# Positive co-degree problems for 3-graphs

## Document Type

Presentation Abstract

## Presentation Date

11-22-2021

## Abstract

How many lines can you place between *n* points before you are guaranteed to find a set of 4 points between which all 6 possible lines are present? How many 3-sets can you take from the first *n* integers before you are guaranteed to find a set of 4 integers among which all 4 possible 3-sets have been chosen? The first question is a basic problem in extremal graph theory. The second is also an extremal question -- this time to do with 3-graphs, a generalization of "normal" graphs in which edges contain 3 points instead of 2.

Extremal problems for hypergraphs (of which 3-graphs are a special type) are rich, interesting, and often very difficult. In this talk, we will introduce a new type of extremal hypergraph problem, that of maximizing the *positive co-degree *of a hypergraph subject to some forbidden sub-hypergraph. We will describe the connections between this question and other extremal questions on hypergraphs, and will present some exact results. Joint work with Cory Palmer and Nathan Lemons.

## Recommended Citation

Halfpap, Anna, "Positive co-degree problems for 3-graphs" (2021). *Colloquia of the Department of Mathematical Sciences*. 619.

https://scholarworks.umt.edu/mathcolloquia/619

## Additional Details

November 22, 2021 at 3:00 p.m. in Math 305