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Erdős problem 550

Let m1mkm_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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