# Recent Problems in Hypergraph Saturation

## Document Type

Presentation Abstract

## Presentation Date

10-31-2018

## Abstract

Extremal graph theory is the branch of mathematics concerned with maximizing or minimizing some parameter across a restricted set of graphs. The most studied problem in extremal graph theory involves maximizing the number of edges over all (simple) graphs on a fixed number of vertices that avoid a certain substructure. For example, the seminal problem in this field, solved by Mantel in 1907, studies the maximum number of edges over all triangle-free graphs on *n* vertices. This was later generalized to all complete graphs by Turán in 1941. In this talk, we will give a brief overview of extremal problems for graphs and hypergraphs (graphs where edges may contain more than two vertices), and then talk about some recent advances on the saturation problem, which is a minimization problem, in some sense the dual of the classical extremal question of maximizing the number of edges.

## Recommended Citation

English, Sean, "Recent Problems in Hypergraph Saturation" (2018). *Colloquia of the Department of Mathematical Sciences*. 550.

https://scholarworks.umt.edu/mathcolloquia/550

## Additional Details

Wednesday, October 31, 2018 at 3:00 p.m. in Math 103

Refreshments at 4:00 p.m. in Math Lounge 109