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

Date and Time: Tuesday, April 29, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Henning Thomas

Balanced Online Ramsey Games in Random Graphs

We consider the following one-player game: The player, called Painter, starts with the empty graph on n vertices. In every step she is presented r edges drawn u.a.r. from all remaining ones, which she has to color instantly with r available colors using each color exactly once. Her goal is to avoid a monochromatic copy of a given fixed graph F as long as possible. Marciniszyn, Mitsche and Stojakovic proved a threshold phenomenon for the duration of this game for r=2 and a variety of graphs F, e.g. cycles. Using different techniques (the methods of first and second moment) we extend their result to an arbitrary number of colors and a larger class of graphs, e.g. cliques of size t if r \geq t. We also discuss ideas on a general threshold for arbitrary graphs.

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