FAN-COMPLETE GRAPH RAMSEY NUMBERS

It is shown that if G and H are arbitrary fixed graphs and n is suffic iently large, then r(K-2 + G, K-1 + nH) = (k + 1)mn + 1, where k = chi (G) and m = \V(H)\. Also, we prove that r(K-1 + F, K-n) less than or e qual to (m + o(1)) n(2)/log n (n --> infinity) for any forest F whose largest component has m edges. Thus r(Fe, K-n) less than or equal to ( 1 + o(1))) n(2)/log n,, where Fe = K-1 + lK(2). We conjecture that r(F e, K-n) similar to n(2)/log n (n --> infinity). (C) 1996 John Wiley & Sons, Inc.