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Paper   IPM / M / 14926
School of Mathematics
  Title:   Stars versus stripes Ramsey numbers
1.  Gholam Reza Omidi
2.  Ghaffar Raeisi (Joint with Z. Rahimi)
  Status:   Published
  Journal: European J. Combin.
  Vol.:  67
  Year:  2018
  Pages:   268-274
  Supported by:  IPM
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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