Gallai-Ramsey Multiplicity for Rainbow Small Trees.

Let G, H be two non-empty graphs and k be a positive integer. The Gallai-Ramsey number gr k (G : H) is defined as the minimum positive integer N such that for all n ≥ N , every k-edge-coloring of K n contains either a rainbow subgraph G or a monochromatic subgraph H. The Gallai-Ramsey multiplicity GM k (G : H) is defined as the minimum total number of rainbow subgraphs G and monochromatic subgraphs H for all k-edge-colored K gr k (G : H) . In this paper, we get some exact values of the Gallai-Ramsey multiplicity for rainbow small trees versus general monochromatic graphs under a sufficiently large number of colors. We also study the bipartite Gallai-Ramsey multiplicity. [ABSTRACT FROM AUTHOR]