Edge-apexing in hereditary classes of graphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-09-04 DOI:10.1016/j.disc.2024.114234

Jagdeep Singh , Vaidy Sivaraman

{"title":"Edge-apexing in hereditary classes of graphs","authors":"Jagdeep Singh , Vaidy Sivaraman","doi":"10.1016/j.disc.2024.114234","DOIUrl":null,"url":null,"abstract":"<div>A class <math><mi>G</mi></math> of graphs is called hereditary if it is closed under taking induced subgraphs. We denote by <math><msup><mrow><mi>G</mi></mrow><mrow><mi>epex</mi></mrow></msup></math> the class of graphs that are at most one edge away from being in <math><mi>G</mi></math>. We note that <math><msup><mrow><mi>G</mi></mrow><mrow><mi>epex</mi></mrow></msup></math> is hereditary and prove that if a hereditary class <math><mi>G</mi></math> has finitely many forbidden induced subgraphs, then so does <math><msup><mrow><mi>G</mi></mrow><mrow><mi>epex</mi></mrow></msup></math>.The hereditary class of cographs consists of all graphs G that can be generated from <math><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub></math> using complementation and disjoint union. Cographs are precisely the graphs that do not have the 4-vertex path as an induced subgraph. For the class of edge-apex cographs our main result bounds the order of such forbidden induced subgraphs by 8 and finds all of them by computer search.</div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 1","pages":"Article 114234"},"PeriodicalIF":0.7000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0012365X24003650/pdfft?md5=3a7b1576f400f1b5803871014f7dd340&pid=1-s2.0-S0012365X24003650-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24003650","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 class $G$ of graphs is called hereditary if it is closed under taking induced subgraphs. We denote by $G^{epex}$ the class of graphs that are at most one edge away from being in $G$ . We note that $G^{epex}$ is hereditary and prove that if a hereditary class $G$ has finitely many forbidden induced subgraphs, then so does $G^{epex}$ .

The hereditary class of cographs consists of all graphs G that can be generated from $K_{1}$ using complementation and disjoint union. Cographs are precisely the graphs that do not have the 4-vertex path as an induced subgraph. For the class of edge-apex cographs our main result bounds the order of such forbidden induced subgraphs by 8 and finds all of them by computer search.

查看原文本刊更多论文

遗传图类中的边缘apexing

如果一类图 G 在取诱导子图时是封闭的，则该类图 G 称为遗传类图。我们用 Gepex 表示离 G 最多只有一条边的一类图。我们注意到 Gepex 是遗传的，并证明如果一个遗传类 G 有有限多个禁止的诱导子图，那么 Gepex 也是遗传的。Cographs 正是没有 4 顶点路径作为诱导子图的图。对于无边 Cographs 类，我们的主要结果将此类禁止诱导子图的阶数限定为 8，并通过计算机搜索找到所有这些子图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.