Contract grant sponsor: NSF; contract grant numbers: DMS 0701111; DMS 1000475 (to L. L. and X. P.).
On Meyniel's conjecture of the cop number
Article first published online: 22 NOV 2011
© 2011 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 71, Issue 2, pages 192–205, October 2012
How to Cite
Lu, L. and Peng, X. (2012), On Meyniel's conjecture of the cop number. J. Graph Theory, 71: 192–205. doi: 10.1002/jgt.20642
- Issue published online: 10 AUG 2012
- Article first published online: 22 NOV 2011
- Manuscript Revised: 9 AUG 2011
- Manuscript Received: 1 JUN 2010
- NSF. Grant Numbers: DMS 0701111, DMS 1000475
- cop number;
- Meyniel's conjecture;
- cop–robber game
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.