# Noon lecture

list of noon lectures ( 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | newer lectures)

On 13.6.2013 at 12:20 in S6, there is the following noon lecture:

# Sparse halves in dense triangle-free graphs

## Liana Yepremyan

## McGill University

## Abstract

This talk is about one of well-known conjectures of Erdős stating that every triangle-free graph G on n vertices should contain a set of floor(n/2) vertices that spans at most n^2/50 edges. Krivelevich proved the conjecture for graphs with minimum degree at least 2n/5. Keevash and Sudakov improved this result to graphs with average at least 2n/5. We strengthen these results by showing that the conjecture holds for graphs with minimum degree at least 5n/14 and average degree at least (2/5-epsilon)n for some absolute epsilon>0.

list of noon lectures ( 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | newer lectures)

Webmaster: kamweb.mff.cuni.cz Archive page