{"title":"Hamilton cycles in vertex-transitive graphs of order $6p$","authors":"Shaofei Du, Tianlei Zhou","doi":"arxiv-2409.06138","DOIUrl":null,"url":null,"abstract":"It was shown that every connected vertex-transitive graph of order $6p$,\nwhere $p$ is a prime, contains a Hamilton path \\cite{KS09}. It will be shown in\nthis paper that every such graph contains a Hamilton cycle, except for the\ntriangle-replaced graph of the Petersen graph.","PeriodicalId":501407,"journal":{"name":"arXiv - MATH - Combinatorics","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06138","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
It was shown that every connected vertex-transitive graph of order $6p$,
where $p$ is a prime, contains a Hamilton path \cite{KS09}. It will be shown in
this paper that every such graph contains a Hamilton cycle, except for the
triangle-replaced graph of the Petersen graph.
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