Channel: PBS Infinite Series

Category: Education

Tags: pbscopsgamevertexgraph theorymathematicsverticesmathslazydeterministicrobbersrandompathgraphsdrunkstochasticwinprobabilityfiniteedgesanalysisgraphpathsmathmathematical

Description: Viewers like you help make PBS (Thank you 😃) . 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 “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 (kornhaberbrown.com) Resources: M. Aigner and M. Fromme -- A Game of Cops and Robbers: math.ucdavis.edu/~erikslivken/classes/2016_spring_180/aigner%20fromme.pdf What is Cop Number? -Anthony Bonato 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" 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!