{"title":"Matching cut and variants on bipartite graphs of bounded radius and diameter","authors":"Felicia Lucke","doi":"10.1016/j.tcs.2025.115429","DOIUrl":null,"url":null,"abstract":"<div><div>In the <span>Matching Cut</span> problem we ask whether a graph <em>G</em> has a matching cut, that is, a matching which is also an edge cut of <em>G</em>. We consider the variants <span>Perfect Matching Cut</span> and <span>Disconnected Perfect Matching</span> where we ask whether there exists a matching cut equal to, respectively, contained in a perfect matching. In addition, in the problem <span>Maximum Matching Cut</span> we ask for a matching cut with a maximum number of edges. The last problem we consider is <em>d</em><span>-Cut</span> where we ask for an edge cut where each vertex is incident to at most <em>d</em> edges in the cut.</div><div>We investigate the computational complexity of these problems on bipartite graphs of bounded radius and diameter. Our results extend known results for <span>Matching Cut</span> and <span>Disconnected Perfect Matching</span>. We give complexity dichotomies for <em>d</em><span>-Cut</span> and <span>Maximum Matching Cut</span> and solve one of two open cases for <span>Disconnected Perfect Matching</span>. For <span>Perfect Matching Cut</span> we give the first hardness result for bipartite graphs of bounded radius and diameter and extend the known polynomial cases.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1052 ","pages":"Article 115429"},"PeriodicalIF":1.0000,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Computer Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304397525003676","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
In the Matching Cut problem we ask whether a graph G has a matching cut, that is, a matching which is also an edge cut of G. We consider the variants Perfect Matching Cut and Disconnected Perfect Matching where we ask whether there exists a matching cut equal to, respectively, contained in a perfect matching. In addition, in the problem Maximum Matching Cut we ask for a matching cut with a maximum number of edges. The last problem we consider is d-Cut where we ask for an edge cut where each vertex is incident to at most d edges in the cut.
We investigate the computational complexity of these problems on bipartite graphs of bounded radius and diameter. Our results extend known results for Matching Cut and Disconnected Perfect Matching. We give complexity dichotomies for d-Cut and Maximum Matching Cut and solve one of two open cases for Disconnected Perfect Matching. For Perfect Matching Cut we give the first hardness result for bipartite graphs of bounded radius and diameter and extend the known polynomial cases.
期刊介绍:
Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.