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

Dariusz Dereniowski, Danny Dyer, Ryan M. Tifenbach () and Boting Yang
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Dariusz Dereniowski: Gdańsk University of Technology
Danny Dyer: Memorial University of Newfoundland
Ryan M. Tifenbach: Memorial University of Newfoundland
Boting Yang: University of Regina

Journal of Combinatorial Optimization, 2015, vol. 29, issue 3, No 3, 564 pages

Abstract: 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.

Keywords: Cops and robber; Graph searching; Pathwidth; Pursuit-evasion; 05C57 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-014-9712-6

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