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Abstract

Cops and Robbers is a turn-based game traditionally played on graphs. Similar to the classic children's game, one cop and one robber move along edges in a graph with the cop trying to catch the robber, and the robber trying to evade capture. In this article, we extend this game to oriented graphs. Although a complete characterization of 1-cop-win graphs is known, there is not yet a corresponding characterization for oriented graphs. Necessary conditions are described for an oriented graph to be 1-cop-win, and several results are provided toward finding sufficient conditions.

Author Bio

Elise Darlington is a 2014 graduate of Morningside College with a BS in Mathematics. She is currently teaching mathematics at Booker T. Washington High School in Pensacola, Florida.

Claire Gibbons is a 2014 graduate of Morningside College with a BS in Mathematics. She is currently pursuing a PhD in Mathematics at Oregon State University with an emphasis in Mathematics Education.

Kelly Guy graduated from Morningside College in 2014 with a major in mathematics and a minor in physics. He started working on this research in Fall 2013. Kelly presented the findings at the University of South Dakota. He currently works for the Siouxland Community Health Center as a Quality and Data Analyst for the HIV Center..

Jon Hauswald graduated from Morningside College in 2014. He is currently working at Sioux Center High School in the Mathematics Department.

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