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

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

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

Duration: 30 minutes

Location: CAB G51

Speaker: Frank Mousset

The probability that G(n,p) is triangle-free

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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