@inproceedings{dcb716d8e10d4595938c3a0852a429a5,

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.",

keywords = "Approximation algorithm, Bipartite graphs, Chordal graphs, Graph algorithm, Matching, NP-completeness",

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

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020.; 31st International Workshop on Combinatorial Algorithms, IWOCA 2020 ; Conference date: 08-06-2020 Through 10-06-2020",

year = "2020",

month = jan,

day = "1",

doi = "10.1007/978-3-030-48966-3_31",

language = "English",

isbn = "9783030489656",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer",

pages = "409--421",

editor = "Leszek Gasieniec and Leszek Gasieniec and Ralf Klasing and Tomasz Radzik",

booktitle = "Combinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings",

address = "Germany",

}