Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**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

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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