The complexity of the perfect matching-cut problem

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-10-06 DOI:10.1002/jgt.23167

Valentin Bouquet, Christophe Picouleau

{"title":"The complexity of the perfect matching-cut problem","authors":"Valentin Bouquet, Christophe Picouleau","doi":"10.1002/jgt.23167","DOIUrl":null,"url":null,"abstract":"<p>PERFECT MATCHING-CUT is the problem of deciding whether a graph has a perfect matching that contains an edge-cut. We show that this problem is NP-complete for planar graphs with maximum degree four, for planar graphs with girth five, for bipartite five-regular graphs, for graphs of diameter three, and for bipartite graphs of diameter four. We show that there exist polynomial-time algorithms for the following classes of graphs: claw-free, <span></span><math>\n <semantics>\n <mrow>\n \n <mrow>\n <msub>\n <mi>P</mi>\n \n <mn>5</mn>\n </msub>\n </mrow>\n </mrow>\n <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt23167:jgt23167-math-0001\" wiley:location=\"equation/jgt23167-math-0001.png\"><mrow><mrow><msub><mi>P</mi><mn>5</mn></msub></mrow></mrow></math></annotation>\n </semantics></math>-free, diameter two, bipartite with diameter three, and graphs with bounded treewidth.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"108 3","pages":"432-462"},"PeriodicalIF":0.9000,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.23167","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Graph Theory","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jgt.23167","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

PERFECT MATCHING-CUT is the problem of deciding whether a graph has a perfect matching that contains an edge-cut. We show that this problem is NP-complete for planar graphs with maximum degree four, for planar graphs with girth five, for bipartite five-regular graphs, for graphs of diameter three, and for bipartite graphs of diameter four. We show that there exist polynomial-time algorithms for the following classes of graphs: claw-free, $P_{5}$ -free, diameter two, bipartite with diameter three, and graphs with bounded treewidth.

Abstract Image

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .