Zero-visibility cops & robber and the pathwidth of a graph
نویسندگان
چکیده
We examine the zero-visibility cops and robber graph searching model, which differs from the classical cops & robber game in one way: the robber is invisible. We show that this model is not monotonic. We also provide bounds on both the zero-visibility copnumber and monotonic zerovisibility copnumber in terms of the pathwidth.
منابع مشابه
Graph Searching in a Crime Wave
We define helicopter cops and robber games with multiple robbers, extending previous research, which considered only the pursuit of a single robber. Our model is defined for robbers that are visible (their position in the graph is known to the cops) and active (they can move at any point in the game) but is easily adapted to other variants of the single-robber game that have been considered in ...
متن کاملCops, Robber and Medianwidth Parameters
In previous work, we introduced median decompositions of graphs, a generalisation of tree decompositions where a graph can be modelled after any median graph, along with a hierarchy of i-medianwidth parameters (mwi)i≥1 starting from treewidth and converging to the clique number. We introduce another graph parameter based on the concept of median decompositions, to be called i-latticewidth and d...
متن کاملThe role of information in the cop-robber game
We investigate the role of the information available to the players on the outcome of the cops and robbers game. This game takes place on a graph and players move along the edges in turns. The cops win the game if they can move onto the robber’s vertex. In the standard formulation, it is assumed that the players can “see” each other at all times. A graph G is called cop-win if a single cop can ...
متن کاملLimited Visibility Cops and Robbers
We consider a variation of the Cops and Robber game where the cops can only see the robber when the distance between them is at most a fixed parameter `. We consider the basic consequences of this definition for some simple graph families, and show that this model is not monotonic, unlike common models where the robber is invisible. We see that cops’ strategy consists of a phase in which they n...
متن کاملLocalization game on geometric and planar graphs
The main topic of this paper is motivated by a localization problem in cellular networks. Given a graph G we want to localize a walking agent by checking his distance to as few vertices as possible. The model we introduce is based on a pursuit graph game that resembles the famous Cops and Robbers game. It can be considered as a game theoretic variant of the metric dimension of a graph. We provi...
متن کامل