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Cops and robbers on graphs and hypergraphs

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thesis
posted on 22.05.2021, 17:04 by William David Baird
Cops and Robbers is a vertex-pursuit game played on a graph where a set of cops attempts to capture a robber. Meyniel's Conjecture gives as asymptotic upper bound on the cop number, the number of cops required to win on a connected graph. The incidence graphs of affine planes meet this bound from below, they are called Meyniel extremal. The new parameters mқ and Mқ describe the minimum orders of k-cop-win graphs. The relation of these parameters to Meyniel's Conjecture is discussed. Further, the cop number for all connected graphs of order 10 or less is given. Finally, it is shown that cop win hypergraphs, a generalization of graphs, cannot be characterized in terms of retractions in the same manner as cop win graphs. This thesis presents some small steps towards a solution to Meyniel's Conjecture.

History

Language

eng

Degree

Master of Science

Program

Applied Mathematics

Granting Institution

Ryerson University

LAC Thesis Type

Thesis

Thesis Advisor

Anthony Bonato