{"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":null,"pages":null},"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}
引用次数: 0
Abstract
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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