REU: Aspects of graph coloring
Project descriptionGraph coloring is one of the most fundamental and well-studied topics in graph theory. A proper coloring of a graph G is an assignment of labels (called colors) to the vertices of G such that adjacent vertices receive different labels. The chromatic number χ(G) of G is the minimum total number of colors necessary for a proper coloring of G. Recently, graph coloring theory has seen new exciting developments, including the introduction of far-reaching generalizations of graph coloring (for instance, the so-called correspondence coloring) and the discovery of novel powerful tools for approaching graph coloring problems (such as the opccupancy method coming from statistical mechanics). In this project, we will explore some these new avenues of research. |