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Mathematics  2012 

Convex Hull of Face Vectors of Colored Complexes

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Abstract:

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.

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