THE RAMSEY NUMBERS OF LARGE TREES VERSUS WHEELS

For two given graphs G(1) and G(2), the Ramsey number R(G(1), G(2)) is the smallest integer n such that for any graph G of order n, either G contains G(1) or the complement of G contains G(2). Let T-n denote a tree of order n and W-m a wheel of order m + 1. To the best of our knowledge, only R(T-n, W-m) with small wheels are known. In this paper, we show that R(T-m, W-m) = 3n - 2 for odd m with n > 756m(10).