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

Author

Listed:
  • Dariusz Dereniowski

    (Gdańsk University of Technology)

  • Danny Dyer

    (Memorial University of Newfoundland)

  • Ryan M. Tifenbach

    (Memorial University of Newfoundland)

  • Boting Yang

    (University of Regina)

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.

Suggested Citation

  • Dariusz Dereniowski & Danny Dyer & Ryan M. Tifenbach & Boting Yang, 2015. "Zero-visibility cops and robber and the pathwidth of a graph," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 541-564, April.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:3:d:10.1007_s10878-014-9712-6
    DOI: 10.1007/s10878-014-9712-6
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    References listed on IDEAS

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    1. Boting Yang, 2007. "Strong-mixed searching and pathwidth," Journal of Combinatorial Optimization, Springer, vol. 13(1), pages 47-59, January.
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