# An Introduction to Extremal Problems for Forests in Graphs and Hypergraphs

## Document Type

Presentation Abstract

## Presentation Date

4-24-2019

## Abstract

Extremal graph theory is the study of how the intrinsic structure of graphs ensures certain types of properties under appropriate conditions. One of the main problems in extremal graph theory is determining the Turán number for graphs. The Turán number, ex(*n,H*), of a graph *H* is deﬁned as the maximum number of edges in a graph on n vertices which does not contain *H* as a subgraph. A hypergraph is a generalization of a graph, except that instead of having edges that only made up of two vertices, their edges are sets of any number of vertices. Compared to what we know for graphs, there is much less known about hypergraph Turán problems. In this talk, we introduce the fundamentals of graph and hypergraph extremal theory. We present several classical results and conclude with the proof a new result on the extremal number for a particular hypergraph.

## Recommended Citation

Khormali, Omid, "An Introduction to Extremal Problems for Forests in Graphs and Hypergraphs" (2019). *Colloquia of the Department of Mathematical Sciences*. 556.

https://scholarworks.umt.edu/mathcolloquia/556

## Additional Details

Link to the presenter's dissertation.

Wednesday, April 24, 2019 3:00 pm in Math 211

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