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Zero-visibility cops and robber and the pathwidth of a graph

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Abstract

We examine the zero-visibility cops and robber graph searching model, which differs from the classical cops and robber game in one way: the robber is invisible. We show that this model is not monotonic. We show that the zero-visibility copnumber of a graph is bounded above by its pathwidth and cannot be bounded below by any nontrivial function of the pathwidth. As well, we define a monotonic version of this game and show that the monotonic zero-visibility copnumber can be bounded both above and below by positive multiples of the pathwidth.

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Acknowledgments

D. Dereniowski has been partially supported by Narodowe Centrum Nauki under contract DEC-2011/02/A/ST6/00201 and by a scholarship for outstanding young researchers founded by the Polish Ministry of Science and Higher Education.

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Authors and Affiliations

  1. Department of Algorithms and System Modeling, Gdańsk University of Technology, Gdańsk, Poland

    Dariusz Dereniowski

  2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, Canada

    Danny Dyer & Ryan M. Tifenbach

  3. Department of Computer Science, University of Regina, Regina, SK, Canada

    Boting Yang

Authors
  1. Dariusz Dereniowski
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  2. Danny Dyer
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  3. Ryan M. Tifenbach
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  4. Boting Yang
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Corresponding author

Correspondence to Ryan M. Tifenbach.

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Dereniowski, D., Dyer, D., Tifenbach, R.M. et al. Zero-visibility cops and robber and the pathwidth of a graph. J Comb Optim 29, 541–564 (2015). https://doi.org/10.1007/s10878-014-9712-6

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  • DOI: https://doi.org/10.1007/s10878-014-9712-6

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