Topical Studies in Graph and Matroid Theory

图是一种数学抽象，用来对结构进行建模，表现出一种“离散”的性质。例如通信和运输网络、乘务调度、车辆路线、计算机芯片设计和数字设备。拟阵是比图更抽象的结构，对于理解几何、刚性和优化问题的良好算法至关重要。我的研究试图了解这种结构的基本属性，目的是优化各种感兴趣的参数。例如，在电影节上为场馆分配放映时间的问题可以被建模为一种图着色问题。我们知识的进步可以带来更好的调度算法。随着数字通信的出现，这种研究对于有效设计和部署新兴技术至关重要。

Graphs are mathematical abstractions which are used to model structures exhibiting a "discrete" nature. Examples include communication and transportation networks, crew scheduling, vehicle routing, computer chip design and digital devices. Matroids are structures which are more abstract than graphs, which are vital to the understanding of geometry, rigidity, and good algorithms for optimization problems. My research seeks to understand fundamental properties of such structures, with an aim toward optimizing various parameters of interest. For example, the problem of assigning shows to venues at a film festival can be modeled as a type of graph colouring problem. Advances in our knowledge can lead to improved scheduling algorithms. With the advent of digital communication such studies are vital to the efficient design and deployment of arising technologies.