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.

Additional Details

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

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