Local limit theorem in random graphs and graphs on non-constant surfaces - Saller, S (2019)
The thesis is split into two parts. In the first part we prove a local limit theorem for the number of appearances of the complete graph on four vertices, K4, in the Erdös-Rényi Random graph G(n, p) for p in (0, 1) a fixed constant. The proof of this is based on bounding the characteristic function of the number of K4 in G(n, p) by using different conditioning arguments for different ranges of t.