Lazy Cops and Robbers on Hypercubes. (29th January 2015)

• Record Type: Journal Article
• Authors: BAL, DEEPAK; BONATO, ANTHONY; KINNERSLEY, WILLIAM B.; PRAŁAT, PAWEŁ
• Is Part Of: Combinatorics, probability and computing. Volume 24:Number 6(2015:Nov.)
• Page Start: 829
• Page End: 837
• Publication Date: 2015-01-29
• Subjects: Primary 05C57, -- Secondary 05C80; Combinatorial analysis -- Periodicals; Probabilities -- Periodicals; Computer science -- Mathematics -- Periodicals; 511.6
• DOI: 10.1017/S0963548314000807
• Languages: English
• ISSNs: 0963-5483

Abstract

Abstract : 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.