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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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