Graph Theory

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Coloring and flows are two important and storied subfields in graph theory. A major area of study has been the chromatic properties of planar graphs. Dr. Postle is interested in proving theorems that extend to larger classes of graphs, either about graph coloring through restrictions on other graph invariants, or, using flows which are the natural dual to vertex coloring for graphs embedded on topological surfaces. Dr. Postle's research plan is to develop structural techniques to prove the existence of colorings or flows or to understand the minimal graphs which do not have the desired coloring or flow. The motivation is to solve a number of deep and long-standing conjectures in these areas.