{"title":"Anti-van der Waerden Numbers of Some 2-Connected Outerplanar Graphs","authors":"Xin Feng, Xingchao Deng, Junqing Cai","doi":"10.1142/s0219265924500051","DOIUrl":null,"url":null,"abstract":"Given a graph [Formula: see text] and a positive integer [Formula: see text], the anti-van der Waerden number [Formula: see text] is defined as the minimum positive integer [Formula: see text] such that every exact [Formula: see text]-coloring of the vertices of [Formula: see text] admits a rainbow [Formula: see text]-AP. In this paper, we determine the exact value of [Formula: see text] if [Formula: see text] is a [Formula: see text]-connected outerplanar graph with diameters [Formula: see text].","PeriodicalId":0,"journal":{"name":"","volume":"31 122","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219265924500051","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
Given a graph [Formula: see text] and a positive integer [Formula: see text], the anti-van der Waerden number [Formula: see text] is defined as the minimum positive integer [Formula: see text] such that every exact [Formula: see text]-coloring of the vertices of [Formula: see text] admits a rainbow [Formula: see text]-AP. In this paper, we determine the exact value of [Formula: see text] if [Formula: see text] is a [Formula: see text]-connected outerplanar graph with diameters [Formula: see text].
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