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On Meyniel's conjecture of the cop number
Authors:Linyuan Lu  Xing Peng
Affiliation:University of South Carolina, , Columbia, South Carolina 29208
Abstract:Meyniel conjectured that the cop number c(G) of any connected graph G on n vertices is at most urn:x-wiley:03649024:jgt20642:equation:jgt20642-math-0001 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 urn:x-wiley:03649024:jgt20642:equation:jgt20642-math-0002, improving the best previously known upper‐bound O(n/ lnn) due to Chiniforooshan.
Keywords:cop number  Meyniel's conjecture  cop–  robber game
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