Year: 2013
Type: preprint
Abstract: In this short paper we study the game of Cops and Robbers, played on the vertices of some fixed graph $G$ of order $n$. The minimum number of cops required to capture a robber is called the cop number of $G$. We show that the cop number of graphs of diameter 2 is at most $\sqrt{2n}$, improving a recent result of Lu and Peng by a constant factor. We conjecture that this bound is still not optimal, and obtain some partial results towards the optimal bound.
Source: arXiv (Cornell University)
Author: Wagner, Zsolt Adam
Institution: University of Illinois Urbana-Champaign
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950504367