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

Date and Time: Tuesday, September 23, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Luca Gugelmann

Balanced Online Vertex-Coloring Games in Random Graphs

Consider the following game on an initially hidden random graph G_{n,p}: in each step r vertices are revealed together with all edges leading to previously revealed vertices. The player has r colors at her disposal and must assign a different color to each of the newly revealed vertices. The player wins if she manages to color all n vertices without creating a monochromatic copy of some fixed graph F. We prove an upper bound p_0(r,F,n) such that for p >> p_0 the player cannot avoid creating a monochromatic copy of F with probability tending to 1 for n tending to infinity, regardless of the chosen strategy. We believe this bound is tight in the sense that there is a strategy for the player such that for all p << p_0 she wins with probability tending to 1 for n to infinity.

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