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Lazy Cops and Robbers on Hypercubes

Part of: Graph theory

Published online by Cambridge University Press:  29 January 2015

DEEPAK BAL ,
ANTHONY BONATO ,
WILLIAM B. KINNERSLEY  and
PAWEŁ PRAŁAT
DEEPAK BAL
Affiliation:
Department of Mathematics, Ryerson University, Toronto, ON, Canada, M5B 2K3 (e-mail: deepak.c.bal@ryerson.ca, abonato@ryerson.ca, pralat@ryerson.ca)
ANTHONY BONATO
Affiliation:
Department of Mathematics, Ryerson University, Toronto, ON, Canada, M5B 2K3 (e-mail: deepak.c.bal@ryerson.ca, abonato@ryerson.ca, pralat@ryerson.ca)
WILLIAM B. KINNERSLEY
Affiliation:
Department of Mathematics, University of Rhode Island, Kingston, RI, USA, 02881 (e-mail: billk@mail.uri.edu)
PAWEŁ PRAŁAT
Affiliation:
Department of Mathematics, Ryerson University, Toronto, ON, Canada, M5B 2K3 (e-mail: deepak.c.bal@ryerson.ca, abonato@ryerson.ca, pralat@ryerson.ca)
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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.

MSC classification

Primary: 05C57: Games on graphs
Secondary: 05C80: Random graphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 24 , Issue 6 , November 2015 , pp. 829 - 837
Copyright
Copyright © Cambridge University Press 2015 

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