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

• DOI: 10.1007/s10878-014-9712-6
• Publication Date: 2014-02-18T08:58:25Z
• Authors: Dariusz Dereniowski; Danny Dyer; Ryan M. Tifenbach; Boting Yang
• Keywords: Visibility; Theory of computation; Zero (linguistics); Visibility graph

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.