The Ramsey number for a linear forest versus two identical copies of complete graphs

Abstract

Let H be a graph with the chromatic number h and the chromatic surplus s. A connected graph G of order n is called H-good if R(G,H)=(n-1)(h-1)+s. We show that P n is 2K m -good for n > 3. Furthermore, we obtain the Ramsey number R(L,2K m ), where L is a linear forest. In addition, we also give the Ramsey number R(L,H m ) which is an extension for R(kP n ,H m ) proposed by Ali et al. [1], where H m is a cocktail party graph on 2m vertices. © 2010 Springer-Verlag Berlin Heidelberg.