Minimum maximal acyclic matching in proper interval graphs

Given a graph G, Min-Max-Acy-Matching is the problem of finding a maximal matching M in G of minimum cardinality such that the set of M-saturated vertices induces an acyclic subgraph in G. The decision version of Min-Max-Acy-Matching is known to be NP-complete. In this paper, we strengthen this resu...

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Vydané v:Discrete Applied Mathematics Ročník 360; s. 414 - 427
Hlavní autori: Chaudhary, Juhi, Mishra, Sounaka, Panda, B.S.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 15.01.2025
Predmet:
Acyclic matching
Dually chordal graphs
Linear-time algorithm
Matching
Minimum maximal acyclic matching
Proper interval graphs
Matching
Dually chordal graphs
Acyclic matching
Proper interval graphs
Minimum maximal acyclic matching
Linear-time algorithm
ISSN:0166-218X
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Shrnutí:Given a graph G, Min-Max-Acy-Matching is the problem of finding a maximal matching M in G of minimum cardinality such that the set of M-saturated vertices induces an acyclic subgraph in G. The decision version of Min-Max-Acy-Matching is known to be NP-complete. In this paper, we strengthen this result by proving that the decision version of Min-Max-Acy-Matching is NP-complete even for dually chordal graphs. Also, we give the first positive algorithmic result for Min-Max-Acy-Matching by proposing a linear-time algorithm for computing a minimum cardinality maximal acyclic matching in proper interval graphs, a subclass of dually chordal graphs.
ISSN:0166-218X
DOI:10.1016/j.dam.2024.10.012