Note on down-set thresholds

Lutz Warnke
{"title":"Note on down-set thresholds","authors":"Lutz Warnke","doi":"10.1002/rsa.21194","DOIUrl":null,"url":null,"abstract":"Gunby–He–Narayanan showed that the logarithmic gap predictions of Kahn–Kalai and Talagrand (proved by Park–Pham and Frankston–Kahn–Narayanan–Park) about thresholds of up‐sets do not apply to down‐sets. In particular, for the down‐set of triangle‐free graphs, they showed that there is a polynomial gap between the threshold and the factional expectation threshold. In this short note we give a simpler proof of this result, and extend the polynomial threshold gap to down‐sets of ‐free graphs.","PeriodicalId":20948,"journal":{"name":"Random Structures and Algorithms","volume":"2 6","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Structures and Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/rsa.21194","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

Gunby–He–Narayanan showed that the logarithmic gap predictions of Kahn–Kalai and Talagrand (proved by Park–Pham and Frankston–Kahn–Narayanan–Park) about thresholds of up‐sets do not apply to down‐sets. In particular, for the down‐set of triangle‐free graphs, they showed that there is a polynomial gap between the threshold and the factional expectation threshold. In this short note we give a simpler proof of this result, and extend the polynomial threshold gap to down‐sets of ‐free graphs.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
注意下限阈值
Gunby-He-Narayanan表明,Kahn-Kalai和Talagrand(由Park-Pham和Frankston-Kahn-Narayanan-Park证明)关于上升阈值的对数间隙预测不适用于下降阈值。特别地,对于无三角图的下集,他们证明了阈值与分式期望阈值之间存在多项式间隙。在这篇简短的笔记中,我们给出了这个结果的一个更简单的证明,并将多项式阈值间隙扩展到F $$ F $$自由图的下集。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
The square of a Hamilton cycle in randomly perturbed graphs Transference for loose Hamilton cycles in random 3-uniform hypergraphs The hitting time of clique factors Weight distribution of random linear codes and Krawtchouk polynomials A polynomial-time approximation scheme for the maximal overlap of two independent Erdős–Rényi graphs
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1