Gallai—Ramsey Number for the Union of Stars

Given a graph G and a positive integer k , define the Gallai—Ramsey number to be the minimum number of vertices n such that any k -edge coloring of K n contains either a rainbow (all different colored) triangle or a monochromatic copy of G . In this paper, we obtain exact values of the Gallai—Ramsey numbers for the union of two stars in many cases and bounds in other cases. This work represents the first class of disconnected graphs to be considered as the desired monochromatic subgraph.