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

Abstract

‎For given bipartite graphs G 1 ‎,‎G 2 ,…‎,‎G t , the bipartite Ramsey number bR(G 1 ‎,‎G 2 ,…‎,‎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 ,…‎,‎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 ,…‎,‎G t ) ‎, ‎in the case that G 1 ‎,‎G 2 ,…‎,‎G t being either stars and stripes or stars and a path‎.

Keywords

• Bipartite Ramsey Number
• Path
• Star
• Stripe