The Ramsey Numbers of Fans Versus K 4

Abstract

For two given graphs G and H, the Ramsey number R( G, H) is the smallest positive integer N such that for every graph F of order N the following holds- either F contains G as a subgraph or the complement of F contains H as a subgraph. In this paper, we determine the Ramsey number R(F1, K4), where Fl is the graph obtained from l disjoint triangles by identifying precisely one vertex of every triangle (Fl is the join of K1 and lK2) .