Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, October 25, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Konstantinos Panagiotou

On the Chromatic Number of Random Graphs

Determining the chromatic number of a graph is a fundamental though notoriously hard computational problem. Therefore, a large number of heuristics, i.e., efficient algorithms that are supposed to yield "reasonable" results on "most" instances, were developed. In order to understand and quantify rigorously the performance of such algorithms, their behavior is analyzed on random graphs. Hence, the asymptotic structure of the considered random graph model is strongly related to the design and the analysis of algorithms for the coloring problem.

In this talk we will consider one of the most studied random graph models, namely the binomial random graph G_{n,p}. Our main focus is on the chromatic number chi(G_{n,p}), where p = p(n) is asymptotically smaller than n^{-3/4}. We prove that almost surely chi(G_{n,p}) is k, k+1, or k+2, where k is the maximum integer satisfying 2(k-1)\log(k-1) < np. This improves the currently best bounds, which locate chi(G_{n,p}) in an interval of unbounded size.

Joint work with Amin Coja-Oghlan and Angelika Steger.

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