Lazy cops and robbers on generalized hypercubes

The lazy cop number is the minimum number of cops needed for the cops to have a winning strategy in the game of Cops and Robbers where at most one cop may move in any round. This variant of the game of Cops and Robbers, called Lazy Cops and Robbers, was introduced by Offner and Ojakian, who provided...

Full description

Saved in:
Bibliographic Details
Published in:Discrete mathematics 2017-07, Vol.340 (7), p.1693-1704
Main Authors: Sim, Kai An, Tan, Ta Sheng, Wong, Kok Bin
Format: Article
Language:English
Subjects:
Cops and Robbers
Hypercubes
Vertex-pursuit games
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The lazy cop number is the minimum number of cops needed for the cops to have a winning strategy in the game of Cops and Robbers where at most one cop may move in any round. This variant of the game of Cops and Robbers, called Lazy Cops and Robbers, was introduced by Offner and Ojakian, who provided bounds for the lazy cop number of the hypercube. In this paper, we are interested in the game of Lazy Cops and Robbers on generalized hypercubes. Generalizing existing methods, we will give asymptotic upper and lower bounds on the lazy cop number of the generalized hypercube.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2016.09.031