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

Date and Time: Tuesday, May 21, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Frank Mousset

Hypergraph Containers

This talk is about the recent Balogh-Morris-Samotij and Saxton-Thomason container theorems for independent sets in hypergraphs. In its most typical application, that of H-free graphs, these theorems state roughly that every H-free graph is contained in one of few graphs that are almost H-free.

We will see how such a theorem can be used to prove the following random version of Turán's Theorem: every H-free subgraph of G(n,p) contains at most (1-1/(χ(H)-1)+o(1))pn²/2 edges. Finally, we will present some ideas used in the proof of the container theorem by proving a simplified version due to Kleitman and Winston.

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