Lazy Cops and Robbers on Hypercubes

Deepak Bal, Anthony Bonato, William B. Kinnersley, PaweŁ PraŁat

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


We consider a variant of the game of Cops and Robbers, called Lazy Cops and Robbers, where at most one cop can move in any round. We investigate the analogue of the cop number for this game, which we call the lazy cop number. Lazy Cops and Robbers was recently introduced by Offner and Ojakian, who provided asymptotic upper and lower bounds on the lazy cop number of the hypercube. By coupling the probabilistic method with a potential function argument, we improve on the existing lower bounds for the lazy cop number of hypercubes.

Original languageEnglish
Pages (from-to)829-837
Number of pages9
JournalCombinatorics Probability and Computing
Issue number6
StatePublished - 1 Nov 2015


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