A study of cops and robbers in oriented graphs
Abstract
We consider the well-studied cops and robbers game in the context of oriented graphs, which has received surprisingly little attention to date.We examine the relationship between the cop numbers of an oriented graph and its underlying undirected graph, giving a surprising result that there exists at least one graph G for which every strongly connected orientation of G has cop number strictly less than that of G.We also refute a conjecture on the structure of cop-win digraphs, study orientations of outerplanar graphs, and study the cop number of line digraphs.Finally, we consider some aspects of the optimal play, in particular the capture time of cop-win digraphs and properties of the relative positions of the cop(s) and robber.
Fields of Study & Subjects
Advanced Graph Theory Research
Game Theory and Applications
Graph Labeling and Dimension Problems
Publication details
- Journal / source
- Discussiones Mathematicae Graph Theory
- Publisher
- University of Zielona Góra, Poland
- Volume
- 46
- Issue
- 4
- Pages
- 1057
- Publication date
- 1 January 2026
- Language
- EN