{"title":"Forbidden Subgraphs for Existences of (Connected) 2-Factors of a Graph","authors":"Xiaojing Yang, Liming Xiong","doi":"10.7151/dmgt.2366","DOIUrl":null,"url":null,"abstract":"Abstract Clearly, having a 2-factor in a graph is a necessary condition for a graph to be hamiltonian, while having an even factor in graph is a necessary condition for a graph to have a 2-factor. In this paper, we completely characterize the forbidden subgraph and pairs of forbidden subgraphs that force a 2-connected graph admitting a 2-factor (a necessary condition) to be hamiltonian and a connected graph with an even factor (a necessary condition) to have a 2-factor, respectively. Our results show that these pairs of forbidden subgraphs become wider than those in Faudree, Gould and in Fujisawa, Saito, respectively, if we impose the two necessary conditions, respectively.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7151/dmgt.2366","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
Abstract Clearly, having a 2-factor in a graph is a necessary condition for a graph to be hamiltonian, while having an even factor in graph is a necessary condition for a graph to have a 2-factor. In this paper, we completely characterize the forbidden subgraph and pairs of forbidden subgraphs that force a 2-connected graph admitting a 2-factor (a necessary condition) to be hamiltonian and a connected graph with an even factor (a necessary condition) to have a 2-factor, respectively. Our results show that these pairs of forbidden subgraphs become wider than those in Faudree, Gould and in Fujisawa, Saito, respectively, if we impose the two necessary conditions, respectively.