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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, February 17, 2015, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Marcelo Gauy

The classical Erdős-Ko-Rado Theorem answers the following question: given a set A with n elements, what is the largest size of a family of subsets of size k(k-subsets) such that every two of them intersect? If n is at least 2k, the answer is found to be the binomial number n-1 choose k-1. We study a probabilistic version of this problem: given a random family of all k-subsets of A, where each k-subset is kept with probability p, what is the largest size of a family of k-subsets, among the chosen ones, such that every two of them intersect? This is a random variable and we determine its behaviour for almost all functions k and p of n. For k asymptotically larger than $n^{1/2+\epsilon}$, our results imply that this random variable goes through three phases. In the first phase it has size almost equal to the number of k subsets of our random set. In the third phase, its size is what is expected from the Erdős-Ko-Rado Theorem: around p times the binomial number n-1 choose k-1. The intermediary phase represents the transition between the two regimes and the random variable almost does not grow as p increases. A similar version of this problem was first studied by Balogh, Bohman and Mubayi in 2008. In recent years, many different groups studied related versions of this problem. This is joint work with Hiêp Hàn and Igor Oliveira.

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

Previous talks by year: 2024 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