### Hamiltonian Cycles in Uniform Hypergraphs with Large Minimum Degree

- Series
- Combinatorics Seminar
- Time
- Friday, February 8, 2019 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Andrzej Rucinski – Emory and AMU Poznań

Abstract: Reiher, Rödl, Ruciński, Schacht, and Szemerédi proved, via a modification of the absorbing method, that every 3-uniform $n$-vertex hypergraph, $n$ large, with minimum vertex degree at least $(5/9+\alpha)n^2/2$ contains a tight Hamiltonian cycle. Recently, owing to a further modification of the method, the same group of authors joined by Bjarne Schuelke, extended this result to 4-uniform hypergraphs with minimum pair degree at least, again, $(5/9+\alpha)n^2/2$. In my talk I will outline these proofs and point to the crucial ideas behind both modifications of the absorbing method.