Counting Gallai 3-colorings of complete graphs

被引：3

作者：

Bastos, Josefran de Oliveira ^{[1
]}

Benevides, Fabricio Siqueira ^{[2
]}

Mota, Guilherme Oliveira ^{[3
]}

Sau, Ignasi ^{[4
]}

机构：

[1] Univ Fed Ceara, Engn Comp, Fortaleza, Ceara, Brazil

[2] Univ Fed Ceara, Dept Matemat, Fortaleza, Ceara, Brazil

[3] Univ Fed ABC, Ctr Matemat Comp & Cognicao, Santo Andre, Brazil

[4] Univ Montpellier, CNRS, LIRMM, Montpellier, France

来源：

DISCRETE MATHEMATICS | 2019年 / 342卷 / 09期

基金：

巴西圣保罗研究基金会;

关键词：

Gallai colorings; Rainbow triangles; Complete graphs; Counting; EDGE-COLORINGS; NUMBER; SETS;

D O I：

10.1016/j.disc.2019.05.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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((n2)), which improves the best known upper bound of 3/2(n - 1)! . 2((n-12)) in Benevides et al. (2017). (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：2618 / 2631

页数：14

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