Variations on cops and robbers

Alan Frieze, Michael Krivelevich, Po Shen Loh

Research output: Contribution to journalArticlepeer-review

Abstract

We consider several variants of the classical Cops and Robbers game. We treat the version where the robber can move R≤yen;1 edges at a time, establishing a general upper bound of n/,α(1-0(1)) √logαn, 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≤yen;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.

Original languageEnglish
Pages (from-to)383-402
Number of pages20
JournalJournal of Graph Theory
Volume69
Issue number4
DOIs
StatePublished - Apr 2012

Keywords

  • Cop number
  • Games on graphs
  • Meyniel's conjecture

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