PBS Infinite Series | How Many Cops to Catch a Robber? | Infinite Series @pbsinfiniteseries | Uploaded 7 years ago | Updated 3 hours ago
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Last episode, we used graph theory to figure out how a cop could catch a robber. But what happens when we introduce multiple cops? What happens if you have "lazy" cops or "drunk" robbers?
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Previous Episode
The Cops and Robbers Theorem | Infinite Series
youtube.com/watch?v=9mJEu-j1KT0
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 âoccupiesâ 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. Weâll assume that the cop always goes first. If, eventually, the cop lands on the robberâs vertex, the game is over -- we say that the game is a âwinâ 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
What is Cop Number? -Anthony Bonato
http://www.math.ryerson.ca/~abonato/papers/whatis_copnumber_new.pdf
The Game of Cops and Robbers on Graph - Anthony Bonato and Richard Nowakowski
Anthony Bonato -- "What is... Cops and Robbers"
http://www.ams.org/notices/201208/rtx120801100p.pdf
Special Thanks to Anthony Bonato and Brendan Sullivan
Big 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!
Viewers like you help make PBS (Thank you đ) . Support your local PBS Member Station here: to.pbs.org/donateinfi
Last episode, we used graph theory to figure out how a cop could catch a robber. But what happens when we introduce multiple cops? What happens if you have "lazy" cops or "drunk" robbers?
Tweet at us! @pbsinfinite
Facebook: facebook.com/pbsinfinite series
Email us! pbsinfiniteseries [at] gmail [dot] com
Previous Episode
The Cops and Robbers Theorem | Infinite Series
youtube.com/watch?v=9mJEu-j1KT0
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 âoccupiesâ 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. Weâll assume that the cop always goes first. If, eventually, the cop lands on the robberâs vertex, the game is over -- we say that the game is a âwinâ 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
What is Cop Number? -Anthony Bonato
http://www.math.ryerson.ca/~abonato/papers/whatis_copnumber_new.pdf
The Game of Cops and Robbers on Graph - Anthony Bonato and Richard Nowakowski
Anthony Bonato -- "What is... Cops and Robbers"
http://www.ams.org/notices/201208/rtx120801100p.pdf
Special Thanks to Anthony Bonato and Brendan Sullivan
Big 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!
