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The Erdos-Hajnal High-Girth Subgraph Conjecture

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erdos-hajnal-high-girth-subgraphCombinatoricsposed by Paul Erdos, Andras Hajnal, 1966recorded: 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.

Context

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

A long-standing Erdos-Hajnal question tying chromatic number to high-girth subgraphs, one of the classical hard questions about chromatic number.

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  • #1

    Attempt 1

    proof attemptChatGPT with Eric Li ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    ChatGPT
    people
    Eric Li

    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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