{"title":"最大度图$k+1的$k$-转换数的一个下界$","authors":"C. Mynhardt, Jane L. Wodlinger","doi":"10.22108/TOC.2019.112258.1579","DOIUrl":null,"url":null,"abstract":"We derive a new sharp lower bound on the $k$-conversion number of graphs of maximum degree $k+1$. This generalizes a result of W.~Staton [Induced forests in cubic graphs, Discrete Math.,49 (1984) 175--178], which established a lower bound on the $k$-conversion number of $(k+1)$-regular graphs.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":" ","pages":"1-12"},"PeriodicalIF":0.6000,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A lower bound on the $k$-conversion number of graphs of maximum degree $k+1$\",\"authors\":\"C. Mynhardt, Jane L. Wodlinger\",\"doi\":\"10.22108/TOC.2019.112258.1579\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We derive a new sharp lower bound on the $k$-conversion number of graphs of maximum degree $k+1$. This generalizes a result of W.~Staton [Induced forests in cubic graphs, Discrete Math.,49 (1984) 175--178], which established a lower bound on the $k$-conversion number of $(k+1)$-regular graphs.\",\"PeriodicalId\":43837,\"journal\":{\"name\":\"Transactions on Combinatorics\",\"volume\":\" \",\"pages\":\"1-12\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2019-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions on Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22108/TOC.2019.112258.1579\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/TOC.2019.112258.1579","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
A lower bound on the $k$-conversion number of graphs of maximum degree $k+1$
We derive a new sharp lower bound on the $k$-conversion number of graphs of maximum degree $k+1$. This generalizes a result of W.~Staton [Induced forests in cubic graphs, Discrete Math.,49 (1984) 175--178], which established a lower bound on the $k$-conversion number of $(k+1)$-regular graphs.
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