Gallai–Ramsey numbers for multiple triangles

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

“…The construction that will serve as the basis for our new constructions is the one that gives the lower bound for gr t (K 3 ) when t is even. We follow the notation introduced in [19] and denote by (G, τ ) a Gallai t-colored complete graph, with t-coloring τ .…”

“…In the following theorem, we consider Gallai-Ramsey numbers involving K 3 -subgraphs and 2K 3 -subgraphs, when t ≥ 4 is assumed to be even. In order to simplify notations, we follow the approach used in [19] and define gr(s; t − s) := gr(2K 3 , 2K 3 , . .…”

“…Proof. It was proved in Corollary 1.5 of [19] that when t ≥ 3 is odd, the t-color Gallai-Ramsey number satisfies…”

“…In a recent article, Su and Liu [17] considered the analogous concept for Gallai-Ramsey numbers. We seek to evaluate several star-critical Gallai-Ramsey numbers for disjoint unions of K 3subgraphs, building off of some recent results by Zhang, Zhu, and Chen [19] involving the corresponding Gallai-Ramsey numbers.…”