Acyclic Matching in Some Subclasses of Graphs

B. S. Panda; Juhi Chaudhary

doi:10.1007/978-3-030-48966-3_31

Acyclic Matching in Some Subclasses of Graphs

B. S. Panda, Juhi Chaudhary

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

8 Scopus citations

Abstract

A subset (Formula Presented) of edges of a graph G = (V, E) is called a matching if no two edges of M share a common vertex. A matching M in a graph G is called an acyclic matching if G[V (M)], the subgraph of G induced by the M-saturated vertices of G is acyclic. The Acyclic Matching Problem is the problem of finding an acyclic matching of maximum size. The decision version of the Acyclic Matching Problem is known to be NP-complete for general graphs as well as for bipartite graphs. In this paper, we strengthen this result by showing that the decision version of the Acyclic Matching Problem remains NP-complete for comb-convex bipartite graphs and dually-chordal graphs. On the positive side, we present linear time algorithms to compute an acyclic matching of maximum size in split graphs and proper interval graphs. Finally, we show that the Acyclic Matching Problem is hard to approximate within a factor of n^1−ɛ for any ɛ > 0, unless P = NP and the Acyclic Matching Problem is APX-complete for 2k + 1-regular graphs for k ≥ 3, where k is a constant.

Original language	English
Title of host publication	Combinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings
Editors	Leszek Gasieniec, Leszek Gasieniec, Ralf Klasing, Tomasz Radzik
Publisher	Springer
Pages	409-421
Number of pages	13
ISBN (Print)	9783030489656
DOIs	https://doi.org/10.1007/978-3-030-48966-3_31
State	Published - 1 Jan 2020
Externally published	Yes
Event	31st International Workshop on Combinatorial Algorithms, IWOCA 2020 - Bordeaux, France Duration: 8 Jun 2020 → 10 Jun 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12126 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	31st International Workshop on Combinatorial Algorithms, IWOCA 2020
Country/Territory	France
City	Bordeaux
Period	8/06/20 → 10/06/20

Keywords

Approximation algorithm
Bipartite graphs
Chordal graphs
Graph algorithm
Matching
NP-completeness

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-48966-3_31

Cite this

Panda, B. S., & Chaudhary, J. (2020). Acyclic Matching in Some Subclasses of Graphs. In L. Gasieniec, L. Gasieniec, R. Klasing, & T. Radzik (Eds.), Combinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings (pp. 409-421). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12126 LNCS). Springer. https://doi.org/10.1007/978-3-030-48966-3_31

Panda, B. S. ; Chaudhary, Juhi. / Acyclic Matching in Some Subclasses of Graphs. Combinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings. editor / Leszek Gasieniec ; Leszek Gasieniec ; Ralf Klasing ; Tomasz Radzik. Springer, 2020. pp. 409-421 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Acyclic Matching in Some Subclasses of Graphs",

abstract = "A subset (Formula Presented) of edges of a graph G = (V, E) is called a matching if no two edges of M share a common vertex. A matching M in a graph G is called an acyclic matching if G[V (M)], the subgraph of G induced by the M-saturated vertices of G is acyclic. The Acyclic Matching Problem is the problem of finding an acyclic matching of maximum size. The decision version of the Acyclic Matching Problem is known to be NP-complete for general graphs as well as for bipartite graphs. In this paper, we strengthen this result by showing that the decision version of the Acyclic Matching Problem remains NP-complete for comb-convex bipartite graphs and dually-chordal graphs. On the positive side, we present linear time algorithms to compute an acyclic matching of maximum size in split graphs and proper interval graphs. Finally, we show that the Acyclic Matching Problem is hard to approximate within a factor of n1−ɛ for any ɛ > 0, unless P = NP and the Acyclic Matching Problem is APX-complete for 2k + 1-regular graphs for k ≥ 3, where k is a constant.",

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author = "Panda, {B. S.} and Juhi Chaudhary",

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Panda, BS & Chaudhary, J 2020, Acyclic Matching in Some Subclasses of Graphs. in L Gasieniec, L Gasieniec, R Klasing & T Radzik (eds), Combinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12126 LNCS, Springer, pp. 409-421, 31st International Workshop on Combinatorial Algorithms, IWOCA 2020, Bordeaux, France, 8/06/20. https://doi.org/10.1007/978-3-030-48966-3_31

Acyclic Matching in Some Subclasses of Graphs. / Panda, B. S.; Chaudhary, Juhi.
Combinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings. ed. / Leszek Gasieniec; Leszek Gasieniec; Ralf Klasing; Tomasz Radzik. Springer, 2020. p. 409-421 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12126 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - A subset (Formula Presented) of edges of a graph G = (V, E) is called a matching if no two edges of M share a common vertex. A matching M in a graph G is called an acyclic matching if G[V (M)], the subgraph of G induced by the M-saturated vertices of G is acyclic. The Acyclic Matching Problem is the problem of finding an acyclic matching of maximum size. The decision version of the Acyclic Matching Problem is known to be NP-complete for general graphs as well as for bipartite graphs. In this paper, we strengthen this result by showing that the decision version of the Acyclic Matching Problem remains NP-complete for comb-convex bipartite graphs and dually-chordal graphs. On the positive side, we present linear time algorithms to compute an acyclic matching of maximum size in split graphs and proper interval graphs. Finally, we show that the Acyclic Matching Problem is hard to approximate within a factor of n1−ɛ for any ɛ > 0, unless P = NP and the Acyclic Matching Problem is APX-complete for 2k + 1-regular graphs for k ≥ 3, where k is a constant.

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Panda BS, Chaudhary J. Acyclic Matching in Some Subclasses of Graphs. In Gasieniec L, Gasieniec L, Klasing R, Radzik T, editors, Combinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings. Springer. 2020. p. 409-421. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-48966-3_31

Acyclic Matching in Some Subclasses of Graphs

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