Counting Gallai 3-colorings of complete graphs
Combinatorics
2018-05-18 v1
Abstract
An edge coloring of the n-vertex complete graph K_n 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 K_n with at most three colors is at most 7(n+1)*2^{n choose 2}, which improves the best known upper bound of \frac{3}{2} * (n-1)! * 2^{(n-1) choose 2} in [Discrete Mathematics, 2017].
Cite
@article{arxiv.1805.06805,
title = {Counting Gallai 3-colorings of complete graphs},
author = {Josefran de Oliveira Bastos and Fabricio Siqueira Benevides and Guilherme Oliveira Mota and Ignasi Sau},
journal= {arXiv preprint arXiv:1805.06805},
year = {2018}
}
Comments
17 pages, 9 pages of appendix, 7 figures