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

Date and Time: Tuesday, July 30, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Ralph Keusch

The game chromatic number of dense random graphs

In this thesis we study the game in which two players take turns coloring the vertices of a given graph G with k colors. In each move the current player colors a vertex such that neighboring vertices get different colors. The first player wins if and only if at the end, all the vertices are colored. Then the game chromatic number χ_g(G) is defined as the smallest k for which the first player has a winning strategy.
We analyse this parameter for random graphs G_n,p, where p is a constant. We improve the existing results on this class of graphs and prove that with high probability, the game chromatic number χ_g(G_n,p) is exactly twice as large as the ordinary chromatic number χ(G_n,p).

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