{"title":"Every Graph Embedded on the Surface with Euler Characteristic Number ε = −1 is Acyclically 11-choosable","authors":"Lin Sun, Guang Long Yu, Xin Li","doi":"10.1007/s10114-023-1518-y","DOIUrl":null,"url":null,"abstract":"<div><p>A proper vertex coloring of a graph <i>G</i> is acyclic if there is no bicolored cycles in <i>G</i>. A graph <i>G</i> is <i>acyclically k-choosable</i> if for any list assignment <i>L</i> = {<i>L</i>(<i>v</i>): <i>v</i> ∈ <i>V</i>(<i>G</i>)} with ∣<i>L</i>(<i>v</i>)∣ ≥ <i>k</i> for each vertex <i>v</i> ∈ <i>V</i>(<i>G</i>), there exists an acyclic proper vertex coloring <i>ϕ</i> of <i>G</i> such that <i>ϕ</i>(<i>v</i>) ∈ <i>L</i>(<i>v</i>) for each vertex <i>v</i> ∈ <i>V</i>(<i>G</i>). In this paper, we prove that every graph <i>G</i> embedded on the surface with Euler characteristic number <i>ε</i> = −1 is acyclically 11-choosable.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-023-1518-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
A proper vertex coloring of a graph G is acyclic if there is no bicolored cycles in G. A graph G is acyclically k-choosable if for any list assignment L = {L(v): v ∈ V(G)} with ∣L(v)∣ ≥ k for each vertex v ∈ V(G), there exists an acyclic proper vertex coloring ϕ of G such that ϕ(v) ∈ L(v) for each vertex v ∈ V(G). In this paper, we prove that every graph G embedded on the surface with Euler characteristic number ε = −1 is acyclically 11-choosable.
期刊介绍:
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.