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

Date and Time: Thursday, June 27, 2019, 12:15 pm

Duration: 30 minutes

Location: CAB G 11

Speaker: Maxime Larcher

Win Conditions in Maker-Breaker Games on Uniform Hypergraphs

We study win conditions in Maker-Breaker games on uniform hypergraphs.

In a first step, we find an approximation of the minimal number of boxes required for the Maker to win on uniform box games. We then study a variation of the box game and show that, if few boxes are missing, adding few new edges on the remaining vertices suffices to have the Maker win.

In a second step, we find a win condition for the Maker based on the maximal degree of the hypergraph, still assuming uniformity.

Finally, we take a look at games on random hypergraphs and find threshold probabilities above which the Maker is able to win w.h.p.

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