Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

9-2018

Journal or Book Title

Discrete Mathematics

Volume

341

Issue

9

First Page

2418

Last Page

2430

DOI

10.1016/j.disc.2018.05.017

Abstract

We consider the cop-throttling number of a graph G for the game of Cops and Robbers, which is defined to be the minimum of (k + capt(k)(G)), where k is the number of cops and capt(k)(G) is the minimum number of rounds needed for k cops to capture the robber on G over all possible games. We provide some tools for bounding the cop-throttling number, including showing that the positive semidefinite (PSD) throttling number, a variant of zero forcing throttling, is an upper bound for the cop-throttling number. We also characterize graphs having low cop-throttling number and investigate how large the cop-throttling number can be for a given graph. We consider trees, unicyclic graphs, incidence graphs of finite projective planes (a Meyniel extrema] family of graphs), a family of cop-win graphs with maximum capture time, grids, and hypercubes. All the upper bounds on the cop throttling number we obtain for families of graphs are O(root n).

Comments

This is a manuscript of an article published as Breen, Jane, Boris Brimkov, Joshua Carlson, Leslie Hogben, K. E. Perry, and Carolyn Reinhart. "Throttling for the game of Cops and Robbers on graphs." Discrete Mathematics 341, no. 9 (2018): 2418-2430. DOI: 10.1016/j.disc.2018.05.017. Posted with permission.

Copyright Owner

Elsevier B.V.

Language

en

File Format

application/pdf

Available for download on Saturday, June 06, 2020

Published Version

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