Graph Theory

着色和流是图论中两个重要而又有历史意义的子域。平面图的色性一直是研究的一个主要领域。波斯尔博士感兴趣的是证明推广到更大类图的定理，要么是关于通过对其他图不变量的限制进行图着色的，要么是使用嵌入在拓扑面上的图的自然对偶到顶点着色的流。波斯尔博士的研究计划是开发结构技术来证明着色或流的存在，或者理解没有所需着色或流的最小图。其动机是为了解决这些领域一些深层次和长期存在的猜测。

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.