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The Espuny Diaz-Lichev-Wesolek Conjecture on Dirac Subgraphs

Combinatorics · posed by Alberto Espuny Diaz, Lyuben Lichev, Alexandra Wesolek · 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.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Richard Lang, Alp Muyesser, Mathias Schacht and Carl Schneider, using ChatGPT 5.5 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    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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