1->12->8->2->10->7->5->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph378",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (2,13) (12,1) (11,6) (7,10) (10,6) (1,16) (12,15) (8,7) (0,15) (13,3) (11,0) (7,4) (8,11) (13,0) (13,15) (6,5) (12,2) (9,3) (0,7) (7,13) (5,9) (15,4) (5,0) (8,3) (6,12) (14,6) (0,9) (9,6) (10,11) (12,4) (3,16) (6,15) (12,3) (8,1) (5,13) (7,2) (9,4) (5,16) (16,8) (16,6) (1,9) (4,8) (4,1) (8,13) (15,7) (1,10) (15,8) (9,7)\nQ: Is there a path in this graph that visits every 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->12->1->16->3->13->2->7->10->11->8->4->9->5->6->14."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph8",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,10) (5,3) (0,2) (3,6) (2,3) (1,6) (9,0) (5,0) (10,0) (9,10) (8,0) (3,0) (1,3) (1,10) (7,3) (2,1) (7,8) (7,5) (8,5) (4,7) (1,9) (2,10) (0,1) (4,2)\nQ: Is there a path in this graph that visits every 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->6->1->9->10->5->8->7->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph134",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (0,12) (10,7) (3,11) (2,11) (0,1) (0,9) (5,8) (4,10) (2,6) (1,7) (1,11) (1,3) (3,7) (12,5) (0,8) (9,3) (10,6) (7,2) (0,4) (12,8) (3,4) (5,7) (12,2) (7,11) (11,10) (1,6) (11,6) (4,11) (5,4) (11,9) (4,7) (8,4) (6,3)\nQ: Is there a path in this graph that visits every 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->8->4->10->7->1->11->2->6->3->9."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph317",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (11,5) (9,1) (2,7) (0,3) (11,4) (7,0) (1,5) (10,0) (3,8) (6,9) (6,11) (8,9) (5,8) (5,3) (15,13) (10,13) (15,14) (4,15) (0,11) (9,11) (5,14) (4,7) (15,7) (10,6) (14,10) (10,5) (8,6) (7,8) (12,3) (12,6) (3,13) (2,9) (0,12) (2,15) (2,0) (13,9) (4,12) (12,1) (6,14) (14,1) (7,13) (14,9) (14,8) (9,7) (4,1)\nQ: Is there a path in this graph that visits every 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->9->1->5->11->4->15->2->7->13->10->14->6->12."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph166",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (11,6) (3,1) (6,12) (4,11) (12,11) (1,8) (2,9) (9,7) (9,11) (1,0) (8,12) (12,1) (4,6) (0,9) (2,6) (10,1) (2,0) (12,3) (10,2) (8,11) (11,5) (4,1) (9,8) (5,2) (3,7) (2,7) (2,4) (12,10) (1,2) (0,5) (7,8) (0,12) (1,5) (12,7) (12,9) (2,12) (8,3) (5,10) (8,0) (9,4) (7,4) (4,8) (0,11) (4,12) (3,0) (7,1) (0,6) (5,12) (10,7) (3,6)\nQ: Is there a path in this graph that visits every 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->12->6->11->4->2->9->8->7->10->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph463",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (9,7) (8,1) (7,5) (7,3) (16,7) (13,3) (13,2) (15,1) (4,8) (10,5) (14,2) (14,1) (8,9) (13,4) (5,16) (3,5) (17,1) (8,6) (15,4) (17,5) (4,17) (11,17) (15,17) (9,6) (1,10) (7,10) (8,2) (17,14) (11,13) (12,7) (5,11) (14,16) (4,6) (0,8) (11,0) (15,14) (7,14) (10,3) (17,12) (13,5) (15,2) (4,1) (17,13) (17,0) (5,8) (11,14) (7,1) (14,12) (2,10) (11,12) (7,2) (17,3) (15,10) (0,10) (2,11) (4,7) (2,9) (11,16) (3,2) (16,4) (14,5) (9,3) (13,9) (4,9) (6,11) (2,6) (16,2) (17,9) (12,8) (6,12) (0,14) (3,1) (3,16) (13,7) (6,3) (9,15) (12,0) (15,8) (5,12) (12,3) (5,4) (12,13) (8,3) (4,10)\nQ: Is there a path in this graph that visits every 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->15->4->13->3->7->9->6->11->17->5->10->2->16->14->12."