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Counting Independent Sets in Graphs with Bounded Bipartite Pathwidth

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Graph-Theoretic Concepts in Computer Science (WG 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11789))

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Abstract

The Glauber dynamics can efficiently sample independent sets almost uniformly at random in polynomial time for graphs in a certain class. The class is determined by boundedness of a new graph parameter called bipartite pathwidth. This result, which we prove for the more general hardcore distribution with fugacity \(\lambda \), can be viewed as a strong generalisation of Jerrum and Sinclair’s work on approximately counting matchings. The class of graphs with bounded bipartite pathwidth includes line graphs and claw-free graphs, which generalise line graphs. We consider two further generalisations of claw-free graphs and prove that these classes have bounded bipartite pathwidth.

M. Dyer and H. Müller—Research supported by EPSRC grant EP/S016562/1.

C. Greenhill—Research supported by Australian Research Council grant DP19010097.

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Authors and Affiliations

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

    Martin Dyer & Haiko Müller

  2. School of Mathematics and Statistics, UNSW, Sydney, 2052, Australia

    Catherine Greenhill

Authors
  1. Martin Dyer
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  2. Catherine Greenhill
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  3. Haiko Müller
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Correspondence to Haiko Müller .

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Editors and Affiliations

  1. CNRS, LIRMM, Université de Montpellier, Montpellier, France

    Ignasi Sau

  2. CNRS, LIRMM, Université de Montpellier, Montpellier, France

    Dimitrios M. Thilikos

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Dyer, M., Greenhill, C., Müller, H. (2019). Counting Independent Sets in Graphs with Bounded Bipartite Pathwidth. In: Sau, I., Thilikos, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2019. Lecture Notes in Computer Science(), vol 11789. Springer, Cham. https://doi.org/10.1007/978-3-030-30786-8_23

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  • DOI: https://doi.org/10.1007/978-3-030-30786-8_23

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  • Online ISBN: 978-3-030-30786-8

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