## Combinatorics Seminar

When: Sunday, December 15, 10am
Where: Schreiber 309
Speaker: Tomasz Luczak, Adam Mickiewicz University at
Poznan
Title: On the chromatic number of generalized shift
graphs
## Abstract:

We study the chromatic number of graphs whose vertices are
k-subsets of {1,2,..., n}, and two vertices a_1< a_2< ...< a_k and
b_1 < b_2 < ... < b_k are adjacent if they interlace with each other
according to some given pattern, such as
a_1 < a_2 < b_1 < a_3 < b_4 < ... < a_{k-1} < b_{k-2} < a_k < b_{k-1} < b_k.
It is shown that the chromatic number of such graph grows
roughly as the iterated logarithm log_{(r)}n, where r=r(k) is
a linear function of k.
This is a joint work with Christian Avart and Vojtech Rodl.