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph459",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 17, and the edges are: (13,14) (3,10) (12,15) (11,5) (8,3) (7,3) (15,1) (11,8) (14,8) (1,6) (3,1) (6,13) (2,3) (5,12) (12,13) (7,13) (4,9) (16,17) (15,2) (9,7) (2,5) (10,12) (16,6) (17,15) (12,8) (10,11) (17,10) (7,17) (5,0) (2,17) (10,8) (7,15) (0,17) (15,5) (3,6) (14,15) (15,4) (12,14) (10,1) (12,11) (16,0) (9,17) (13,8) (17,1) (15,13) (0,15) (5,8) (11,3) (3,13) (4,14) (16,3) (0,10) (16,11) (2,4) (14,9) (3,4) (7,2) (12,2) (5,4) (12,17) (10,2) (9,12) (5,3) (17,8) (14,3) (2,11) (7,4) (5,10) (0,7) (11,13) (11,6) (4,17) (1,5) (6,14) (16,2) (9,16) (15,16) (15,11) (16,1) (4,10) (1,11) (15,6) (1,8) (5,17) (6,12) (10,14) (12,0) (5,6) (12,1) (15,8) (8,9) (14,11) (13,16) (3,0)\nQ: Is there a path in this graph that visits every 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->11->8->3->10->12->15->1->6->13->14->4->9->7->17->16->2."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph16",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (2,4) (3,7) (3,4) (0,3) (7,10) (10,3) (9,8) (10,4) (8,5) (0,7) (4,9) (2,6) (1,4) (0,1) (3,9) (5,2) (10,0) (7,1) (7,6) (5,9) (1,3) (1,9) (3,2)\nQ: Is there a path in this graph that visits every 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->10->4->1->9->8->5->2->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph326",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 15, and the edges are: (8,6) (2,14) (9,7) (10,3) (5,14) (15,7) (15,5) (1,14) (1,5) (7,12) (12,5) (10,7) (11,10) (15,2) (8,4) (11,3) (5,7) (9,8) (6,7) (13,14) (12,0) (3,14) (0,15) (2,0) (3,8) (7,11) (9,1) (8,12) (2,6) (0,3) (10,15) (6,11) (10,5) (14,6) (10,9) (13,15) (13,11) (14,4) (13,1) (4,15) (0,8) (4,0) (6,3) (14,12) (1,2) (11,2) (15,8) (13,6) (5,8) (1,15) (7,13) (1,4) (14,9) (10,13)\nQ: Is there a path in this graph that visits every 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->9->8->6->2->14->5->15->10->3->11->13->1->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph155",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (11,9) (5,11) (6,7) (12,10) (10,11) (6,8) (3,7) (1,9) (5,10) (9,8) (0,12) (5,3) (4,11) (2,0) (2,4) (7,9) (1,6) (12,9) (12,8) (12,2) (8,4) (1,3) (12,7) (11,0) (1,8) (5,6) (2,6) (7,2) (7,0) (7,10) (9,0) (0,4) (12,3) (7,1) (0,3) (3,8) (6,0) (3,10) (5,4) (4,6) (4,12) (10,6) (8,5) (10,2) (3,2) (7,8) (5,7)\nQ: Is there a path in this graph that visits every 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->10->11->9->1->6->7->3->5->8->4->2."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph105",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (4,11) (7,5) (7,10) (8,1) (4,2) (9,4) (2,9) (8,6) (9,6) (0,9) (4,6) (0,4) (6,0) (5,1) (4,1) (3,0) (3,8) (7,8) (5,4) (2,6) (1,6) (7,9) (2,10) (3,7) (3,6) (1,9) (6,5) (7,2) (11,7) (11,3) (3,1) (7,6) (7,1) (9,5) (9,3) (10,11) (7,4) (0,1)\nQ: Is there a path in this graph that visits every 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->11->7->5->1->8->3->6->2->10."