{"title":"Breaking small automorphisms by list colourings","authors":"Jakub Kwaśny, Marcin Stawiski","doi":"10.1002/jgt.23181","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/jgt.23181","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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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