Counting Gallai 3-colorings of complete graphs
Abstract
An edge coloring of the n-vertex complete graph Kn is a Gallai coloring if it does not contain any rainbow triangle, that is, a triangle whose edges are colored with three distinct colors. We prove that the number of Gallai colorings of Kn with at most three colors is at most 7(n+1)*2n choose 2, which improves the best known upper bound of 32 * (n-1)! * 2(n-1) choose 2 in [Discrete Mathematics, 2017].
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