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph90",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (11,3) (5,10) (10,11) (6,5) (6,1) (4,5) (11,8) (10,8) (4,2) (5,3) (9,8) (5,7) (2,1) (0,10) (2,7) (7,9) (11,9) (6,0) (8,5) (1,7) (6,11) (4,3) (5,1) (10,1) (10,4) (10,9) (9,2) (5,0) (1,8) (6,3) (2,5) (9,1) (2,6)\nQ: Is there a path in this graph that visits every 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->3->11->8->9->7->2->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph239",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,10) (2,3) (8,12) (4,2) (13,11) (4,3) (4,11) (6,10) (0,4) (13,7) (0,6) (4,13) (5,11) (9,6) (6,12) (9,0) (7,10) (1,4) (12,9) (10,9) (1,10) (6,3) (3,11) (10,8) (4,10) (3,12) (5,0) (2,13) (3,10) (5,12) (8,9) (6,1) (5,2) (1,13) (8,11) (9,7) (0,1) (8,5) (7,3) (8,0) (8,3) (0,7) (12,4) (5,10) (8,1) (0,10) (12,10) (12,7) (8,7) (6,7) (13,12) (2,9) (1,11) (12,2) (0,13) (13,3) (8,2)\nQ: Is there a path in this graph that visits every 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->3->6->10->13->11->5->12->9->7->8->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph549",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,19) (4,8) (2,18) (13,11) (10,18) (3,9) (13,8) (8,3) (18,17) (11,10) (9,0) (8,7) (8,11) (1,15) (2,17) (18,16) (3,2) (0,18) (7,18) (1,10) (1,6) (16,19) (8,2) (19,1) (17,8) (14,1) (14,10) (5,8) (18,5) (15,12) (10,6) (17,5) (17,16) (17,9) (6,8) (6,11) (6,0) (15,0) (3,14) (7,14) (6,14) (10,16) (14,9) (13,19) (11,16) (16,0) (15,5) (12,3) (0,17) (0,3) (0,19) (7,4) (15,16) (4,17) (2,14) (16,4) (10,13) (9,10) (19,8) (4,5) (0,4) (18,14) (0,5) (2,10) (13,6) (9,18) (9,13) (4,19) (9,5) (16,12) (10,8) (13,15) (12,0) (3,10)\nQ: Is there a path in this graph that visits every 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->8->4->7->18->2->17->5->19->16->10->11->13->6->14->1->15->12."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph588",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (8,7) (12,3) (15,5) (0,10) (0,14) (7,0) (12,18) (3,16) (0,9) (15,8) (12,1) (14,2) (4,14) (6,14) (8,13) (8,4) (5,3) (3,4) (3,9) (12,2) (3,18) (0,2) (15,13) (9,12) (0,5) (13,17) (17,8) (2,6) (11,15) (9,15) (10,13) (13,18) (19,18) (8,1) (9,2) (1,14) (3,17) (1,19) (6,18) (0,4) (19,10) (19,13) (4,5) (14,9) (0,13) (15,6) (13,7) (2,1) (16,0) (6,19) (15,1) (17,16) (16,7) (2,19) (14,18) (11,4) (1,5) (4,2) (9,11) (12,15) (15,14) (19,12) (8,19) (14,17) (17,4) (12,6) (10,12) (4,15) (16,14) (16,19) (13,9) (16,10) (9,8) (18,1) (4,7) (13,11) (5,7) (0,3) (10,1) (12,13) (1,11) (11,8) (6,11) (3,7) (10,4) (5,11) (6,16) (6,17) (8,16) (3,19) (18,16) (0,15) (7,17) (10,11) (2,11) (8,10) (5,14) (10,15) (9,7) (5,18) (2,5) (6,10) (11,19) (7,1) (7,14) (1,13) (8,14) (0,1) (5,6) (11,0) (10,7) (5,19) (15,18) (12,8) (12,0) (19,7) (8,5) (7,18)\nQ: Is there a path in this graph that visits every 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->8->7->16->3->12->18->19->1->14->2->6->15->9->11->5->4->17."