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Hoa's Conjecture on Maximal Non-Hamiltonian Graphs

Combinatorics · posed by Vu Dinh Hoa, 1994 · disproved

1 attempt

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 GV(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.

Context

A named 1994 conjecture in Hamiltonian graph theory with a small but real literature; the audience is specialists in cycle structure.

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Attempts

1 attempt

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  • #1

    Attempt 1

    constructionChatGPT with Xingzhi Zhan ·
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    Xingzhi Zhan

    The declaration of AI use says ChatGPT assisted in developing and checking the constructions and proofs, with the author independently verifying all arguments.

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