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

Date and Time: Tuesday, October 21, 2003, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Tibor Szabó

Maker/Breaker games on the complete graph

Let P be some (possibly nice) graph theoretic property. We condsider certain games played on the complete graph, where this property P is somehow the focus of the game.
The players, called Maker and Breaker, alternately take edges which were not yet taken. At the end Maker wins, if the graph he obtained has property P, whereas Breaker wins if Maker's graph does not have P.

First I describe a classic method: the Erdos-Selfridge scoring system. Then we'll see some extension of it, which implies that Maker can create (1/4-\epsilon)*n edge-disjoint Hamiltonian cycles (where \epsilon tends to 0). This result is obviously best possible up to the \epsilon and confirms a conjecture of Lu.

(Joint work with A. Frieze, M. Krivelevich and O. Pikhurko.)

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