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph598",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 19, and the edges are: (5,7) (12,15) (15,8) (8,17) (10,8) (11,1) (4,19) (12,7) (10,9) (12,11) (18,19) (9,3) (1,17) (19,3) (19,14) (11,3) (16,4) (1,18) (11,18) (18,8) (6,12) (14,10) (6,9) (11,16) (10,18) (2,13) (5,14) (5,19) (1,7) (14,0) (13,17) (2,9) (0,19) (1,13) (11,17) (8,12) (6,19) (16,5) (17,12) (2,3) (0,6) (9,8) (13,9) (9,0) (12,1) (5,13) (3,4) (9,19) (2,18) (9,18) (4,18) (2,14) (3,16) (19,10) (16,8) (11,4) (3,6) (6,7) (1,14) (7,15) (6,13) (7,0) (17,15) (3,10) (6,1) (19,12) (17,19) (0,4) (1,15) (19,2) (2,10) (11,2) (6,5) (10,5) (17,4) (15,2) (5,1) (15,11) (18,6) (2,7) (14,12) (15,19) (6,14) (7,16) (9,11) (1,2) (18,16) (8,6) (6,16) (17,7) (7,18) (10,4) (14,8) (2,8) (14,3) (1,10) (2,16) (2,4) (1,0) (10,7) (8,0) (12,3) (19,1) (1,8) (17,3) (7,13) (17,9) (9,16) (1,9) (5,3) (18,15) (4,6) (17,14)\nQ: Is there a path in this graph that visits every 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->19->4->16->11->1->17->8->15->12->7->5->13->2->9->10->18->6->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph171",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (1,9) (0,11) (0,12) (10,6) (9,0) (6,3) (9,8) (12,6) (7,4) (10,11) (4,10) (2,9) (1,5) (4,12) (8,11) (7,8) (8,0) (4,3) (7,3) (5,2) (9,12) (6,8) (2,7) (7,6) (11,2) (10,9) (0,7) (2,0) (1,7) (5,9) (12,8) (8,3) (3,2) (1,3) (12,5) (4,11) (3,9) (3,5) (5,8) (1,6) (9,4) (9,6) (12,11) (2,8) (4,2) (6,2) (10,12) (7,11) (5,10)\nQ: Is there a path in this graph that visits every 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->6->3->4->7->8->12->9->1->5->2."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph204",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (13,4) (12,1) (6,4) (1,9) (11,8) (12,4) (13,11) (12,13) (9,12) (5,11) (4,9) (2,12) (7,6) (12,3) (9,13) (10,3) (5,8) (10,4) (0,11) (5,9) (0,5) (6,9) (5,10) (11,12) (5,2) (4,7) (7,8) (9,3) (1,5) (8,2) (5,3) (1,10) (2,0) (10,2) (1,3) (13,1)\nQ: Is there a path in this graph that visits every 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->8->5->9->1->3->10->2->12->13->4->6->7."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph213",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 13, and the edges are: (2,4) (10,4) (13,7) (4,11) (11,1) (7,2) (3,5) (5,9) (0,8) (5,6) (13,6) (13,10) (8,5) (3,4) (13,2) (13,3) (12,11) (9,3) (6,8) (0,12) (9,2) (7,4) (4,9) (8,4) (1,4) (6,3) (4,6) (4,0) (6,0) (6,10) (8,2) (5,10) (8,7) (8,10) (5,2) (7,6) (3,12) (10,3) (0,9) (11,5) (12,4) (12,6) (10,0) (9,11) (6,2) (10,9) (0,11) (10,1)\nQ: Is there a path in this graph that visits every 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->5->3->4->2->7->13->6->12->11->1->10->9."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph273",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 14, and the edges are: (1,13) (4,3) (14,3) (13,0) (11,13) (11,2) (10,6) (4,12) (11,10) (9,2) (12,10) (1,8) (5,7) (7,0) (1,11) (9,6) (3,13) (1,10) (6,5) (3,5) (12,7) (2,13) (13,12) (3,10) (5,9) (4,1) (8,11) (4,7) (4,13) (9,14) (7,3) (3,2) (3,8) (8,10) (5,11) (2,7) (14,2) (8,7) (4,6) (11,4) (1,0) (10,13) (8,4) (12,8) (11,14) (5,2) (9,8) (4,5) (7,14) (14,6) (5,1) (9,0) (5,8) (4,0) (0,12) (1,9) (10,4) (14,10) (9,13) (4,2) (0,6) (1,6) (2,6) (13,14) (5,10) (10,9)\nQ: Is there a path in this graph that visits every 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->8->11->2->9->6->10->12->4->3->14->7->5."