The Cops and Robbers Theorem | Infinite Series

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Can a cop catch a robber? There's some surprising and compelling graph theory that go into answering that question.

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Cops and Robbers is played on a finite and connected graph - meaning that any two vertices are joined by a path of edges. The game begins by placing a cop and a robber each on a single vertex; we say it “occupies” that vertex. They alternate moving along the edges, from a vertex to neighboring vertex. Or, on any given turn, the player can choose to not move -- to stay where they are. We’ll assume that the cop always goes first. If, eventually, the cop lands on the robber’s vertex, the game is over -- we say that the game is a “win” for the cop. But, if the robber can avoid the cop indefinitely, we say that the game is a win for the robber.

Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux
Assistant Editing and Sound Design by Mike Petrow
Made by Kornhaber Brown (www.kornhaberbrown.com)

Resources:

M. Aigner and M. Fromme -- A Game of Cops and Robbers:
https://www.math.ucdavis.edu/~erikslivken/classes/2016_spring_180/aigner%20fromme.pdf

The Game of Cops and Robbers on Graphs - Anthony Bonato and Richard Nowakowski

Anthony Bonato -- "What is... Cops and Robbers" http://www.ams.org/notices/201208/rtx120801100p.pdf

Brendan W. Sullivan, Nikolas Townsend, Mikayla Werzanski - “An Introduction to Lazy Cops and Robbers on Graphs,” to appear in College Mathematics Journal in 2017

Brendan W. Sullivan, Nikolas Townsend, Mikayla Werzanski "The 3x3 rooks graph is the unique smallest graph with lazy cop number 3" -- https://arxiv.org/abs/1606.08485

Special Thanks to Anthony Bonato and Brendan Sullivan

Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!

And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!

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