Date of Submission
Spring 2012
Academic Program
Mathematics
Project Advisor 1
James Belk
Abstract/Artist's Statement
The Shannon switching game is a combinatorial game for two players, which we refer to as the cop and the robber. In this project, we explore a few variations of the original rules that make the game more interesting. One of these variations is a game involving multiple cops and one robber. We present a formal recursive definition of this game which we use to prove several basic theoretical results. Next, we consider this game on complete graphs and complete bipartite graphs. On each family of graphs, we investigate the winning conditions for the players depending on who goes first. We describe these conditions as functions and prove several asymptotic results. Finally, after looking at the variation with multiple cops and one robber, we also study the game with multiple cops and multiple robbers and compare the two variations.
Distribution Options
Access restricted to On-Campus only
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Recommended Citation
Wood, Kimberly Y., "Switching the Shannon Switching Game" (2012). Senior Projects Spring 2012. 292.
https://digitalcommons.bard.edu/senproj_s2012/292
This work is protected by a Creative Commons license. Any use not permitted under that license is prohibited.
Bard Off-campus DownloadBard College faculty, staff, and students can login from off-campus by clicking on the Off-campus Download button and entering their Bard username and password.