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 A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, December 10, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Anders Martinsson

The edge statistics conjecture for small ℓ

Inspired by the problem of inducibility of graphs, a recent paper by Alon, Hefetz, Krivelevich and Tyomkyn posed the following problem. Given parameters ℓ, k and n what is the maximum probability, taken over all n-vertex graphs G, that k random vertices of G induces exactly ℓ edges? For ℓ equal to 0 or k choose 2, this is trivially one as attained by the empty and complete graphs respectively. Alon et al conjectured an upper bound of 1/e+o(1) for any other ℓ. A stronger version of this statement was shown by Kwan, Sudakov, and Tran (as seen in a past Mise 🙂) under the assumtion that ℓ is at least linear in k. In this talk I will present a simple argument that the bound holds also for small ℓ, thus resolving the conjecture affirmatively. This is joint work with Mousset, Noever and Trujić.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login