Algorithms solving the Matching Cut problem

In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete. This paper provides a first branching algorithm solving Matching Cut in time O⁎(2n/2)=O⁎(1.4143n) for an n-vertex i...

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Bibliographic Details
Published in:Theoretical computer science Vol. 609; pp. 328 - 335
Main Authors: Kratsch, Dieter, Le, Van Bang
Format: Journal Article
Language:English
Published: Elsevier B.V 04.01.2016
Elsevier
Subjects:
Algorithms
Automatic
Engineering Sciences
Graph algorithm
Graph theory
Graphs
Matching
Matching cut
Matching cut
Graph algorithm
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:In a graph, a matching cut is an edge cut that is a matching. Matching Cut is the problem of deciding whether or not a given graph has a matching cut, which is known to be NP-complete. This paper provides a first branching algorithm solving Matching Cut in time O⁎(2n/2)=O⁎(1.4143n) for an n-vertex input graph, and shows that Matching Cut parameterized by the vertex cover number τ(G) can be solved by a single-exponential algorithm in time 2τ(G)O(n2). Moreover, the paper also gives a polynomially solvable case for Matching Cut which covers previous known results on graphs of maximum degree three, line graphs, and claw-free graphs.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2015.10.016