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The Espuny Diaz-Lichev-Wesolek Conjecture on Dirac Subgraphs

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espuny-diaz-lichev-wesolek-conjectureCombinatoricsposed by Alberto Espuny Diaz, Lyuben Lichev, Alexandra Wesolekrecorded: partial

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Statement

Espuny Diaz, Lichev and Wesolek conjectured that a Dirac-type minimum degree condition forces Hamiltonicity in spanning subgraphs of cycle powers. Asymptotically true: for every ε>0\varepsilon > 0 and all large kk, any spanning subgraph of the kkth power of a cycle with minimum degree at least (1+ε)k(1+\varepsilon)k has a Hamilton cycle.

Context

asymptotic in k; the paper also shows the analogous statement is false for d = 2

A named conjecture extending Dirac's theorem to powers of cycles, in an actively worked corner of Hamiltonicity.

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  • #1

    Attempt 1

    constructionChatGPT 5.5 Pro with Richard Lang, Alp Muyesser, Mathias Schacht, Carl Schneider ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    ChatGPT 5.5 Pro
    people
    Richard Lang, Alp Muyesser, Mathias Schacht, Carl Schneider

    The credit is specific and negative-result shaped: the authors show the analogous statement fails for d=2d = 2, and say the crucial construction behind that was suggested to them by ChatGPT 5.5 Pro, with a dedicated appendix discussing it.

    asymptotic in k; the paper also shows the analogous statement is false for d = 2

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