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, May 29, 2012, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Luca Gugelmann

Sharp thresholds and hypergraph 2-colorability

A sharp threshold p0 for e.g. a monotone graph property A in the random graph G(n,p) is a function of n and A such that for any epsilon > 0 we have that for p < (1-epsilon)p0 the probability that A holds is asymptotically 0 while for (1+epsilon)p0 it is asymptotically 1. A threshold function which is not sharp is called coarse. Many interesting graph properties are conjectured to have sharp thresholds, however proving that this is the case (let alone determining p0 exactly) is pretty hard in general. In his PhD thesis Ehud Friedgut proved several results characterizing properties with coarse thresholds. These results then can be used to prove by contradiction that other thresholds must be sharp. In this talk I will give an overview of these results and present a nice proof by Friedgut and Alon showing that the threshold for 2-colorability of a k-uniform hypergraph (with k > 2) is sharp.

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