The perfect matching cut problem revisited

In a graph, a perfect matching cut is an edge cut that is a perfect matching. perfect matching cut (pmc) is the problem of deciding whether a given graph has a perfect matching cut, and is known to be NP-complete. We revisit the problem and show that pmc remains NP-complete when restricted to bipart...

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Bibliographic Details
Published in:Theoretical computer science Vol. 931; pp. 117 - 130
Main Authors: Le, Van Bang, Telle, Jan Arne
Format: Journal Article
Language:English
Published: Elsevier B.V 29.09.2022
Subjects:
Computational complexity
Exact branching algorithm
Graph algorithm
Matching cut
Perfect matching cut
Matching cut
Perfect matching cut
Computational complexity
Exact branching algorithm
Graph algorithm
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:In a graph, a perfect matching cut is an edge cut that is a perfect matching. perfect matching cut (pmc) is the problem of deciding whether a given graph has a perfect matching cut, and is known to be NP-complete. We revisit the problem and show that pmc remains NP-complete when restricted to bipartite graphs of maximum degree 3 and arbitrarily large girth. Complementing this hardness result, we give two graph classes in which pmc is polynomial-time solvable. The first one includes claw-free graphs and graphs without an induced path on five vertices, the second one properly contains all chordal graphs. Assuming the Exponential Time Hypothesis, we show there is no O⁎(2o(n))-time algorithm for pmc even when restricted to n-vertex bipartite graphs, and also show that pmc can be solved in O⁎(1.2721n) time by means of an exact branching algorithm.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2022.07.035