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The Department of Mathematics is a bustling place full of new ideas. We host several events that occur throughout the year, including seminars, colloquium, conferences, and social events. Our seminars and colloquium are open to the public: all students, faculty, or alumni who are interested are welcome to join us for exciting talks on the leading edge of mathematics research!

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Graph Theory and Combinatorics Seminar: Dirac's Theorem for Hamiltonian Berge cycles in uniform hypergraphs

Event Type
Seminar/Symposium
Sponsor
N/A
Location
345 AH
Date
Feb 8, 2022   1:00 pm  
Speaker
Grace McCourt (UIUC)
Contact
Sean English
E-Mail
senglish@illinois.edu
Views
5

The famous Dirac's Theorem gives an exact bound on the minimum degree of an n-vertex graph guaranteeing the existence of a Hamiltonian cycle. Last semester at this seminar, Ruth Luo presented exact bounds of similar type for Hamiltonian Berge cycles in r-uniform, n-vertex hypergraphs for all 2 < r < n. This talk will present bounds on the minimum degree guaranteeing existence of Berge cycles of length at least k in such hypergraphs. The bounds are exact for all k at least n/2, and the bounds differ for r less than n/2 and r at least n/2.

This is joint work with Alexandr Kostochka and Ruth Luo.

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