Bipartite rainbow ramsey numbers and multiplicity problems in ramsey theory

Abstract

This thesis primarily deals with Bipartite Rainbow Ramsey numbers and multiplicity problems in Ramsey theory Given any two simple bipartite graphs G1 and G2 the Bipartite Rainbow Ramsey number BRRG1G2 is defined to be the smallest positive integer N such that any coloring of the edges of KNN with any number of colors contains a monochromatic copy of G1 or a rainbow copy of G2 It was introduced by Linda Eroh and Ortrud R Oellermann in the year 2004 They proved that BRRG1G2 exists if and only if G1 is a star or G2 is a star forest and they have determined Bipartite Rainbow Ramsey numbers for a few classes of graphs In Chapter 2 we have discussed the Bipartite Rainbow Ramsey number of two graphs G1 and G2 where G1 and G2 belong to the family of stars bistars and matchings In Chapter 3 we have discussed the Bipartite Rainbow Ramsey number of two graphs G1 and G2 where G1 and G2 belong to the family of stars union of two stars and matchings newline