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| Paper IPM / M / 14926 |
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| Abstract: | |||||
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For given simple graphs G1, G2, …, Gt, the Ramsey
number R(G1, G2, …, Gt) is the smallest positive
integer n such that if the edges of the complete graph Kn are
partitioned into t disjoint color classes giving t graphs
H1,H2,…,Ht, then at least one Hi has a subgraph
isomorphic to Gi. In this paper, for positive integers t1,t2,…, ts and n1,n2,…, nc the Ramsey number R(St1, St2,…,Sts, n1K2,n2K2,…,ncK2) is computed exactly, where nK2 denotes a matching (stripe) of size n, i.e., n pairwise disjoint edges and Sn is a star with n edges. This result generalizes and strengthens significantly a well-known result of Cockayne and Lorimer and also a known result of Gyárfás and Sárközy.
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