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph112",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 11, and the edges are: (8,1) (10,11) (4,1) (0,9) (1,11) (0,2) (11,2) (7,6) (0,6) (8,4) (10,9) (5,8) (7,5) (6,2) (8,0) (8,7) (11,9) (10,2) (1,5) (1,9) (5,2) (0,10) (10,6) (3,11) (0,7) (8,3) (4,10) (8,6) (2,9) (6,5) (4,9) (7,4) (5,0) (5,3) (3,2) (3,7) (9,8) (2,7) (5,9) (1,10) (1,0)\nQ: Is there a path in this graph that visits every 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->11->1->8->4->7->6->2->5->3."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph415",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 16, and the edges are: (3,16) (13,14) (8,15) (11,5) (8,3) (16,7) (4,11) (4,1) (2,11) (13,4) (2,1) (6,8) (15,11) (0,11) (13,8) (15,14) (11,6) (3,12) (0,15) (1,13) (15,9) (8,0) (4,0) (13,7) (4,3) (11,14) (7,2) (3,13) (13,10) (16,6) (16,4) (15,16) (7,8) (9,4) (14,16) (13,0) (8,16) (11,8) (4,8) (12,14) (3,11) (4,14) (9,5) (5,1) (10,0) (12,13) (1,7) (14,5) (8,9) (10,9) (2,10) (5,4) (12,11) (0,3) (12,10) (11,7) (10,5) (2,16) (15,4) (7,10) (14,6) (14,7) (6,10) (15,3) (4,7) (16,10) (0,14) (12,5) (16,0) (15,5) (6,7) (5,16) (16,1) (3,5) (15,12) (3,6) (11,10) (8,10) (16,9) (7,15) (2,6) (6,4) (2,5) (6,5) (15,2) (13,5) (1,0) (7,12) (14,10)\nQ: Is there a path in this graph that visits every 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->9->15->8->3->16->7->13->14->12->10->2->1->4->6."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph484",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 18, and the edges are: (16,10) (1,8) (7,3) (2,3) (1,13) (11,4) (5,0) (6,12) (18,9) (7,11) (12,7) (1,7) (17,2) (13,0) (18,8) (4,5) (13,11) (1,17) (7,13) (12,15) (3,8) (5,16) (12,0) (7,8) (2,16) (5,8) (4,13) (4,18) (5,18) (11,8) (17,6) (15,14) (1,9) (10,2) (0,1) (11,5) (0,7) (18,3) (8,15) (11,16) (12,11) (7,4) (8,9) (0,4) (12,18) (7,9) (6,3) (5,7) (15,17) (8,13) (15,1) (11,10) (1,12) (2,4) (12,5) (14,6) (6,0) (15,5) (1,4)\nQ: Is there a path in this graph that visits every 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->11->7->3->8->13->1->9->18->12->6->14->15->17->2->16->10."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph570",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (18,11) (0,8) (9,1) (12,13) (5,15) (5,7) (6,7) (16,0) (4,9) (3,13) (1,5) (17,8) (17,12) (12,6) (0,7) (0,10) (13,19) (3,8) (14,4) (2,6) (7,1) (8,16) (10,17) (15,13) (11,1) (2,14) (7,3) (0,17) (12,19) (1,2) (11,16) (4,10) (6,15) (12,11) (5,3) (3,17) (15,12) (6,8) (15,9) (4,8) (2,3) (3,12) (10,16) (7,16) (16,5) (3,4) (13,14) (2,0) (14,16) (17,18) (18,14) (6,1) (18,15) (16,2) (19,7) (9,5) (16,6) (8,5) (17,11) (3,0) (9,8) (1,4) (7,15) (0,13) (9,16) (16,3) (2,10) (12,4) (9,17) (7,8) (10,12) (12,8) (7,12) (13,18) (18,0) (10,5) (11,0) (12,14) (2,19) (15,19) (8,14) (10,11) (9,19) (19,17) (2,11) (14,0) (3,9) (4,19) (15,17) (2,8) (2,5) (15,11) (18,10) (3,6) (11,5) (5,13) (14,1) (5,12) (11,7) (12,18) (13,2) (18,8) (17,14) (4,0) (7,2) (0,6) (3,19) (0,19) (14,10) (15,2) (4,2) (3,18) (5,19)\nQ: Is there a path in this graph that visits every 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->13->3->7->5->15->6->2->14->4->1->11->18->10->16->9->19."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph203",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (10,4) (13,4) (10,12) (8,2) (7,8) (1,11) (7,10) (5,11) (3,2) (9,2) (0,7) (4,3) (3,7) (10,9) (6,3) (5,8) (1,12) (10,3) (11,8) (3,9) (6,10) (1,5) (12,4) (3,1) (3,0) (1,8)\nQ: Is there a path in this graph that visits every 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->3->9->2->8->5->11->1->12->4->13."