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

Date and Time: Tuesday, October 15, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Miloš Stojaković (University of Novi Sad)

Maker-Breaker games on random geometric graphs

In a Maker-Breaker game on a graph G, Breaker and Maker alternately claim edges of G. Maker wins if, after all edges have been claimed, the graph induced by his edges has some desired property. A random geometric graph G(n,r) is obtained by choosing n points uniformly at random in the unit square; two points x and y are adjacent if their distance d(x,y) is at most r. The hitting radius for an increasing graph property P is inf{r>=0: G(n,r) satisfies P}. For each of four standard positional games, the connectivity game, the Hamilton cycle game, the perfect matching game and the H-game (for a fixed graph H), we show that the hitting radius of Maker's win on a random geometric graph is w.h.p. the same as the hitting radius of a simple graph-theoretic condition. This is joint work with Andrew Beveridge, Andrzej Dudek, Alan Frieze and Tobias Müller.

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