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A Partition Approach to Lower Bounds for Zero-Visibility Cops and Robber

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Combinatorial Algorithms (IWOCA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11638))

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Abstract

The zero-visibility cops and robber game is a variant of Cops and Robbers subject to the constraint that the cops have no information at any time about the location of the robber. We first study a partition problem in which for a given graph and an integer k, we want to find a partition of the vertex set such that the size of the boundary of the smaller subset in the partition is at most k while the size of this subset is as large as possible under some conditions. Then we apply such partitions to prove lower bounds on the zero-visibility cop numbers of graph products. We also investigate the monotonic zero-visibility cop numbers of graph products.

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Authors and Affiliations

  1. Department of Computer Science, University of Regina, Regina, Canada

    Yuan Xue, Boting Yang & Sandra Zilles

  2. College of Math, Physics and Information Technology, Zhejiang Normal University, Jinhua, China

    Farong Zhong

Authors
  1. Yuan Xue
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  2. Boting Yang
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  3. Farong Zhong
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  4. Sandra Zilles
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Corresponding author

Correspondence to Boting Yang .

Editor information

Editors and Affiliations

  1. Arizona State University, Tempe, AZ, USA

    Charles J. Colbourn

  2. University of Pisa, Pisa, Italy

    Roberto Grossi

  3. University of Pisa, Pisa, Italy

    Nadia Pisanti

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Xue, Y., Yang, B., Zhong, F., Zilles, S. (2019). A Partition Approach to Lower Bounds for Zero-Visibility Cops and Robber. In: Colbourn, C., Grossi, R., Pisanti, N. (eds) Combinatorial Algorithms. IWOCA 2019. Lecture Notes in Computer Science(), vol 11638. Springer, Cham. https://doi.org/10.1007/978-3-030-25005-8_36

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  • DOI: https://doi.org/10.1007/978-3-030-25005-8_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-25004-1

  • Online ISBN: 978-3-030-25005-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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