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph12",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (7,6) (3,2) (0,10) (9,10) (3,5) (8,0) (0,4) (7,1) (7,10) (6,5) (9,1) (5,2) (2,6) (6,4) (8,4) (5,1) (10,2) (9,6) (2,4) (8,3) (3,9)\nQ: Is there a path in this graph that visits every 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->1->7->6->5->3->2->4->8."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph194",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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) (0,1) (13,11) (7,6) (8,2) (13,7) (10,12) (9,0) (0,7) (12,7) (9,5) (3,12) (8,12) (6,1) (6,2) (10,9) (9,6) (4,12) (9,13) (1,9) (6,10) (8,10) (2,7) (2,5) (5,8) (8,6) (8,11) (13,0) (12,6) (10,2) (10,11) (0,3) (1,3) (5,10) (4,0) (6,5) (12,11) (12,2) (4,13) (9,7)\nQ: Is there a path in this graph that visits every 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->13->11->8->2->5->9->10->3->12->4."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph158",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 12, and the edges are: (5,7) (8,1) (2,4) (2,10) (3,5) (11,0) (4,12) (1,7) (5,9) (9,1) (10,1) (2,9) (3,7) (12,6) (10,3) (0,12) (6,1) (12,7) (8,10) (11,2) (11,10) (4,5) (2,5) (10,7) (6,7) (6,4) (8,0) (9,10) (12,5) (3,1) (11,8) (1,12) (5,8) (1,11) (12,3) (8,4) (5,6) (2,8) (6,11) (9,7) (11,5) (6,3) (2,12) (2,6) (0,10) (8,6) (5,10) (0,4) (2,7) (5,1) (8,9) (8,7)\nQ: Is there a path in this graph that visits every 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->4->12->6->1->8->10->3->5->7->9."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph30",
        "conversations": [
            {
                "from": "human",
                "value": "In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge.\nThe nodes are numbered from 0 to 10, and the edges are: (5,6) (6,4) (2,7) (5,10) (3,2) (5,7) (5,2) (1,3) (10,0) (0,5) (0,4) (4,8) (1,2) (6,7) (9,7) (3,10) (0,9) (1,10) (10,8) (7,8) (5,3) (4,5) (2,0) (10,2) (8,0) (9,10) (7,10) (2,8) (5,9) (5,8) (1,0) (6,2) (9,2) (10,6) (0,6)\nQ: Is there a path in this graph that visits every 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->4->8->7->9->2->3->1."
            }
        ]
    },
    {
        "id": "hamilton-hard-graph350",
        "conversations": [
            {
                "from": "human",
                "value": "In an 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: (14,4) (13,10) (5,2) (0,5) (6,12) (6,9) (8,15) (12,14) (2,13) (15,10) (11,10) (5,13) (15,11) (12,1) (12,10) (10,3) (12,4) (3,12) (1,14) (9,13) (10,2) (14,9) (13,7) (3,0) (13,15) (8,0) (7,3) (2,11) (9,11) (10,8) (3,5) (1,13) (14,3) (8,12) (4,1) (0,12) (15,14) (3,15) (14,8) (4,6) (7,4) (0,4) (6,1) (13,8) (2,3) (1,9) (11,1) (1,8) (13,4) (5,4) (9,2) (8,5) (0,1) (14,10) (2,0) (7,12) (15,5) (12,5) (2,6) (0,9) (15,6) (7,1) (10,6) (0,11) (12,9) (4,15) (1,3) (13,14) (4,3) (5,6) (7,2) (0,10)\nQ: Is there a path in this graph that visits every 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->13->10->15->8->12->6->9->14->4->7->3->1->11."
            }
        ]
    }
]