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

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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.

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完美匹配割问题的复杂性

PERFECT matching -cut是判定一个图是否有一个包含边切的完美匹配的问题。我们证明了对于最大度为4的平面图，对于周长为5的平面图，对于二部五正则图，对于直径为3的图，以及对于直径为4的二部图，这个问题是np完全的。我们证明了对于以下几类图，存在多项式时间算法：claw-free,P 5 <math xmlns="http://www.w3.org/1998/Math/MathML" altimg=“urn:x-wiley:03649024:media:jgt23167:jgt23167-math-0001”威利:位置= "方程/ jgt23167 -数学- 0001. png”祝辞& lt; mrow> & lt; mrow> & lt; msub> & lt; mi>术中;/ mi> & lt; mn> 5 & lt; / mn> & lt; / msub> & lt; / mrow> & lt; / mrow> & lt; / math>自由，直径二，直径三的二部，以及有界树宽的图。

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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 .