## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, April 06, 2017, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Alexey Pokrovskiy

## Fast draws in strong games

For an r-uniform hypergraph H, the strong Ramsey game SR(H,n) is a two player game defined as follows. The game is played on the edges of a complete r-uniform, n-vertex hypergraph K_n^r, and the players alternately claim edges of K_n^r. The first player to claim a copy of H wins the game. If neither player is able to build a copy of H, then the game is declared a draw. By an argument known as strategy stealing, the starting player is guaranteed at least a draw in SR(H,n) for every n and H. Moreover, it follows from Ramsey's Theorem that for fixed H and sufficiently large n there is no drawing position in SR(H,n). Therefore we know that the starting player wins the game as long as n is sufficiently large. However no explicit wining strategy is known for q ≥ 4. It is not even known whether the number of moves the starting player needs to win SR(H, n) should depend on n. When H is a (2-uniform) complete graph, Beck conjectured that there is some function f(q) such that for sufficiently large n, the starting player wins SR(Kq, n) in less than f(q) moves. This seminar will be about producing a hypergraph H for which starting player needs linearly many moves to win SR(H, n). This is joint work with Hefetz, Kusch, Narins, Requilé, and Sarid.

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