Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

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

Mittagsseminar Talk Information

Date and Time: Thursday, April 23, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Rajko Nenadov

Upper bounds for asymmetric Ramsey properties of random hypergraphs

Transferring Ramsey's theorem from dense (complete) to sparse hypergraphs is a well-studied problem: Is there a red/blue coloring of the edges of the random k-uniform hypergraph such that there is no red copy of a k-uniform hypergraph F_1 and no blue copy of a k-uniform hypergraph F_2? While the symmetric (F_1 = F_2) and graph (k = 2) cases are reasonably well understood, nothing is known for the asymmetric (F_1 different from F_2) hypergraph (k > 2) case. In this talk, we present a proof of the upper bound for the threshold of the existence of such a coloring in this case, under certain mild technical assumption on F_1 and F_2. This extends the work of Kohayakawa and Kreuter, and Kohayakawa, Schacht and Spöhel, who proved the upper bound in the asymmetric graph case. Our proof is based on the hypergraph-containers lemma by Samotij, Balogh and Morris, and Saxton and Thomason.

Joint work with Luca Gugelmann, Yury Person, Angelika Steger, Henning Thomas, and Nemanja Škorić.

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