Mixing Times of Tournaments

Abstract

Computer scientists have been interested in sampling uniformly from the space of graphs with a specified degree sequence. A degree sequence of a labelled graph, G = (V, E), is a sequence of natural numbers a_i for i in [n] where a_i represents the degree of vertex i \in V. Solving this problem has several implications in networking theory. In this thesis, we investigate a variant of this problem - sampling directed complete graphs of a certain out-degree sequence.