MTA Rényi Alfréd Matematikai Kutatóintézet - Nagyterem 1053 Budapest, Reáltanoda u. 13-15.
Részletek
14:15 - 14:45 Péter Komjáth (ELTE)
Erdős, Hajnal, and the chromatic number of infinite hypegraphs
After a quick review of the work of Erdős and Hajnal on the chromatic number of infinite graphs, we survey their work (mostly joint with Galvin) on the parallel topic on hypergraphs and the results obtained since.
14:50 - 15:20 Endre Szemerédi (MTA Rényi Institute)
A theorem in graph theory
In 1969 we proved with Hajnal the following conjecture of Erdős:
Suppose that the degree of every node of the graph G is less than k; then the nodes of G can be partitioned into k independent sets such that the sizes of any two of the sets differ by at most one.
In this talk I will recall the history of this result and comment on its many variants that were produced since then.
15:25 - 15:55 István Juhász (MTA Rényi Institute)
The pinning down number
The pinning down number pd(X) of a topological space X is the smallest cardinal k such that for every neighbourhood assignement U on X there is a set of size k that meets every member of U.
It turns out that the question if pd(X) = d(X), the density of X, holds for various classes of spaces, like Hausdorff or regular spaces, is equivalent with a weak version of the generalized continuum hypothesis. This result answers two questions of Banakh and Ravsky.
