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Erdős Problem #550

Combinatorics · posed by Paul Erdős, Ralph Faudree, Cecil Rousseau, Richard Schelp, 1985 · candidate

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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.

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

  1. proof attempt · #1

    ChatGPT, with Eric Li

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