THE RAMSEY NUMBER FOR A LINEAR FOREST VERSUS TWO IDENTICAL COPIES OF COMPLETEGRAPHS

摘要

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) = 1)(h— 1)+s. In this paper, we show that P,, is 2Km-good for n > 3. Furthermore, we obtain the Ramsey number R(L, 21(m), where L is a linear forest. Moreover, we also give the Ramsey number R(L, Hm.) which is an extension for R(kP_n,H_m) proposed by Ali et at. [l], whereH_m is a cocktail party graph on 2m vertices.