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

Date and Time: Tuesday, November 15, 2016, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Ralph Keusch

Lower and Upper Bounds for the general Colorability Saturation Game

We study the following two-player-game: Mini and Maxi start with the empty graph on n vertices and take turns in which they add an edge such that the graph remains k-colorable. The process stops when the graph is saturated, i.e., a complete k-partition. Mini wants that this happens as soon as possible, while Maxi aims to play for as long as possible. The score s(n,k) denotes the number of edges of the final graph, given that both players follow an optimal strategy. In this talk, we improve a previous result of Hefetz, Krivelevich, Naor, and Stojakovic, and provide almost-matching lower and upper bounds on s(n,k).

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