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

‎‎For given bipartite graphs G_۱‎, ‎G_۲,\ldots‎, ‎G_t, the bipartite Ramsey number bR(G_۱‎, ‎G_۲,\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_۱‎, ‎H_۲,\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_۱‎, ‎G_۲,\ldots‎, ‎G_t)‎, ‎in the case that G_۱‎, ‎G_۲,\ldots‎, ‎G_t being either stars and stripes or stars and a path‎.

کلیدواژه ها:

bipartite Ramsey number ، Path ، Star ، Stripe