Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, March 26, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, March 26, 2019

1:00 pm in Altgeld Hall,Tuesday, March 26, 2019

#### To Be Announced

1:00 pm in 345 Altgeld Hall,Tuesday, March 26, 2019

#### Cancelled

2:00 pm in 243 Altgeld Hall,Tuesday, March 26, 2019

#### Linearity of Saturation for Berge Hypergraphs

###### Sean English (Ryerson University)

Abstract: For a graph $F$, we say a hypergraph $H$ is Berge-$F$ if it can be obtained from $F$ be replacing each edge of $F$ with a hyperedge containing it. We say a hypergraph is Berge-$F$-saturated if it does not contain a Berge-$F$, but adding any hyperedge creates a copy of Berge-$F$. The $k$-uniform saturation number of Berge-$F$, $\mathrm{sat}_k(n,\text{Berge-}F)$ is the fewest number of edges possible over all Berge-$F$-saturated $k$-uniform hypergraphs on $n$ vertices.

In this talk we will explore some specific saturation numbers for Berge hypergraphs. We will also see that at least for small uniformities, these numbers grow linearly with $n$, extending a classical result of Kászonyi and Tuza. Finally, we will mention many interesting open problems in this area of research.

3:00 pm in 243 Altgeld Hall,Tuesday, March 26, 2019

#### No Seminar This Week

###### TBA

4:00 pm in 245 Altgeld Hall,Tuesday, March 26, 2019

#### Altgeld-Illini Renovation/Building Project Feedback Session

Abstract: This feedback session will focus on classrooms and technology