Approximating Maximum Acyclic Matchings by Greedy and Local Search Strategies

Baste, Julien; Fürst, Maximilian; Rautenbach, Dieter

doi:10.1007/978-3-030-58150-3_44

Cited by 7 publications

(1 citation statement)

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“…This result contrasts with a result by Kobler and Rotics [20] that deciding if the size of the maximum induced matching of G is equal to the size of the maximum matching is polynomially solvable for general graphs. Also, Furst and Rautenbach et al [3] proved that every graph with n vertices, the maximum degree ∆, and no isolated vertex, has an acyclic matching of size at least (1 − o ∆ (1)) 6n/∆ 2 , and they explained how to find such an acyclic matching in polynomial time. Moreover, they provided a (2∆ + 2)/3-approximation algorithm for the Acyclic Matching problem, based on greedy and local search strategies.…”

Section: Introductionmentioning

confidence: 99%

On the Parameterized Complexity of the Acyclic Matching Problem

Hajebi¹,

Javadi²

2021

Preprint

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A matching is a set of edges in a graph with no common endpoint. A matching M is called acyclic if the induced subgraph on the endpoints of the edges in M is acyclic. Given a graph G and an integer k, Acyclic Matching Problem seeks for an acyclic matching of size k in G. The problem is known to be NP-complete. In this paper, we investigate the complexity of the problem in different aspects. First, we prove that the problem remains NP-complete for the class of planar bipartite graphs of maximum degree three and arbitrarily large girth. Also, the problem remains NP-complete for the class of planar line graphs with maximum degree four. Moreover, we study the parameterized complexity of the problem. In particular, we prove that the problem is W[1]-hard on bipartite graphs with respect to the parameter k. On the other hand, the problem is fixed parameter tractable with respect to k, for line graphs, C 4 -free graphs and every proper minor-closed class of graphs (including bounded tree-width and planar graphs).

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Section: Introductionmentioning

confidence: 99%