Caroline Accurso, Vitaliy Chernyshov, Leaha Hand, Sogol Jahanbekam, Paul Wenger
{"title":"Weak Dynamic Coloring of Planar Graphs","authors":"Caroline Accurso, Vitaliy Chernyshov, Leaha Hand, Sogol Jahanbekam, Paul Wenger","doi":"10.1007/s00373-023-02748-3","DOIUrl":null,"url":null,"abstract":"<p>The <i>k</i>-<i>weak-dynamic number</i> of a graph <i>G</i> is the smallest number of colors we need to color the vertices of <i>G</i> in such a way that each vertex <i>v</i> of degree <i>d</i>(<i>v</i>) sees at least min<span>\\(\\{k,d(v)\\}\\)</span> colors on its neighborhood. We use reducible configurations and list coloring of graphs to prove that all planar graphs have 3-weak-dynamic number at most 6.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00373-023-02748-3","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
The k-weak-dynamic number of a graph G is the smallest number of colors we need to color the vertices of G in such a way that each vertex v of degree d(v) sees at least min\(\{k,d(v)\}\) colors on its neighborhood. We use reducible configurations and list coloring of graphs to prove that all planar graphs have 3-weak-dynamic number at most 6.
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