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Efficient Enumeration of Bipartite Subgraphs in Graphs

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Computing and Combinatorics (COCOON 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10976))

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Abstract

Subgraph enumeration problems ask to output all subgraphs of an input graph that belong to a specified graph class or satisfy a given constraint. These problems have been widely studied in theoretical computer science. So far, many efficient enumeration algorithms for the fundamental substructures such as spanning trees, cycles, and paths, have been developed. This paper addresses the enumeration problem of bipartite subgraphs. Even though bipartite graphs are quite fundamental and have numerous applications in both theory and practice, their enumeration algorithms have not been intensively studied, to the best of our knowledge. We propose the first non-trivial algorithms for enumerating all bipartite subgraphs in a given graph. As the main results, we develop two efficient algorithms: the one enumerates all bipartite induced subgraphs of a graph with degeneracy k in \(\mathcal {O}\left( k\right) \) time per solution. The other enumerates all bipartite subgraphs in \(\mathcal {O}\left( 1\right) \) time per solution.

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Authors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    Kunihiro Wasa & Takeaki Uno

Authors
  1. Kunihiro Wasa
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  2. Takeaki Uno
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Correspondence to Kunihiro Wasa .

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Editors and Affiliations

  1. City University of Hong Kong, Hong Kong, China

    Lusheng Wang

  2. Shandong University, Jinan, China

    Daming Zhu

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Wasa, K., Uno, T. (2018). Efficient Enumeration of Bipartite Subgraphs in Graphs. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_38

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  • DOI: https://doi.org/10.1007/978-3-319-94776-1_38

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  • Online ISBN: 978-3-319-94776-1

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