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The Erdos-Hajnal High-Girth Subgraph Conjecture

Combinatorics · posed by Paul Erdos, Andras Hajnal, 1966 · partial

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Statement

Erdos and Hajnal asked whether hr(G)=max⁡{χ(H):H⊆G, girth(H)≥r}h_r(G) = \max\{\chi(H) : H \subseteq G,\ \mathrm{girth}(H) \ge r\} tends to infinity as χ(G)\chi(G) does, for every fixed r≥4r \ge 4. It does in every fixed polynomial edge-density regime.

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

  1. proof attempt · #1

    Eric Li, using ChatGPT

    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 declaration says ChatGPT was used for ideation and formalization during preparation, with the author responsible for the mathematics. Part of the same series of Erdos-problem resolutions in this catalog.

    in polynomial edge-density regimes; the general question remains open

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open in Claude →open in ChatGPT →

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