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Keywords:

  • cop number;
  • Meyniel's conjecture;
  • cop–robber game

Abstract

Meyniel conjectured that the cop number c(G) of any connected graph G on n vertices is at most inline image 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 inline image, improving the best previously known upper-bound O(n/ lnn) due to Chiniforooshan.