Remarks on an Edge-coloring Problem

Q3 Computer Science

Electronic Notes in Theoretical Computer Science Pub Date : 2019-08-30 DOI:10.1016/j.entcs.2019.08.045

Carlos Hoppen , Hanno Lefmann

引用次数: 6

Abstract

We consider a multicolored version of a problem that was originally proposed by Erdős and Rothschild. For positive integers n and r, we look for n-vertex graphs that admit the maximum number of r-edge-colorings with no copy of a triangle where exactly two colors appear. It turns out that for 2 ≤ r ≤ 12 colors and n sufficiently large, the complete bipartite graph on n vertices with balanced bipartition (the n-vertex Turán graph for the triangle) yields the largest number of such colorings, and this graph is unique with this property.

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一个边着色问题的注释

我们考虑一个由Erdős和Rothschild最初提出的问题的多色版本。对于正整数n和r，我们寻找n顶点图，它允许最大数量的r边着色，而不复制恰好出现两种颜色的三角形。结果表明，当2≤r≤12种颜色且n足够大时，n顶点平衡双分的完全二部图(三角形的n顶点Turán图)产生的这种着色数量最多，并且该图具有该性质是唯一的。

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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Electronic Notes in Theoretical Computer Science Computer Science-Computer Science (all)

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