Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, November 07, 2017, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Dmitry Shabanov (Lomonosov Moscow State University)

On the chromatic number of a sparse random hypergraph

The talk deals with estimating the chromatic number of a random n-vertex k-uniform hypergraph in the binomial model H(n,k,p). We concentrate on the sparse regime when the expected number of edges is a linear function of n. It is well known that in this case the chromatic number of H(n,k,p) is bounded and has a two point concentration. We give a new lower bound for the probability threshold for r-colorability property, which improves the previous result of Dyer, Freeze and Greenhill (2015) and complements the recent result of Ayre, Coja-Oghlan and Greenhill. The proof is based on a simple approach to the second moment method.

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