Combinatorics is a field of mathematics that has always fascinated me. Specifically, graph theory, a branch of combinatorics, has always piqued my interest. In general, graph theory deals with the study of mathematical structures, modeled by vertices with edges connecting them. While these graphs can be very simple, they can also get exceedingly complicated in structure; indeed, there are very interesting properties we can say about these graphs. The field is both enormously complex as well as incredibly enlightening … In the summer of ninth grade, I had my first experience with graph theory at a summer math camp called PROMYS.

Oftentimes, there are “bad guys” such as diseases, wildfires, or thieves that the “good guys” such as the CDC, firemen, or police wish to control or capture. However, the good guys only have a limited quantity of assets such as money, people, and time, so it is important for them to use the least amount of resources. One well-known way of analyzing such problems is known as “Cops and Robbers on a Graph”.