{"title":"On the Edge-Erdős–Pósa Property of Ladders","authors":"Raphael Steck, Arthur Ulmer","doi":"10.1007/s00373-024-02765-w","DOIUrl":null,"url":null,"abstract":"<p>We prove that the ladder with 3 rungs and the house graph have the edge-Erdős–Pósa property, while ladders with 14 rungs or more have not. Additionally, we prove that the latter bound is optimal in the sense that the only known counterexample graph does not permit a better result.</p>","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":"98 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Graphs and Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00373-024-02765-w","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that the ladder with 3 rungs and the house graph have the edge-Erdős–Pósa property, while ladders with 14 rungs or more have not. Additionally, we prove that the latter bound is optimal in the sense that the only known counterexample graph does not permit a better result.
期刊介绍：
Graphs and Combinatorics is an international journal devoted to research concerning all aspects of combinatorial mathematics. In addition to original research papers, the journal also features survey articles from authors invited by the editorial board.
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