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Paper IPM / M / 14926  


Abstract:  
For given simple graphs G_{1}, G_{2}, …, G_{t}, the Ramsey
number R(G_{1}, G_{2}, …, G_{t}) is the smallest positive
integer n such that if the edges of the complete graph K_{n} are
partitioned into t disjoint color classes giving t graphs
H_{1},H_{2},…,H_{t}, then at least one H_{i} has a subgraph
isomorphic to G_{i}. In this paper, for positive integers t_{1},t_{2},…, t_{s} and n_{1},n_{2},…, n_{c} the Ramsey number R(S_{t1}, S_{t2},…,S_{ts}, n_{1}K_{2},n_{2}K_{2},…,n_{c}K_{2}) is computed exactly, where nK_{2} denotes a matching (stripe) of size n, i.e., n pairwise disjoint edges and S_{n} is a star with n edges. This result generalizes and strengthens significantly a wellknown result of Cockayne and Lorimer and also a known result of Gyárfás and Sárközy.
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