Studies in graphs and matroids

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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 is aimed at understanding the 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. Theoretical considerations of the associated family of graphs 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.