# Acyclic Matching in Some Subclasses of Graphs

B. S. Panda, Juhi Chaudhary

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 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 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.

Original language English Combinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings Leszek Gasieniec, Leszek Gasieniec, Ralf Klasing, Tomasz Radzik Springer 409-421 13 9783030489656 https://doi.org/10.1007/978-3-030-48966-3_31 Published - 1 Jan 2020 Yes 31st International Workshop on Combinatorial Algorithms, IWOCA 2020 - Bordeaux, FranceDuration: 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) 12126 LNCS 0302-9743 1611-3349

### Conference

Conference 31st International Workshop on Combinatorial Algorithms, IWOCA 2020 France Bordeaux 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

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