{"title":"Counterexamples to Hedetniemi's conjecture and infinite Boolean lattices","authors":"Claude Tardif","doi":"10.14712/1213-7243.2023.003","DOIUrl":null,"url":null,"abstract":"We prove that for any c ≥ 5, there exists an infinite family (Gn)n∈N of graphs such that χ(Gn) > c for all n ∈ N and χ(Gm×Gn) ≤ c for all m 6= n. These counterexamples to Hedetniemi’s conjecture show that the Boolean lattices of exponential graphs with Kc as a base are infinite for c ≥ 5.","PeriodicalId":44396,"journal":{"name":"Commentationes Mathematicae Universitatis Carolinae","volume":" ","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Commentationes Mathematicae Universitatis Carolinae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14712/1213-7243.2023.003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
We prove that for any c ≥ 5, there exists an infinite family (Gn)n∈N of graphs such that χ(Gn) > c for all n ∈ N and χ(Gm×Gn) ≤ c for all m 6= n. These counterexamples to Hedetniemi’s conjecture show that the Boolean lattices of exponential graphs with Kc as a base are infinite for c ≥ 5.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
