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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, April 07, 2015, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Frank Mousset

I will talk about how one can determine asymptotically the probability that G(n,p) with p=o(n^{-1/2}) does not contain any triangles. The solution for p=o(n^{-2/3}) was given by Wormald in the 90s (following earlier work by Erdös and Rényi and Janson, Luczak and Rucinski). In this range, the answer is of the form exp(-A+B-C), where the terms A, B, and C correspond in a rather nice way to dependencies between one, two, and three triangles. Recently, we noticed that such a nice description can be given over the whole range p=o(n^{-1/2}). Our observation also applies in the more general setting of Janson's inequality, provided that certain natural conditions are met. The talk is based on joint work with A. Noever, K. Panagiotou, and W. Samotij.

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