Balanced Edge-Colorings Avoiding Rainbow Cliques of Size Four

IF 0.7 4区数学 Q2 MATHEMATICS

Electronic Journal of Combinatorics Pub Date : 2023-08-11 DOI:10.37236/11965

F. Clemen, Adam Zsolt Wagner

引用次数: 0

Abstract

A balanced edge-coloring of the complete graph is an edge-coloring such that every vertex is incident to each color the same number of times. In this short note, we present a construction of a balanced edge-coloring with six colors of the complete graph on $n=13^k$ vertices, for every positive integer $k$, with no rainbow $K_4$. This solves a problem by Erdős and Tuza.

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平衡边缘颜色，避免4号彩虹团

完全图的平衡边着色是这样一种边着色，即每个顶点与每种颜色的关联次数相同。在这篇简短的文章中，我们给出了在$n=13^k$顶点上，对于每一个正整数$k$，没有彩虹$K_4$的完全图的六种颜色的平衡边着色的构造。这解决了Erdős和Tuza的一个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Journal of Combinatorics 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

212

审稿时长

3-6 weeks

期刊介绍： The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems.