Athira Divakaran , Tanja Dravec , Tijo James , Sandi Klavžar , Latha S Nair
{"title":"Maker–Breaker domination game critical graphs","authors":"Athira Divakaran , Tanja Dravec , Tijo James , Sandi Klavžar , Latha S Nair","doi":"10.1016/j.dam.2025.02.038","DOIUrl":null,"url":null,"abstract":"<div><div>The Maker–Breaker domination game (MBD game) is a two-player game played on a graph <span><math><mi>G</mi></math></span> by Dominator and Staller. They alternately select unplayed vertices of <span><math><mi>G</mi></math></span>. The goal of Dominator is to form a dominating set with the set of vertices selected by him while that of Staller is to prevent this from happening. In this paper MBD game critical graphs are studied. Their existence is established and critical graphs are characterized for most of the cases in which the first player can win the game in one or two moves.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"368 ","pages":"Pages 126-134"},"PeriodicalIF":1.0000,"publicationDate":"2025-02-28","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/S0166218X25001076","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
Abstract
The Maker–Breaker domination game (MBD game) is a two-player game played on a graph by Dominator and Staller. They alternately select unplayed vertices of . The goal of Dominator is to form a dominating set with the set of vertices selected by him while that of Staller is to prevent this from happening. In this paper MBD game critical graphs are studied. Their existence is established and critical graphs are characterized for most of the cases in which the first player can win the game in one or two moves.
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.
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