The multicolor star-critical Gallai-Ramsey number for a path of order 5

Abstract

In this paper, the t -color star-critical Gallai-Ramsey number for a path of order 5 is determined. It is proved that t +1 edges are both necessary and sufficient to add between a vertex and a critical coloring for the t -color Gallai-Ramsey number for P 5 in order to guarantee the existence of a monochromatic subgraph isomorphic to P 5 . The proof depends on a well-known structural result for Gallai colorings as well as a general lower bound due to Faudree, Gould, Jacobson, and Magnant.