通过列表着色打破小自变形

Pub Date : 2024-09-17 DOI:10.1002/jgt.23181

Jakub Kwaśny, Marcin Stawiski

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引用次数: 0

摘要

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。

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Breaking small automorphisms by list colourings

For a graph , we define a small automorphism as one that maps some vertex into its neighbour. We investigate the edge colourings of that break every small automorphism of . 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 yields a total colouring which breaks all the small automorphisms of . These results are sharp, and they match the known bounds for the nonlist variant.

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