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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Vydáno v:Theoretical computer science Ročník 931; s. 117 - 130
Hlavní autoři: Le, Van Bang, Telle, Jan Arne
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 29.09.2022
Témata:
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
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Shrnutí: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