William T. Trotter ( Georgia Institute of Technology) Stability Analysis for Posets

May 27, 2019 | 02:15 PM

Trivially, the maximum chromatic number of a graph on n vertices is n, and the only graph which achieves this value is the complete graph  K_n.  It is natural to ask whether this result is "stable", i.e.,  if n  is large, G  has n vertices and the chromatic number of G is close to n, must G  be close to being a complete graph? It is easy to see that for each  c>0, if  G  has n  vertices and chromatic number at least  nc, then it contains a clique whose size is at least  n−2c.

We will consider the analogous questions for posets and dimension.  Now the discussion will really become interesting.

Time & Location

May 27, 2019 | 02:15 PM

Technische Universität Berlin
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
Room MA 041 (Ground Floor)

Freie Universität Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
Deutsche Forschungsgemeinschaft (DFG)