{"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}
引用次数: 9
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.
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