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

Date and Time: Tuesday, January 21, 2014, 12:15 pm

Duration: 30 minutes

Location: CAB G11

Speaker: Bartosz Walczak (EPFL)

On-line coloring games and the chromatic number of geometric intersection graphs

The on-line graph coloring problem is modeled by a game between two players: Presenter, who constructs a graph of some fixed class presenting new vertices one by one, and Algorithm, who colors each vertex right after it is presented without the possibility of changing the color afterwards. The goal of Algorithm is to use as few colors as possible, while Presenter tries to force Algorithm to use many colors. Any game of this kind gives rise to a new class of graphs, called game graphs, each of which "encodes" some strategy of Presenter in the game. The chromatic number of such a game graph is equal to the number of colors that Algorithm is forced to use playing against the corresponding strategy. It turns out that game graphs of appropriately defined games can be characterized as intersection graphs of geometric objects. This allows us, for many classes of geometric intersection graphs, to provide lower and upper bounds on their maximum possible chromatic number by analyzing the corresponding on-line coloring games. I will present a survey of results obtained with this method and a detailed example of its application for constructing triangle-free geometric intersection graphs with large chromatic number.

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