Patrolling cop vs omniscient robber
Nina Chiarelli, Paul Dorbec, Milo\v{s} Stojakovi\'c, Andrej Taranenko

TL;DR
This paper investigates a pursuit-evasion game where a cop follows a fixed patrol and a fully informed robber aims to evade capture, analyzing the minimum capture radius needed across various graph classes.
Contribution
It introduces and systematically studies the parameter (G), providing exact values for trees, bounds for grids, and analysis for chordal graphs, advancing understanding of pursuit-evasion with fixed patrols.
Findings
Exact (G) for trees
Bounds for (G) on grids
Analysis of (G) for chordal graphs
Abstract
We study a variant of the classical Cops and Robbers game with one cop and one robber, in which the cop follows a fixed walk on the graph, a patrol, that is chosen before the game begins, while the robber is omniscient, he knows the entire patrol in advance. A capture occurs when the robber comes within a given radius of capture of the cop. This model arises naturally at the intersection of recent work on limited-visibility games and offline versions of pursuit-evasion problems. By we denote the minimum radius of capture that the cop must have to always capture the robber on in this setting, under optimal play, where is a connected graph. We initiate a systematic study of this parameter for several graph classes. We determine the exact value of for trees, establish upper and lower bounds for grids, and analyze the parameter for various…
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Taxonomy
TopicsGuidance and Control Systems · Advanced Graph Theory Research · Complexity and Algorithms in Graphs
