Abstract
A connected graphG is said to beF-good if the Ramsey numberr(F, G) is equal to(x(F) ? 1)(p(G) ? 1) + s(F), wheres(F) is the minimum number of vertices in some color class under all vertex colorings by ? (F) colors. It is of interest to know which graphsF have the property that all trees areF-good. It is shown that any large tree isK(1, 1,m 1,m 2,...,m t )-good.
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