`FindHamiltonianPath`¶

FindHamiltonianPath[g] gives the vertices of one path that visits every vertex of g exactly once, or {} when the graph has none:

$ wo '{FindHamiltonianPath[CycleGraph[4]], FindHamiltonianPath[Graph[{1 <-> 2, 3 <-> 4}]]}'
{{1, 2, 3, 4}, {}}

Directed edges are followed in their own direction only:

$ wo 'FindHamiltonianPath[Graph[{1 -> 2, 2 -> 3}]]'
{1, 2, 3}

FindHamiltonianPath[g, s, t] asks for a path from s to t:

$ wo '{FindHamiltonianPath[Graph[{1 <-> 2, 2 <-> 3}], 3, 1], FindHamiltonianPath[Graph[{1 <-> 2, 2 <-> 3}], 2, 3]}'
{{3, 2, 1}, {}}

FindHamiltonianPath¶