{"title":"An introduction to the deduction number","authors":"Andrea Burgess , Danny Dyer , Mozhgan Farahani","doi":"10.1016/j.dam.2025.02.024","DOIUrl":null,"url":null,"abstract":"<div><div>The deduction game is a variation of the game of cops and robber on graphs in which searchers must capture an invisible evader in at most one move. Searchers know each others’ initial locations, but can only communicate if they are on the same vertex. Thus, searchers must deduce other searchers’ movement and move accordingly. We introduce the deduction number and study it for various classes of graphs. We provide upper bounds for the deduction number of the Cartesian product of graphs.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"369 ","pages":"Pages 20-27"},"PeriodicalIF":1.0000,"publicationDate":"2025-07-15","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/S0166218X25000940","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/3/7 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The deduction game is a variation of the game of cops and robber on graphs in which searchers must capture an invisible evader in at most one move. Searchers know each others’ initial locations, but can only communicate if they are on the same vertex. Thus, searchers must deduce other searchers’ movement and move accordingly. We introduce the deduction number and study it for various classes of graphs. We provide upper bounds for the deduction number of the Cartesian product of graphs.
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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