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The Ramsey number R(G1,G2) is the smallest integer p such that for any graph G on p vertices either G contains G1 or G¯ contains G2, where G¯ denotes the complement of G. In this paper, some new bounds with two parameters for the Ramsey number R(G1,G2), under some assumptions, are obtained. Especially, we prove that R(K6−e,K6)≤116 and R(K6−e,K7)≤202, these improve the two upper bounds for the classical...
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