Claims

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1977_03_01_chvatal: Chvátal (J. Graph Theory 1977) proves R(T,K_m) = (m-1)(n-1)+1 for every tree T on n vertices, the case of Problem 550 in which every class has one vertex; refereed.

1985_12_01_erdos_faudree_rousseau_schelp: Theorem 1 of the 1985 Combinatorica paper gives R(T,K(m_1,...,m_k)) = (k-1)(n-1)+m_1 for every large tree of bounded maximum degree, which yields the inequality of Problem 550 for those trees; refereed.

1989_12_01_erdos_faudree_rousseau_schelp: The Theorem of the 1989 multipartite graph-tree paper (Ann. New York Acad. Sci. 576) proves the inequality of Problem 550 for large trees when the smallest class has size 1; a proceedings paper, claimed.

2026_06_22_li: Theorem 1.1 of Li's 2026 preprint claims the inequality of Problem 550 for fixed class sizes and every large tree; unrefereed, with Lean developments this corpus has not built.

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