无三角形平面图的分解

IF 0.9 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics Pub Date : 2025-08-19 DOI:10.1016/j.ejc.2025.104227

Rongxing Xu , Xuding Zhu

{"title":"无三角形平面图的分解","authors":"Rongxing Xu , Xuding Zhu","doi":"10.1016/j.ejc.2025.104227","DOIUrl":null,"url":null,"abstract":"<div><div>A decomposition of a graph <span><math><mi>G</mi></math></span> is a family of subgraphs of <span><math><mi>G</mi></math></span> whose edge sets form a partition of <span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. In this paper, we prove that every triangle-free planar graph <span><math><mi>G</mi></math></span> can be decomposed into a 2-degenerate graph and a matching. Consequently, every triangle-free planar graph <span><math><mi>G</mi></math></span> has a matching <span><math><mi>M</mi></math></span> such that <span><math><mrow><mi>G</mi><mo>−</mo><mi>M</mi></mrow></math></span> is online 3-DP-colorable. This strengthens an earlier result in Škrekovski (1999) that every triangle-free planar graph is 1-defective 3-choosable.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"130 ","pages":"Article 104227"},"PeriodicalIF":0.9000,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Decomposition of triangle-free planar graphs\",\"authors\":\"Rongxing Xu , Xuding Zhu\",\"doi\":\"10.1016/j.ejc.2025.104227\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>A decomposition of a graph <span><math><mi>G</mi></math></span> is a family of subgraphs of <span><math><mi>G</mi></math></span> whose edge sets form a partition of <span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. In this paper, we prove that every triangle-free planar graph <span><math><mi>G</mi></math></span> can be decomposed into a 2-degenerate graph and a matching. Consequently, every triangle-free planar graph <span><math><mi>G</mi></math></span> has a matching <span><math><mi>M</mi></math></span> such that <span><math><mrow><mi>G</mi><mo>−</mo><mi>M</mi></mrow></math></span> is online 3-DP-colorable. This strengthens an earlier result in Škrekovski (1999) that every triangle-free planar graph is 1-defective 3-choosable.</div></div>\",\"PeriodicalId\":50490,\"journal\":{\"name\":\"European Journal of Combinatorics\",\"volume\":\"130 \",\"pages\":\"Article 104227\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-08-19\",\"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/S0195669825001167\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0195669825001167","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

摘要

图G的分解是G的一组子图，这些子图的边集构成E(G)的一个划分。本文证明了每一个无三角形平面图G都可以分解为一个2-简并图和一个匹配图。因此，每一个无三角形平面图G都有一个匹配的M，使得G−M是在线3- dp可着色的。这加强了Škrekovski（1999）中先前的一个结果，即每个无三角形平面图都是1-缺陷3-可选的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Decomposition of triangle-free planar graphs

A decomposition of a graph

G

is a family of subgraphs of

G

whose edge sets form a partition of

E (G)

. In this paper, we prove that every triangle-free planar graph

G

can be decomposed into a 2-degenerate graph and a matching. Consequently, every triangle-free planar graph

G

has a matching

M

such that

G - M

is online 3-DP-colorable. This strengthens an earlier result in Škrekovski (1999) that every triangle-free planar graph is 1-defective 3-choosable.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

European Journal of Combinatorics 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

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.