How can I prove that no bipartite graph is hamiltonian-connected?
I thought I could use another problem of my homework: Ks,t is hamiltonian iff s=t But I don't really see how
Or Should I try induction?
2026-03-25 20:17:10.1774469830
Bipartite graphs not hamiltonian-connected
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You have all you need right now.
A graph is Hamilton-connected if any two vertices can be joined by a Hamilton path. So all you need to do is show that if two vertices from different parts of a bipartition can be joined by a Hamilton path, then two vertices from the same part cannot.
(With the exception of $K_{1,1}$, which is Hamilton-connected.)