Star-critical Gallai-Ramsey numbers involving the disjoint union of triangles

Abstract

In the Ramsey theory of graphs, star-critical Gallai-Ramsey numbers serve as a measure of the strength of their corresponding Gallai-Ramsey numbers. In this paper, we evaluate some classes of star-critical Gallai-Ramsey numbers when the arguments are the disjoint unions of K 3 -subgraphs. The methods used are constructive and in all cases considered, we find that the removal of a single edge destroys the Ramsey property.