{"title":"The Rupture Degree of Graphs with k-Tree","authors":"Yinkui Li, Qingning Wang, Xiaolin Wang","doi":"10.4236/OJDM.2016.62011","DOIUrl":null,"url":null,"abstract":"A k-tree of a connected graph G is a spanning tree with maximum degree \nat most k. The rupture degree for a \nconnected graph G is defined by , where and , \nrespectively, denote the order of the largest component and number of \ncomponents in . In this \npaper, we show that for a connected graph G, \nif for any cut-set , then G has a k-tree.","PeriodicalId":61712,"journal":{"name":"离散数学期刊(英文)","volume":"06 1","pages":"105-107"},"PeriodicalIF":0.0000,"publicationDate":"2016-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"离散数学期刊(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/OJDM.2016.62011","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
A k-tree of a connected graph G is a spanning tree with maximum degree
at most k. The rupture degree for a
connected graph G is defined by , where and ,
respectively, denote the order of the largest component and number of
components in . In this
paper, we show that for a connected graph G,
if for any cut-set , then G has a k-tree.
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