On Ramsey (C4, K1, n)-minimal graphs

Abstract

Let F , G and H be any simple graphs. The notation F → ( G , H ) means for any red-blue coloring on the edges of graph F , there exists either a red copy of G or a blue copy of H . If F → ( G , H ) , then graph F is called a Ramsey graph for ( G , H ) . Additionally, if the graph F satisfies that F − e ↛ ( G , H ) for any edge e of F , then graph F is called a Ramsey ( G , H ) -minimal. The set of all Ramsey ( G , H ) -minimal graphs is denoted by ℛ( G , H ) . In this paper, we construct a new class of Ramsey ( C 4 , K 1, n ) -minimal graphs.