Breaking small automorphisms by list colourings

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-09-16 DOI:10.1002/jgt.23181

Jakub Kwaśny, Marcin Stawiski

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引用次数: 0

Abstract

For a graph $G$ , we define a small automorphism as one that maps some vertex into its neighbour. We investigate the edge colourings of $G$ that break every small automorphism of $G$ . We show that such a colouring can be chosen from any set of lists of length 3. In addition, we show that any set of lists of length 2 on both edges and vertices of $G$ yields a total colouring which breaks all the small automorphisms of $G$ . These results are sharp, and they match the known bounds for the nonlist variant.

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通过列表着色打破小自变形

对于图，我们将小自变量定义为将某个顶点映射到其邻近顶点的自变量。我们研究了能打破 ......的所有小自形性的边着色，结果表明，这种着色可以从任意一组长度为 3 的列表中选择。此外，我们还证明，在 ......的边和顶点上任意一组长度为 2 的列表都能产生一种总着色，它能打破 ......的所有小自形性。这些结果非常尖锐，而且与非列表变体的已知界限相吻合。

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

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .