Min-max theorem for the game of Cops and Robber on geodesic spaces
Combinatorics
2021-12-07 v1 Metric Geometry
Optimization and Control
Abstract
The game of Cops and Robber is traditionally played on a finite graph. The purpose of this note is to introduce and analyze the game that is played on an arbitrary geodesic space. The game is defined in such a way that it preserves the beauty and power of discrete games played on graphs and also keeps the specialties of the pursuit-evasion games played on polyhedral complexes. It is shown that the game can be approximated by finite games of discrete type and as a consequence a min-max theorem is obtained.
Keywords
Cite
@article{arxiv.2112.03018,
title = {Min-max theorem for the game of Cops and Robber on geodesic spaces},
author = {Bojan Mohar},
journal= {arXiv preprint arXiv:2112.03018},
year = {2021}
}