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

Date and Time: Thursday, June 01, 2023, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Rajko Nenadov

The determinism of randomness: a game-theoretic approach

Consider the following two-player game played on the edges of Kn, a complete graph with n vertices: In each round the first player chooses b edges, which they have not previously chosen, and the second player immediately and irrevocably picks one of them and adds it to the initially empty graph G. The game ends when there are less than b edges that the first player can offer. The first player wins if G contains some graph H, which the players have agreed upon in advance, and otherwise the second player wins. How large can b be such that the first player has a winning strategy? The answer is closely related to random graphs and intuition we have about them. The proof is, at the same time, entirely deterministic and completely probabilistic.

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