On Meyniel's conjecture of the cop number

Authors:
Linyuan Lu;Xing Peng
Affiliations:
University of South Carolina, Columbia, South Carolina 29208;University of South Carolina, Columbia, South Carolina 29208
Venue:
Journal of Graph Theory
Year:
2012

Citing 7
Cited 0

On a pursuit game played on graphs for which a minor is excluded

Journal of Combinatorial Theory Series B
Cops and robbers in graphs with large girth and Cayley graphs

Discrete Applied Mathematics
Regular Article: On the Cop Number of a Graph

Advances in Applied Mathematics
A better bound for the cop number of general graphs

Journal of Graph Theory
Cops and Robbers from a distance

Theoretical Computer Science
Chasing robbers on random graphs: Zigzag theorem

Random Structures & Algorithms
Variations on Cops and Robbers

Journal of Graph Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

Meyniel conjectured that the cop number c(G) of any connected graph G on n vertices is at most for some constant C. In this article, we prove Meyniel's conjecture in special cases that G has diameter 2 or G is a bipartite graph of diameter 3. For general connected graphs, we prove , improving the best previously known upper-bound O(n/ lnn) due to Chiniforooshan. © 2012 Wiley Periodicals, Inc. (Contract grant sponsor: NSF; contract grant numbers: DMS 0701111; DMS 1000475 (to L. L. and X. P.).)