## Proposed topics for student talks in the Mittagsseminar

For more information, visit the Mittagsseminar
website.

### A counterexample to the DeMarco-Kahn Upper Tail Conjecture

Matas Šileikis and Lutz Warnke,
**A counterexample to the DeMarco-Kahn Upper Tail Conjecture**,
arXiv preprint arXiv:1809.09595, 2018.

Given a fixed graph H, what is the probability that the number of copies of H
in the binomial random graph G(n, p) is at least twice its mean? This
intensively studied upper tail problem remains a challenge for researchers
still. DeMarco and Kahn proposed a conjecture in 2011 about the exponential rate
of decay of the probability above. However, in this manuscript the authors give
a surprisingly simple counterexample to the conjecture of DeMarco and Kahn as
well as several extensions and
generalisations.

Contact: Miloš Trujić, mtrujic@inf.ethz.ch, CAB G 33.2