论图形细分幂的色度数

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-10-23 DOI:10.1016/j.dam.2024.10.002

Michael Anastos , Simona Boyadzhiyska , Silas Rathke , Juanjo Rué

{"title":"论图形细分幂的色度数","authors":"Michael Anastos , Simona Boyadzhiyska , Silas Rathke , Juanjo Rué","doi":"10.1016/j.dam.2024.10.002","DOIUrl":null,"url":null,"abstract":"<div><div>For a given graph <math><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math>, we define its <math><mi>n</mi></math>th subdivision as the graph obtained from <math><mi>G</mi></math> by replacing every edge by a path of length <math><mi>n</mi></math>. We also define the <math><mi>m</mi></math>th power of <math><mi>G</mi></math> as the graph on vertex set <math><mi>V</mi></math> where we connect every pair of vertices at distance at most <math><mi>m</mi></math> in <math><mi>G</mi></math>. In this paper, we study the chromatic number of powers of subdivisions of graphs and resolve the case <math><mrow><mi>m</mi><mo>=</mo><mi>n</mi></mrow></math> asymptotically. In particular, our result confirms a conjecture of Mozafari-Nia and Iradmusa in the case <math><mrow><mi>m</mi><mo>=</mo><mi>n</mi><mo>=</mo><mn>3</mn></mrow></math> in a strong sense.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"360 ","pages":"Pages 506-511"},"PeriodicalIF":1.0000,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the chromatic number of powers of subdivisions of graphs\",\"authors\":\"Michael Anastos , Simona Boyadzhiyska , Silas Rathke , Juanjo Rué\",\"doi\":\"10.1016/j.dam.2024.10.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>For a given graph <math><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math>, we define its <math><mi>n</mi></math>th subdivision as the graph obtained from <math><mi>G</mi></math> by replacing every edge by a path of length <math><mi>n</mi></math>. We also define the <math><mi>m</mi></math>th power of <math><mi>G</mi></math> as the graph on vertex set <math><mi>V</mi></math> where we connect every pair of vertices at distance at most <math><mi>m</mi></math> in <math><mi>G</mi></math>. In this paper, we study the chromatic number of powers of subdivisions of graphs and resolve the case <math><mrow><mi>m</mi><mo>=</mo><mi>n</mi></mrow></math> asymptotically. In particular, our result confirms a conjecture of Mozafari-Nia and Iradmusa in the case <math><mrow><mi>m</mi><mo>=</mo><mi>n</mi><mo>=</mo><mn>3</mn></mrow></math> in a strong sense.</div></div>\",\"PeriodicalId\":50573,\"journal\":{\"name\":\"Discrete Applied Mathematics\",\"volume\":\"360 \",\"pages\":\"Pages 506-511\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-10-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0166218X24004323\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X24004323","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

对于给定的图 G=(V,E)，我们将其第 n 次细分定义为将每条边替换为长度为 n 的路径后从 G 中得到的图。我们还将 G 的第 m 次幂定义为顶点集 V 上的图，在该图中，我们以最多 m 的距离连接 G 中的每对顶点。特别是，我们的结果在强意义上证实了 Mozafari-Nia 和 Iradmusa 在 m=n=3 情况下的猜想。

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

On the chromatic number of powers of subdivisions of graphs

For a given graph

G = (V, E)

, we define its

n

th subdivision as the graph obtained from

G

by replacing every edge by a path of length

n

. We also define the

m

th power of

G

as the graph on vertex set

V

where we connect every pair of vertices at distance at most

m

G

. In this paper, we study the chromatic number of powers of subdivisions of graphs and resolve the case

m = n

asymptotically. In particular, our result confirms a conjecture of Mozafari-Nia and Iradmusa in the case

m = n = 3

in a strong sense.

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

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.