Jiangdong successfully defended his PhD thesis “Structure of directed graphs and hypergraphs”.
Jiangdong Ai at RHUL at christmas
The thesis consists of six papers in the general area of directed graphs and hypergraphs. Directed graphs have many applications which can be found in many areas, such as combinatorial optimization, network science, computer science and information security.
In the thesis various orientations of graphs are considered: One starts with an underlying undirected graph and asks, for instance, whether the edges of this graph can be oriented in such a way that neighbouring vertices have different in-degrees. This can in fact always be achieved by inductively removing a vertex of maximum degree and orienting all edges towards this vertex. The next natural step is to minimise the maximum in-degree of an orientation such that neighbouring vertices have different in-degrees. In the thesis various bounds are given for interesting classes of graphs and variants of this question. Other topics that are studied are the connection between “proximity” and “remoteness”, graph products and k-ary spanning subgraphs.
Jiangdong’s achievements are even more remarkable as the Covid pandemic had a massive impact on his time at Royal Holloway. Summer schools and conferences he had already been invited to were cancelled, and most of the meetings with his supervisors Stefanie Gerke and Gregory Gutin (Computer Science) had to take place remotely. We wish him all the best at his post-doc position at the State University of New York (SUNY Korea) and beyond!