Star-path and star-stripe bipartite Ramsey numbers in multicoloring

Document Type : Research Paper

Author

Department of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran

Abstract

‎‎For given bipartite graphs $G_1‎, ‎G_2,\ldots‎, ‎G_t,$ the bipartite Ramsey number $bR(G_1‎, ‎G_2,\ldots‎, ‎G_t)$ is the‎ ‎smallest integer $n$ such that if the edges of the complete bipartite graph $K_{n,n}$ are partitioned into $t$ disjoint color classes giving $t$ graphs $H_1‎, ‎H_2,\ldots‎, ‎H_t$‎, ‎then at least one $H_i$ has a subgraph isomorphic to $G_i$‎. ‎In this paper‎, ‎we study the multicolor bipartite Ramsey number $bR(G_1‎, ‎G_2,\ldots‎, ‎G_t)$‎, ‎in the case that $G_1‎, ‎G_2,\ldots‎, ‎G_t$ being either stars and stripes or stars and a path‎.

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References

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Transactions on Combinatorics
Volume 4, Issue 3 - Serial Number 3
September 2015
Pages 37-42

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History

  • Receive Date: 01 June 2014
  • Revise Date: 27 October 2014
  • Accept Date: 10 November 2014
  • Published Online: 01 September 2015

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