Joint Student Colloquium

John J.C. Saunders, Department of Pure Mathematics, University of Waterloo

"Sieve Methods in Random Graph Theory"

Here we develop the use of some specific sieves called the Turan Sieve and the Simple Sieve first developed by Paul Turan in 1934. Here we use these sieves to solve problems in random graph theory. More specifically, we look at sets of graphs with an arbitrary number of vertices $n$  and allow the probability of any edge appearing in a graph to be expressed as a function in terms of $n$, denoting it by $p(n)$. From this, we obtain bounds on the probability of a graph having diameter $2$ (or diameter $3$ in the case of bipartite graphs) from the asymptotics for the function $p(n)$. This is joint work with Yu-Ru Liu.

MC 5501