{"title":"Monochromatic triangles in the max-norm plane","authors":"Alexander Natalchenko , Arsenii Sagdeev","doi":"10.1016/j.ejc.2024.103977","DOIUrl":null,"url":null,"abstract":"<div><p>For all non-degenerate triangles <span><math><mi>T</mi></math></span>, we determine the minimum number of colors needed to color the plane such that no max-norm isometric copy of <span><math><mi>T</mi></math></span> is monochromatic.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0195669824000623","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
For all non-degenerate triangles , we determine the minimum number of colors needed to color the plane such that no max-norm isometric copy of is monochromatic.
期刊介绍：
The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.
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