{"title":"无奇数孔图的鲍罗丁-科斯托奇卡猜想成立","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":"{\"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}","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}
Borodin–Kostochka Conjecture Holds for Odd-Hole-Free Graphs
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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