{"title":"On a Question of Erdős and Nešetřil About Minimal Cuts in a Graph","authors":"Domagoj Bradač","doi":"10.1002/jgt.23207","DOIUrl":null,"url":null,"abstract":"<p>Answering a question of Erdős and Nešetřil, we show that the maximum number of inclusion-wise minimal vertex cuts in a graph on <span></span><math>\n <semantics>\n <mrow>\n <mi>n</mi>\n </mrow>\n <annotation> $n$</annotation>\n </semantics></math> vertices is at most <span></span><math>\n <semantics>\n <mrow>\n <mn>1.889</mn>\n \n <msup>\n <mn>9</mn>\n \n <mi>n</mi>\n </msup>\n </mrow>\n <annotation> $1.889{9}^{n}$</annotation>\n </semantics></math> for large enough <span></span><math>\n <semantics>\n <mrow>\n <mi>n</mi>\n </mrow>\n <annotation> $n$</annotation>\n </semantics></math>.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 4","pages":"817-818"},"PeriodicalIF":0.9000,"publicationDate":"2024-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23207","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Graph Theory","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jgt.23207","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Answering a question of Erdős and Nešetřil, we show that the maximum number of inclusion-wise minimal vertex cuts in a graph on vertices is at most for large enough .
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 .
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