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 for which every strongly connected orientation of has cop number strictly less than that of . 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 the aspects of optimal play, in particular the capture time of cop-win digraphs and properties of the relative positions of the cop(s) and robber.
Cite
@article{arxiv.1811.06155,
title = {A study of cops and robbers in oriented graphs},
author = {Devvrit Khatri and Natasha Komarov and Aaron Krim-Yee and Nithish Kumar and Ben Seamone and Virgélot Virgile and AnQi Xu},
journal= {arXiv preprint arXiv:1811.06155},
year = {2019}
}
Comments
23 pages, 4 figures. V2 contains an expanded introduction and an improvement on the original result on outerplanar graphs