Abstract
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.
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