{"title":"奇数循环的广义安拉斯费--厄尔多斯--索斯定理","authors":"Zian Chen, Jianfeng Hou, Caiyun Hu, Xizhi Liu","doi":"arxiv-2409.11950","DOIUrl":null,"url":null,"abstract":"In this note, we establish Andr\\'{a}sfai--Erd\\H{o}s--S\\'{o}s-type stability\ntheorems for two generalized Tur\\'{a}n problems involving odd cycles, both of\nwhich are extensions of the Erd\\H{o}s Pentagon Problem. Our results strengthen\nprevious results by Lidick\\'{y}--Murphy~\\cite{LM21} and\nBeke--Janzer~\\cite{BJ24}, while also simplifying parts of their proofs.","PeriodicalId":501407,"journal":{"name":"arXiv - MATH - Combinatorics","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized Andrásfai--Erdős--Sós theorems for odd cycles\",\"authors\":\"Zian Chen, Jianfeng Hou, Caiyun Hu, Xizhi Liu\",\"doi\":\"arxiv-2409.11950\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note, we establish Andr\\\\'{a}sfai--Erd\\\\H{o}s--S\\\\'{o}s-type stability\\ntheorems for two generalized Tur\\\\'{a}n problems involving odd cycles, both of\\nwhich are extensions of the Erd\\\\H{o}s Pentagon Problem. Our results strengthen\\nprevious results by Lidick\\\\'{y}--Murphy~\\\\cite{LM21} and\\nBeke--Janzer~\\\\cite{BJ24}, while also simplifying parts of their proofs.\",\"PeriodicalId\":501407,\"journal\":{\"name\":\"arXiv - MATH - Combinatorics\",\"volume\":\"31 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11950\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11950","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Generalized Andrásfai--Erdős--Sós theorems for odd cycles
In this note, we establish Andr\'{a}sfai--Erd\H{o}s--S\'{o}s-type stability
theorems for two generalized Tur\'{a}n problems involving odd cycles, both of
which are extensions of the Erd\H{o}s Pentagon Problem. Our results strengthen
previous results by Lidick\'{y}--Murphy~\cite{LM21} and
Beke--Janzer~\cite{BJ24}, while also simplifying parts of their proofs.
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