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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, March 30, 2021, 12:15 pm

**Duration**: 30 minutes

**Location**: Zoom: conference room

**Speaker**: Matija Bucic

We consider the following question raised by Erdős and Hajnal in the early 90's. Over all n-vertex graphs G what is the smallest possible value of m for which any m vertices of G contain both a clique and an independent set of size log n? We construct examples showing that m is at most 2^{2^((loglog n)^(1/2+o(1)))} obtaining a twofold sub-polynomial improvement over the upper bound of about square root of n coming from the natural guess, the random graph. Our (probabilistic) construction gives rise to new examples of Ramsey graphs, which while having no very large homogeneous subsets contain both cliques and independent sets of size log n in any small subset of vertices. This is very far from being true in random graphs. Our proofs are based on an interplay between taking lexicographic products and using randomness. This is joint work with Noga Alon and Benny Sudakov.

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