Lazy Cops and Robbers on Hypercubes

Authors

Deepak Bal, Ryerson University
Anthony Bonato, Ryerson University
William B. Kinnersley, University of Rhode Island
PaweŁ PraŁat, Ryerson University

Document Type

Article

Date of Original Version

1-1-2015

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.

Publication Title, e.g., Journal

Combinatorics Probability and Computing

Volume

24

Issue

6

Citation/Publisher Attribution

Bal, Deepak, Anthony Bonato, William B. Kinnersley, and PaweŁ PraŁat. "Lazy Cops and Robbers on Hypercubes." Combinatorics Probability and Computing 24, 6 (2015): 829-837. doi: 10.1017/S0963548314000807.