Matching Cut in Graphs with Large Minimum Degree

Hsieh, Sun Yuan; Le, Hoang Oanh; Lê, Van Bang; Peng, Sheng Lung

doi:10.1007/978-3-030-26176-4_25

Cited by 6 publications

(2 citation statements)

References 13 publications

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“…[1] provided fixed parameter tractable algorithms for various structural parameters including treewidth. Recently various hardness and polynomial time solvable results are also obtained for various structural assumptions in [12,13,9].…”

Section: Previous Workmentioning

confidence: 99%

An FPT algorithm for Matching Cut and d-cut

Aravind¹,

Saxena²

2021

Preprint

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In an undirected graph, a matching cut is an edge cut which is also a matching. we refer MATCHING CUT to the problem of deciding if a given graph contain a matching cut or not. For the matching cut problem, the size of the edge cut also known as the number of crossing edges is a natural parameter. Gomes et al. in [7] showed that MATCH-ING CUT is FPT when parameterized by maximum size of the edge cut using a reduction on results provided by Marx et. al [14]. However, they didn't provide an explicit bound on the running time as the treewidth reduction technique of [14] relies on a MSOL formulation for matching cut and Courcelle's Theorem [5] to show fixed parameter tractability. This motivated us to design an FPT algorithm for the MATCHING CUT where the dependence on the parameter is explicit. In this paper we present an FPT algorithm for matching cut problem for general graphs with running time O(2 O(k log k) n O( 1) ). This is the first FPT algorithm for the MATCHING CUT where the dependence on the matching cut size as a parameter is explicit and bounded.

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Section: Previous Workmentioning

confidence: 99%

An FPT algorithm for Matching Cut and d-cut

Aravind¹,

Saxena²

2021

Preprint

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“…The current-best exact decision algorithm for Matching Cut, the problem of deciding whether a given graph G has a matching cut, has a running time of O(1.328 n ) where n is the number of vertices in G [27]. Faster exact algorithms can be obtained for the case when the minimum degree is large [25]. Matching Cut has FPT-algorithms for the maximum cut size k [23], the vertex cover number of G [29], and weaker parameters such as the twin-cover number [1] or the cluster vertex deletion number [27].…”

Section: Introductionmentioning

confidence: 99%

Refined Notions of Parameterized Enumeration Kernels with Applications to Matching Cut Enumeration

Golovach¹,

Komusiewicz²,

Kratsch³

et al. 2021

Preprint

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An enumeration kernel as defined by Creignou et al. [Theory Comput. Syst. 2017] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a solution-lifting algorithm that efficiently enumerates all solutions from the set of the solutions of the kernel. We propose to consider two new versions of enumeration kernels by asking that the solutions of the original instance can be enumerated in polynomial time or with polynomial delay from the kernel solutions. Using the NP-hard Matching Cut problem parameterized by structural parameters such as the vertex cover number or the cyclomatic number of the input graph, we show that the new enumeration kernels present a useful notion of data reduction for enumeration problems which allows to compactly represent the set of feasible solutions.

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An FPT Algorithm for Matching Cut and d-Cut

Aravind

Saxena

2021

Lecture Notes in Computer Science

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Matching Cut in Graphs with Large Minimum Degree

Cited by 6 publications

References 13 publications

An FPT algorithm for Matching Cut and d-cut

An FPT algorithm for Matching Cut and d-cut

Refined Notions of Parameterized Enumeration Kernels with Applications to Matching Cut Enumeration

An FPT Algorithm for Matching Cut and d-Cut

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