On Ramsey (3K2,K3)−minimal graphs

Abstract

The Ramsey graph theory has many interesting applications, such as in the fields of communications, information retrieval, and decision making. One of growing topics in Ramsey theory is Ramsey minimal graph. For any given graphs G and H, find graphs F such that any red-blue coloring of all edges of F contains either a red copy of G or a blue copy of H. If this condition is not satisfied by the graph F −e, then we call the graph F as a Ramsey (G,H)−minimal. In this paper, we derive the properties of (3K2,K3)−minimal graphs. We, then, characterize all Ramsey (3K2,K3)−minimal graphs