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

Date and Time: Tuesday, April 05, 2016, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Dániel Korándi

Domination in 3-tournaments

A 3-tournament is a complete 3-uniform hypergraph where each edge has a special vertex designated as its tail. A vertex set $X$ dominates $T$ if every vertex not in $X$ is contained in an edge whose tail is in $X$. The domination number of $T$ is the minimum size of such an $X$. Generalizing well-known results about usual (graph) tournaments, Gyárfás conjectured that there are 3-tournaments with arbitrarily large domination number, and that this is not the case if any four vertices induce two triples with the same tail. In this short talk I will solve both problems, proving the first conjecture and refuting the second.

Joint work with Benny Sudakov.

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