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Induced Matching in Some Subclasses of Bipartite Graphs

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Algorithms and Discrete Applied Mathematics (CALDAM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10156))

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Abstract

For a graph \(G=(V,E)\), a set \(M\subseteq E\) is called a matching in G if no two edges in M share a common vertex. A matching M in G is called an induced matching in G if G[M], the subgraph of G induced by M, is same as G[S], the subgraph of G induced by \(S=\{v \in V |\) v is incident on an edge of M\(\}\). The Maximum Induced Matching problem is to find an induced matching of maximum cardinality. Given a graph G and a positive integer k, the Induced Matching Decision problem is to decide whether G has an induced matching of cardinality at least k. The Induced Matching Decision problem is NP-complete on bipartite graphs, but polynomial time solvable for convex bipartite graphs. In this paper, we show that the Induced Matching Decision problem is NP-complete for star-convex bipartite graphs and perfect elimination bipartite graphs. On the positive side, we propose polynomial time algorithms to solve the Maximum Induced Matching problem in circular-convex bipartite graphs and triad-convex bipartite graphs by making polynomial reductions from the Maximum Induced Matching problem in these graph classes to the Maximum Induced Matching problem in convex bipartite graphs.

The work was done when the first author (Arti Pandey) was in IIIT Guwahati.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Ropar, Nangal Road, Rupnagar, 140001, Punjab, India

    Arti Pandey

  2. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India

    B. S. Panda, Piyush Dane & Manav Kashyap

Authors
  1. Arti Pandey
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  2. B. S. Panda
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  3. Piyush Dane
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  4. Manav Kashyap
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Corresponding author

Correspondence to Arti Pandey .

Editor information

Editors and Affiliations

  1. University of Lethbridge, Lethbridge, Alberta, Canada

    Daya Gaur

  2. Indian Institute of Technology Madras, Chennai, India

    N.S. Narayanaswamy

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Pandey, A., Panda, B.S., Dane, P., Kashyap, M. (2017). Induced Matching in Some Subclasses of Bipartite Graphs. In: Gaur, D., Narayanaswamy, N. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2017. Lecture Notes in Computer Science(), vol 10156. Springer, Cham. https://doi.org/10.1007/978-3-319-53007-9_27

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  • DOI: https://doi.org/10.1007/978-3-319-53007-9_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53006-2

  • Online ISBN: 978-3-319-53007-9

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