Colloquium Mathematics / Dr. V.S. Patel
Title:
Quasi Ramsey problems
Abstract:
Ramsey theory is currently one of the most active areas of research in combinatorics. The seminal question in the area, raised by Ramsey in 1930 can be formulated as follows: how large does n have to be to guarantee that in any room with n people we can find a set S of k people such that either every pair in S is acquainted or every pair in S is not acquainted. It is not immediately clear that such an n exists, although it is not hard to show. On the other hand the known bounds for n as a function of k are quite poor.
I will give a gentle introduction to the Ramsey problem as well as variants of it. In particular I will discuss a relaxation of the problem above for which we are able to give quite precise bounds.
(This talk is based on joint work with Janos Pach, Ross Kang, Eoin Long and Guus Regts.)
Colloquium coordinators are Prof.dr. A.J. van der Schaft (
a.j.van.der.schaft@rug.nl
),
Dr. A.V. Kiselev (e-mail:
a.v.kiselev@rug.nl
)
http://www.rug.nl/research/jbi/news/colloquia/mathematics-colloquia/
