Graph Products and Colorings in Relation to the Hedetniemi Conjecture

There are many types of product operations defined in graph theory. These products use the vertices and edges of two (not necessarily distinct) graphs to create a new graph. We focus on four important types of graph products: the Cartesian product, the direct product, the strong product, and the lexicographic product. Additionally, we explore ways of labeling graphs through graph coloring and list coloring, and investigate the chromatic number of a graph. Finally, we relate both topics to one another by examining the Hedetniemi conjecture and researching what work as been done to try to prove or disprove the conjecture.