## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Thursday, January 28, 2016 — 4:00 PM EST

**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

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.