{"title":"Borodin–Kostochka Conjecture Holds for Odd-Hole-Free Graphs","authors":"Rong Chen, Kaiyang Lan, Xinheng Lin, Yidong Zhou","doi":"10.1007/s00373-024-02753-0","DOIUrl":null,"url":null,"abstract":"<p>The Borodin–Kostochka Conjecture states that for a graph <i>G</i>, if <span>\\(\\Delta (G)\\ge 9\\)</span>, then <span>\\(\\chi (G)\\le \\max \\{\\Delta (G)-1,\\omega (G)\\}\\)</span>. In this paper, we prove the Borodin–Kostochka Conjecture holding for odd-hole-free graphs.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00373-024-02753-0","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
The Borodin–Kostochka Conjecture states that for a graph G, if \(\Delta (G)\ge 9\), then \(\chi (G)\le \max \{\Delta (G)-1,\omega (G)\}\). In this paper, we prove the Borodin–Kostochka Conjecture holding for odd-hole-free graphs.
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