Minimum maximal acyclic matching in proper interval graphs

Juhi Chaudhary; Sounaka Mishra; B. S. Panda

doi:10.1016/j.dam.2024.10.012

Minimum maximal acyclic matching in proper interval graphs

Juhi Chaudhary, Sounaka Mishra, B. S. Panda

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	414-427
Number of pages	14
Journal	Discrete Applied Mathematics
Volume	360
DOIs	https://doi.org/10.1016/j.dam.2024.10.012
State	Published - 15 Jan 2025
Externally published	Yes

Keywords

Acyclic matching
Dually chordal graphs
Linear-time algorithm
Matching
Minimum maximal acyclic matching
Proper interval graphs

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2024.10.012

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title = "Minimum maximal acyclic matching in proper interval graphs",

abstract = "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.",

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AU - Mishra, Sounaka

AU - Panda, B. S.

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N2 - 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.

AB - 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.

KW - Acyclic matching

KW - Dually chordal graphs

KW - Linear-time algorithm

KW - Matching

KW - Minimum maximal acyclic matching

KW - Proper interval graphs

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JO - Discrete Applied Mathematics

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ER -

Minimum maximal acyclic matching in proper interval graphs

Abstract

Keywords

ASJC Scopus subject areas

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