Abstract

Let F, G1 and G2 be simple graphs. Denote by F → (G1, G2) each edge coloring of F by red and blue that contains a red G1 or a blue G2. Define the star-critical Ramsey number RS(G1,G2) to be the largest p such that Kr∖K1,p → (G1, G2), where r=R(G1,G2) is the Ramsey number. By Stability Lemma and Regularity Lemma, we determine RS(C2t+1,K1+nG) and RS(C2t+1,Ks+nK1) for large n.

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