Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, February 14, 2017, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Zur Luria (ITS)

Hamiltonian spheres in random hypergraphs

Hamiltonian cycles are a fundamental object in graph theory. 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.

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