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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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