An upper bound for the ramsey number of a cycle of length four versus wheels

Abstract

For given graphs G and H, the Ramsey number R(G,H) is the smallest positive integer n such that every graph F of n vertices satisfies the following property: either F contains G or the complement of F contains H. In this paper, we show that the Ramsey number R(C4, Wm) ≤ m + [m/3] + 1 for m ≥ 6. © Springer-Verlag Berlin Heidelberg 2005.