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Quasimonotone Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11159))

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Abstract

For any class \(\mathcal {C}\) of bipartite graphs, we define quasi-\(\mathcal {C}\) to be the class of all graphs G such that every bipartition of G belongs to \(\mathcal {C}\). This definition is motivated by a generalisation of the switch Markov chain on perfect matchings from bipartite graphs to nonbipartite graphs. The monotone graphs, also known as bipartite permutation graphs and proper interval bigraphs, are such a class of bipartite graphs. We investigate the structure of quasi-monotone graphs and hence construct a polynomial time recognition algorithm for graphs in this class.

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Authors and Affiliations

  1. School of Computing, University of Leeds, Leeds, LS2 9JT, UK

    Martin Dyer & Haiko Müller

Authors
  1. Martin Dyer
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  2. Haiko Müller
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Correspondence to Haiko Müller .

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Editors and Affiliations

  1. Universität Rostock, Rostock, Germany

    Andreas Brandstädt

  2. Brandenburgische Technische Universität Cottbus-Senftenberg, Cottbus, Germany

    Ekkehard Köhler

  3. Brandenburgische Technische Universität Cottbus-Senftenberg, Cottbus, Germany

    Klaus Meer

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Dyer, M., Müller, H. (2018). Quasimonotone Graphs. In: Brandstädt, A., Köhler, E., Meer, K. (eds) Graph-Theoretic Concepts in Computer Science. WG 2018. Lecture Notes in Computer Science(), vol 11159. Springer, Cham. https://doi.org/10.1007/978-3-030-00256-5_16

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  • DOI: https://doi.org/10.1007/978-3-030-00256-5_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00255-8

  • Online ISBN: 978-3-030-00256-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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