check
Combinatorics: Zur Luria (ETH) | Einstein Institute of Mathematics

Combinatorics: Zur Luria (ETH)

Date: 
Mon, 12/12/201611:00-13:00
Location: 
B220 Rothberg (CS)
Speaker: Zur Luria (ETH)
Title: Hamiltonian spheres in random hypergraphs
Abstract:
Hamiltonian cycles are a fundamental object in graph theory, and combinatorics in general. A classical result states that in the random graph model G(n,p), there is a sharp threshold for the appearance of a Hamiltonian cycle. It is natural to wonder what happens in higher dimensions - that is, in random uniform hypergraphs?
How should one define a high-dimensional Hamiltonian cycle? Several definitions have been proposed. We consider one which we think is natural: A Hamiltonian d-sphere is a spanning triangulation of the d-dimensional sphere. Using the second moment method, together with some classical results on triangulations and a couple of new ideas, we show that there is a sharp threshold for the appearance of a Hamiltonian 2-sphere in a random 3-uniform hypergraph.
This is joint work with Ran Tessler.