 
Summary: On a Generalization of Meyniel's Conjecture
on the Cops and Robbers Game
Noga Alon
Tel Aviv University
and Institute for Advanced Study, Princeton
nogaa@tau.ac.il
Abbas Mehrabian
Department of Combinatorics and Optimization
University of Waterloo
amehrabian@uwaterloo.ca
Abstract
We consider a variant of the Cops and Robbers game where the robber can move s edges at a
time, and show that in this variant, the cop number of a connected graph on n vertices can be as
large as (n
s
s+1 ). This improves the (n
s3
s2 ) lower bound of Frieze et al. [5], and extends the result
of the second author [10], which establishes the above bound for s = 2, 4.
1 Introduction
