**ISU
D****ISCRETE**
**M****ATHEMATICS**
**S****EMINAR**

**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.

For more information, link to recodrings, or to get on the mailing list, please contact

Bernard Lidický
(lidicky AT iastate DOT edu)

Some talks are recorded and available to public on Youtube

Date |
Speaker |
Title |

Jul 27
| Chris Cox | Inverting the Tur\'an problem |

**Jul 27, 2018.** Chris Cox - Inverting the Tur\'an problem

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)

**Selected conferences in 2017-2018:**

- Oct 6-7, Allendale, Michigan, The 58th MIdwestern GrapH TheorY conference
- Jan 10-13, Joint Math Meeting San Diego, CA
- Mar 5-9, Florida Atlantic University, Boca Raton, FL, 49th Southeastern International Conference on Combinatorics, Graph Theory and Computing
- Apr 27-28, Morgantown, West Virginia, The 59th MIdwestern GrapH TheorY conference
- May 20-Jun 1, GRWC, Ames, IA
- Jun 4-8, University of Colorado Denver, Denver, CO, 19th SIAM Meeting on Discrete Mathematics (SIAM DM 2018)