Date of Graduation
Spring 2020
Degree
Master of Science in Mathematics
Department
Mathematics
Committee Chair
Richard Belshoff
Abstract
In graph theory, the game of cops and robbers is played on a finite, connected graph. The players take turns moving along edges as the cops try to capture the robber and the robber tries to evade capture forever. This game has received quite a bit of recent attention including several conjectures that have yet to be proven. In this paper, we restricted our attention to planar graphs in order to try to prove the conjecture that the dodecahedron graph is the smallest planar graph, in terms of vertices, that has cop number three. Along the way we discuss several other graphs with interesting properties connected with the cop number including a proof that the Tutte graph has cop number two.
Keywords
cop number, graph, retraction, planar, cop win, dodecahedron, tutte graph
Subject Categories
Discrete Mathematics and Combinatorics
Copyright
© Jordon S. Daugherty
Recommended Citation
Daugherty, Jordon S., "The Game of Cops and Robbers on Planar Graphs" (2020). MSU Graduate Theses. 3522.
https://bearworks.missouristate.edu/theses/3522
