Cristina López-Ramírez, Jorge Eduardo Gutiérrez Gómez, Guillermo De Ita Luna
{"title":"Building a Maximal Independent Set for the Vertex-coloring Problem on Planar Graphs","authors":"Cristina López-Ramírez, Jorge Eduardo Gutiérrez Gómez, Guillermo De Ita Luna","doi":"10.1016/j.entcs.2020.10.007","DOIUrl":null,"url":null,"abstract":"<div><p>We analyze the vertex-coloring problem restricted to planar graphs and propose to consider classic wheels and polyhedral wheels as basic patterns for the planar graphs. We analyze the colorability of the composition among wheels and introduce a novel algorithm based on three rules for the vertex-coloring problem. These rules are: 1) Selecting vertices in the frontier. 2) Processing subsumed wheels. 3) Processing centers of the remaining wheels. Our method forms a maximal independent set <em>S</em><sub>1</sub> ⊂ <em>V</em> (<em>G</em>) consisting of wheel's centers, and a maximum number of vertices in the frontier of the planar graph. Thus, we show that if the resulting graph <em>G</em>′ = (<em>G − S</em><sub>1</sub>) is 3-colorable, then this implies the existence of a valid 4-coloring for <em>G</em>.</p></div>","PeriodicalId":38770,"journal":{"name":"Electronic Notes in Theoretical Computer Science","volume":"354 ","pages":"Pages 75-89"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.entcs.2020.10.007","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Notes in Theoretical Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1571066120300839","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Computer Science","Score":null,"Total":0}
引用次数: 1
Abstract
We analyze the vertex-coloring problem restricted to planar graphs and propose to consider classic wheels and polyhedral wheels as basic patterns for the planar graphs. We analyze the colorability of the composition among wheels and introduce a novel algorithm based on three rules for the vertex-coloring problem. These rules are: 1) Selecting vertices in the frontier. 2) Processing subsumed wheels. 3) Processing centers of the remaining wheels. Our method forms a maximal independent set S1 ⊂ V (G) consisting of wheel's centers, and a maximum number of vertices in the frontier of the planar graph. Thus, we show that if the resulting graph G′ = (G − S1) is 3-colorable, then this implies the existence of a valid 4-coloring for G.
期刊介绍：
ENTCS is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication and the availability on the electronic media is appropriate. Organizers of conferences whose proceedings appear in ENTCS, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
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
