AI 中文总结
针对1994年Hoa提出的极大非哈密顿图相关猜想，本文通过构造n≥56阶的反例，成功推翻了该猜想。
AI 中文摘要
若图G是非哈密顿图，且对G的每条非边e，G+e均为哈密顿图，则称G为极大非哈密顿图。1994年，Vu Dinh Hoa猜想：若C是极大非哈密顿图G的最长圈，则G-V(C)是完全图。我们通过构造n≥56阶的反例，证明该猜想不成立。
英文摘要
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.
Comments9 pages, 3 figures
