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Hoa's Conjecture on Maximal Non-Hamiltonian Graphs

Combinatorics · posed by Vu Dinh Hoa, 1994 · disproved

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Statement

A graph GG is maximal non-Hamiltonian if it is non-Hamiltonian but G+eG + e is Hamiltonian for every nonedge ee. In 1994 Vu Dinh Hoa conjectured a property of G−V(C)G - V(C) for a longest cycle CC of such a graph. Disproved by an explicit base graph on 56 vertices, extended to larger orders.

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  1. construction · #1

    Xingzhi Zhan, using ChatGPT

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