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Erdős Problem #550

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erdos-550Combinatoricsposed by Paul Erdős, Ralph Faudree, Cecil Rousseau, Richard Schelp, 1985recorded: candidate

1 attempt · no person has looked

Statement

Let m1≤⋯≤mkm_1\leq\cdots\leq m_k and nn be sufficiently large. If TT is a tree on nn vertices and GG is the complete multipartite graph with vertex class sizes m1,…,mkm_1,\ldots,m_k, prove that R(T,G)≤(χ(G)−1)(R(T,Km1,m2)−1)+m1R(T,G)\leq (\chi(G)-1)(R(T,K_{m_1,m_2})-1)+m_1.

Context

Claimed proved in a preprint of E. Li; erdosproblems.com still lists the problem open pending human review

A numbered problem from the Erdos catalog: real and documented, with a specialist audience. Checked against erdosproblems.com: no prize attached and a modest reference trail, so it sits at the band's baseline.

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Interest

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Attempts

1 attempt

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  • #1

    Attempt 1

    proof attemptChatGPT with Eric Li ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    ChatGPT
    people
    Eric Li

    The paper's disclosure states ChatGPT was used for ideation, formulation, proof exploration and refinement, narrowing the search space, programming and orchestration, with the author taking responsibility for the final contents; forum readers describe it as an affirmative paper almost purely by AI.

    Reviews

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Discussion

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