Date/Time: April 16 at 2pm
Speakers: Josiah Sweatt (UNT undergraduate), Angela Yuan (TAMS)
Mentors: Cody Olsen (UNT graduate), Dr. Nam Trang, Dr. Stephen Jackson
Title: The Game of Cops and Robbers: Tunnels and Other Interests
Abstract: The Game of Cops and Robbers is a turn-based game with perfect information wherein some number of cop pieces and a single robber are placed upon the vertices of a connected graph (finite or otherwise). The cops win if and only if on some turn a cop and the robber share a vertex; otherwise the robber wins. A few of our findings determine the cop number of a few different graphs, which means we found the least number of cops needed for them to win on those graphs. Another of our endeavors is to consider how the cop number of a graph behaves after we "tunnel" the graph. What we mean by this is to increase the length between each vertex by some natural number yielding a new "tunnel graph." We have successfully shown that the cop number of a tunnel graph has both lower and upper bounds relative to the original graph's cop number.