Gallai-Ramsey numbers for fans

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 edge-coloring of Kn using at most k colors contains either a rainbow (all different colored) triangle or a monochromatic copy of G. In this paper, we obtain general upper and lower bounds on the Gallai-Ramsey numbers for fans Fm = K1 + mK2 and prove the sharp result for m = 2 and for m = 3 with k even.(c) 2023 Elsevier B.V. All rights reserved.