ISU DISCRETE MATHEMATICS SEMINAR

2017-2018

Time: 2:10-3:00pm Tuesdays       Place: 401 Carver

The Discrete Mathematics Seminar at Iowa State University is an eclectic mix of topics, including graph theory, combinatorics, linear algebra and abstract algebra. Presentations vary with the speaker and include the speaker's research, related research by others, and expository talks. Many of the expository talks (typically labeled as "Introduction to") are suitable for interested faculty and graduate students who are not specialists in the area.

Bernard Lidický
(lidicky AT iastate DOT edu)

Some talks are recorded and available to public on Youtube

### Fall 2018 Schedule

 Date Speaker Title Jul 27 Chris Cox Inverting the Tur\'an problem
Tentative visitors to come and be scheduled:

Classical questions in extremal graph theory concern the asymptotics of $\operatorname{ex}(G, \mathcal{H})$ where $\mathcal{H}$ is a fixed family of graphs and $G=G_n$ is taken from a standard'' increasing sequence of host graphs $(G_1, G_2, \dots)$, most often $K_n$ or $K_{n,n}$. Inverting the question, we can instead ask how large $|E(G)|$ can be with respect to $\operatorname{ex}(G,\mathcal{H})$. For example, we can ask: how many edges can $G$ have if any $10$ edges must contain an even cycle? or, how many edges can $G$ have if the largest star packing uses at most $20$ edges? (etc) We show that the standard sequences indeed maximize $|E(G)|$ for some choices of $\mathcal{H}$, but not for others. Many interesting questions and previous results arise very naturally in this context, which also, perhaps unusually, gives rise to sensible extremal questions concerning multigraphs and non-uniform hypergraphs. (Joint work with Joe Briggs)