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On the Complexity of Computing a Maximum Acyclic Matching in Undirected Graphs

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  • Samer Nofal

    (Department of Computer Science, German Jordanian University, Amman 11180, Jordan)

Abstract

The problem of finding a maximum acyclic matching in a simple undirected graph is known to be NP-complete. In this paper, we present new results; we show that a maximum acyclic matching in a given undirected graph (with n vertices and m edges) can be computed recursively with a recursion depth O ( ln m ) in expectation. Consequently, employing a recursive computation of a maximum acyclic matching in a given graph, if the recursion depth meets the expectation O ( ln m ) , then a maximum acyclic matching can be computed in time O ( n 3.4 ) and space O ( m ln m ) . However, for the general case, the complexity of the recursive computation of a maximum acyclic matching is in O ( n 2 2 m ) time and in O ( m 2 ) space.

Suggested Citation

  • Samer Nofal, 2025. "On the Complexity of Computing a Maximum Acyclic Matching in Undirected Graphs," Mathematics, MDPI, vol. 13(5), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:889-:d:1607029
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    References listed on IDEAS

    as
    1. M. Fürst & D. Rautenbach, 2019. "On some hard and some tractable cases of the maximum acyclic matching problem," Annals of Operations Research, Springer, vol. 279(1), pages 291-300, August.
    2. Juhi Chaudhary & Sounaka Mishra & B. S. Panda, 2024. "On the complexity of minimum maximal acyclic matchings," Journal of Combinatorial Optimization, Springer, vol. 48(1), pages 1-23, August.
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