{"title":"孤立韧性小于 1 的图形中的分数因子和分量因子","authors":"Isaak H. Wolf","doi":"10.1002/jgt.23179","DOIUrl":null,"url":null,"abstract":"Let be a simple graph and let be two integers with . We prove that for every if and only if has a ‐factor, where denotes the number of isolated vertices of and is a special family of trees. Furthermore, we characterize the trees in in terms of their bipartition.","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fractional factors and component factors in graphs with isolated toughness smaller than 1\",\"authors\":\"Isaak H. Wolf\",\"doi\":\"10.1002/jgt.23179\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let be a simple graph and let be two integers with . We prove that for every if and only if has a ‐factor, where denotes the number of isolated vertices of and is a special family of trees. Furthermore, we characterize the trees in in terms of their bipartition.\",\"PeriodicalId\":16014,\"journal\":{\"name\":\"Journal of Graph Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Graph Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1002/jgt.23179\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Graph Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/jgt.23179","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Fractional factors and component factors in graphs with isolated toughness smaller than 1
Let be a simple graph and let be two integers with . We prove that for every if and only if has a ‐factor, where denotes the number of isolated vertices of and is a special family of trees. Furthermore, we characterize the trees in in terms of their bipartition.
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 .