Convex Hull of Face Vectors of Colored Complexes
  In this paper we verify a conjecture by Kozlov (Discrete Comput Geom 18 (1997) 421--431), which describes the convex hull of the set of face vectors of $r$-colorable complexes on $n$ vertices. As part of the proof we derive a generalization of Tur\'{a}n's graph theorem. 
Afshin Goodarzi
math.CO