GALLAI-RAMSEY NUMBERS FOR RAINBOW TREES AND MONOCHROMATIC COMPLETE BIPARTITE GRAPHS

Given two non-empty graphs G, H and a positive integer k , the GallaiRamsey number gr(k)(G k ( G : H ) is defined as the minimum positive integer N such that for all n > N , every k-edge-colored K- n contains either a rainbow subgraph G or a monochromatic subgraph H . In this paper, we get some exact values or bounds of gr(k)(K-1,K-3 : H ), gr(k)(P-5 : H ), and gr(k) ( P- 4 (+) : H ) for k >= 3, where H is a complete bipartite graph.