On a pursuit game played on graphs for which a minor is excluded
Journal of Combinatorial Theory Series B
On a pursuit game on Cayley graphs
Combinatorica
Cops and robbers in graphs with large girth and Cayley graphs
Discrete Applied Mathematics
On a game of policemen and robber
Discrete Applied Mathematics
On a pursuit game of Cayley diagraphs
European Journal of Combinatorics
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Regular Article: On the Cop Number of a Graph
Advances in Applied Mathematics
The complexity of pursuit on a graph
Theoretical Computer Science
Randomized Pursuit-Evasion with Local Visibility
SIAM Journal on Discrete Mathematics
A better bound for the cop number of general graphs
Journal of Graph Theory
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Pursuing a fast robber on a graph
Theoretical Computer Science
Cops and Robbers from a distance
Theoretical Computer Science
Chasing robbers on random graphs: Zigzag theorem
Random Structures & Algorithms
On Meyniel's conjecture of the cop number
Journal of Graph Theory
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We consider several variants of the classical Cops and Robbers game. We treat the version where the robber can move R≥1 edges at a time, establishing a general upper bound of , where α = 1 + 1/R, thus generalizing the best known upper bound for the classical case R = 1 due to Lu and Peng, and Scott and Sudakov. We also show that in this case, the cop number of an n-vertex graph can be as large as n1 − 1/(R − 2) for finite R≥5, but linear in n if R is infinite. For R = 1, we study the directed graph version of the problem, and show that the cop number of any strongly connected digraph on n vertices is O(n(loglogn)2/logn). Our approach is based on expansion. © 2011 Wiley Periodicals, Inc. J Graph Theory. © 2012 Wiley Periodicals, Inc. (Contract grant sponsor: NSF; Contract grant number: DMS-0753472 (to A. F.); Contract grant sponsor: USA-Israel BSF; Contract grant number: 2006322 (to M. K.); Contract grant sponsor: Israel Science Foundation; Contract grant number: 1063/08 (to M. K.); Contract grant sponsor: Pazy memorial award (to M. K.).)