Mixing properties and the chromatic number of Ramanujan complexes
  Ramanujan complexes are high dimensional simplical complexes generalizing Ramanujan graphs. A result of Oh on quantitative property (T) for Lie groups over local fields is used to deduce a Mixing Lemma for such complexes. As an application we prove that non-partite Ramanujan complexes have 'high girth' and high chromatic number, generalizing a well known result about Ramanujan graphs. 
Shai Evra, Konstantin Golubev, Alexander Lubotzky
math.CO math.GR math.RT