随机比赛中的单色路径

Random Struct. Algorithms Pub Date : 2017-03-30 DOI:10.1002/rsa.20780

Matija Bucić, Shoham Letzter, B. Sudakov

{"title":"随机比赛中的单色路径","authors":"Matija Bucić, Shoham Letzter, B. Sudakov","doi":"10.1002/rsa.20780","DOIUrl":null,"url":null,"abstract":"We prove that, with high probability, any 2-edge-colouring of a random tournament on n vertices contains a monochromatic path of length Ω(n/ √ logn). This resolves a conjecture of Ben-Eliezer, Krivelevich and Sudakov and implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"55 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Monochromatic paths in random tournaments\",\"authors\":\"Matija Bucić, Shoham Letzter, B. Sudakov\",\"doi\":\"10.1002/rsa.20780\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that, with high probability, any 2-edge-colouring of a random tournament on n vertices contains a monochromatic path of length Ω(n/ √ logn). This resolves a conjecture of Ben-Eliezer, Krivelevich and Sudakov and implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.\",\"PeriodicalId\":303496,\"journal\":{\"name\":\"Random Struct. Algorithms\",\"volume\":\"55 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-03-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Random Struct. Algorithms\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/rsa.20780\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Struct. Algorithms","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/rsa.20780","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 9

摘要

我们证明，在高概率下，n个顶点的任意2边着色随机锦标赛包含长度为Ω(n/√logn)的单色路径。这解决了Ben-Eliezer, Krivelevich和Sudakov的一个猜想，并暗示了有向路径的有向大小Ramsey数的近紧上界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Monochromatic paths in random tournaments

We prove that, with high probability, any 2-edge-colouring of a random tournament on n vertices contains a monochromatic path of length Ω(n/ √ logn). This resolves a conjecture of Ben-Eliezer, Krivelevich and Sudakov and implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Random Struct. Algorithms

自引率

0.00%

发文量

期刊最新文献

Monochromatic paths in random tournaments On Generalized Independent Subsets of Trees Inequalities in Probability Theory and Turán-Type Problems for Graphs with Colored Vertices On the effect of selection in genetic algorithms The Boyer-Moore-Horspool heuristic with Markovian input