On the restricted size Ramsey number for P3 versus dense connected graphs

Abstract

Let F , G and H be simple graphs. A graph F is said a ( G,H )-arrowing graph if in any red-blue coloring of edges of F we can find a red G or a blue H . The size Ramsey number of G and H , ŕ ( G , H ), is the minimum size of F . If the order of F equals to the Ramsey number of G and H , r ( G,H ), then the minimum size of F is called the restricted size Ramsey number of G and H , r * ( G,H ). The Ramsey number of G and H , r ( G,H ), is the minimum order of F . In this paper, we study the restricted size number involving a P 3 . The value of r * ( P 3 , K n ) has been given by Faudree and Sheehan. Here, we examine r * ( P 3 , H ) where H is dense connected graph.