Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, June 16, 2020.

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Tuesday, June 16, 2020

2:00 pm in Zoom,Tuesday, June 16, 2020

#### Longest cycles in $3$-connected hypergraphs and bipartite graphs

###### Misha Lavrov (University of Illinois, Urbana-Champaign)

Abstract: Take a bipartite graph $G$ with bipartition $(X,Y)$ such that $|X|=n$ and $|Y|=m \ge n$. In general, this can't possibly be Hamiltonian, but we can still hope to find a cycle of length $2n$, covering $X$. We show that if $G$ is $3$-connected and the minimum degree in $X$ is at least $\max\{n, \frac{m+10}{4}\}$, then such a cycle always exists; this bound is best possible. In the language of hypergraph, this gives a Dirac-type condition for Hamiltonian Berge cycles in $3$-connected hypergraphs.

This is joint work with Alexandr Kostochka, Ruth Luo, and Dara Zirlin.

Please email Sean at SEnglish (at) illinois (dot) edu for the Zoom ID and password.