{"title":"论拉姆齐-图兰理论中的汉密尔顿循环幂","authors":"Ming Chen, Jie Han, Yantao Tang, Donglei Yang","doi":"10.1137/24m163709x","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2489-2508, September 2024. <br/> Abstract. We prove that for [math] with [math] and [math], there exist [math] and [math] such that for every [math], every [math]-vertex graph [math] with [math] and [math] contains an [math]th power of a Hamilton cycle. We also show that the minimum degree condition is asymptotically sharp for [math] and the [math] case was recently conjectured by Staden and Treglown.","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Powers of Hamilton Cycles in Ramsey–Turán Theory\",\"authors\":\"Ming Chen, Jie Han, Yantao Tang, Donglei Yang\",\"doi\":\"10.1137/24m163709x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2489-2508, September 2024. <br/> Abstract. We prove that for [math] with [math] and [math], there exist [math] and [math] such that for every [math], every [math]-vertex graph [math] with [math] and [math] contains an [math]th power of a Hamilton cycle. We also show that the minimum degree condition is asymptotically sharp for [math] and the [math] case was recently conjectured by Staden and Treglown.\",\"PeriodicalId\":49530,\"journal\":{\"name\":\"SIAM Journal on Discrete Mathematics\",\"volume\":\"13 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/24m163709x\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/24m163709x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On Powers of Hamilton Cycles in Ramsey–Turán Theory
SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2489-2508, September 2024. Abstract. We prove that for [math] with [math] and [math], there exist [math] and [math] such that for every [math], every [math]-vertex graph [math] with [math] and [math] contains an [math]th power of a Hamilton cycle. We also show that the minimum degree condition is asymptotically sharp for [math] and the [math] case was recently conjectured by Staden and Treglown.
期刊介绍:
SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution.
Topics include but are not limited to:
properties of and extremal problems for discrete structures
combinatorial optimization, including approximation algorithms
algebraic and enumerative combinatorics
coding and information theory
additive, analytic combinatorics and number theory
combinatorial matrix theory and spectral graph theory
design and analysis of algorithms for discrete structures
discrete problems in computational complexity
discrete and computational geometry
discrete methods in computational biology, and bioinformatics
probabilistic methods and randomized algorithms.