The Complexity of the Matching-Cut Problem

Patrignani, Maurizio; Pizzonia, Maurizio

doi:10.1007/3-540-45477-2_26

Cited by 43 publications

(44 citation statements)

References 7 publications

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“…It is stated in Lemma 5 that Matching-Cut with Roots is NP-complete. This lemma is essentially due to Patrignani and Pizzonia [25] as it immediately follows from the following small observation in their hardness reduction from the Not-AllEqual-3-Satisfiability problem, which is an NP-complete problem [26]. For a given instance of Not-All-Equal-3-Satisfiability, Patrignani and Pizzonia [25] construct a connected graph G of minimum degree at least two with the following property: G contains two disjoint sets F and T of vertices (that compose a so-called false chain and true chain, respectively) such that for every matching-cut M , the sets F and T are in distinct components of G − M .…”

Section: Matching-cut With Rootsmentioning

confidence: 95%

Computing Vertex-Surjective Homomorphisms to Partially Reflexive Trees

Golovach

Paulusma

Song

2011

Computer Science – Theory and Applications

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NOTICE: this is the author's version of a work that was accepted for publication in Theoretical computer science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Theoretical computer science, 457, 2012, 10.1016/j.tcs.2012.06.039 Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract. A homomorphism from a graph G to a graph H is a vertex mapping f : VG → VH such that f (u) and f (v) form an edge in H whenever u and v form an edge in G. The H-Coloring problem is to test if a graph G allows a homomorphism to a given graph H. A well-known result of Hell and Nešetřil determines the computational complexity of this problem for any fixed graph H. We study a natural variant of this problem, namely the Surjective H-Coloring problem, which is to test whether a graph G allows a homomorphism to a graph H that is (vertex-)surjective. We classify the computational complexity of this problem when H is any fixed partially reflexive tree. Thus we identify the first class of target graphs H for which the computational complexity of Surjective H-Coloring can be determined. For the polynomial-time solvable cases we show a number of parameterized complexity results, especially on graph classes with (locally) bounded expansion.

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Section: Matching-cut With Rootsmentioning

confidence: 95%

Computing Vertex-Surjective Homomorphisms to Partially Reflexive Trees

Golovach

Paulusma

Song

2011

Computer Science – Theory and Applications

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“…NP-complete ? Its NPcompleteness has been re-proved in [56], and intractability remains valid on bipartite graphs where one class contains only vertices of degree 2 [54] or one vertex class is 3-regular and the other class is 4-regular [49], and also if the input graph is planar with maximum degree 4 or planar without cycles shorter than 5 [16]. On the other hand, the problem is solvable in polynomial time on graphs of maximum degree 3 [22], line graphs and graphs without induced cycles longer than 4 [54], series-parallel graphs [56], claw-free graphs and planar graphs without cycles shorter than 7 [16], graphs satisfying d(u) + d(v) ≤ 6 for all edges (u, v) [49], graphs of diameter 2 [20] and graphs whose line graphs are planar [48].…”

Section: Theorem 19 ([5])mentioning

confidence: 98%

Satisfactory graph partition, variants, and generalizations

Bazgan

Tuza

Vanderpooten

2010

European Journal of Operational Research

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“…Cut with Roots is known as Matching Cut with Roots and was proved NP-complete by Golovach, Paulusma and Song [10] (by making an observation about the proof of the result of Patrignani and Pizzonia [14] that deciding whether or not any given graph has a matching cut is NP-complete).…”

Section: (I J)-factor Cut With Rootsmentioning

confidence: 99%

Surjective H-colouring: New hardness results

Golovach

Johnson

Martin

et al. 2018

COM

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Abstract. A homomorphism from a graph G to a graph H is a vertex mapping f from the vertex set of G to the vertex set of H such that there is an edge between vertices f (u) and f (v) of H whenever there is an edge between vertices u and v of G. The H-Colouring problem is to decide if a graph G allows a homomorphism to a fixed graph H. We continue a study on a variant of this problem, namely the Surjective H-Colouring problem, which imposes the homomorphism to be vertexsurjective. We build upon previous results and show that this problem is NP-complete for every connected graph H that has exactly two vertices with a self-loop as long as these two vertices are not adjacent. As a result, we can classify the computational complexity of Surjective HColouring for every graph H on at most four vertices.

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The Complexity of the Matching-Cut Problem

Cited by 43 publications

References 7 publications

Computing Vertex-Surjective Homomorphisms to Partially Reflexive Trees

Computing Vertex-Surjective Homomorphisms to Partially Reflexive Trees

Satisfactory graph partition, variants, and generalizations

Surjective H-colouring: New hardness results

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