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arXiv · 2608.00957

Counterexamples to a conjecture of Hoa on maximal non-Hamiltonian graphs

Xingzhi Zhan
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Abstract

A graph G is said to be maximal non-Hamiltonian if G is non-Hamiltonian, but $G+e$ is Hamiltonian for every nonedge $e$ of $G.$ In 1994, Vu Dinh Hoa conjectured that if $C$ is a longest cycle of a maximal non-Hamiltonian graph $G,$ then $G-V(C)$ is a complete graph. We disprove this conjecture by constructing a counterexample of every order $n\ge 56.$ We also pose several related open problems.

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Xingzhi Zhan. 2026-08-14. Counterexamples to a conjecture of Hoa on maximal non-Hamiltonian graphs. https://arxiv.org/abs/2608.00957

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