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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