Summary: DOI:
c 2008 by Institut Mittag-Leffler. All rights reserved
Ark. Mat., 00 (2008), 1­12
Some combinatorial properties of flag simplicial
pseudomanifolds and spheres
Christos A. Athanasiadis
Dedicated to Anders Bj¨orner on the occasion of his sixtieth birthday
Abstract. A simplicial complex is called flag if all minimal nonfaces of have at most two
elements. The following are proved: First, if is a flag simplicial pseudomanifold of dimension d-
1, then the graph of (i) is (2d-2)-vertex-connected and (ii) has a subgraph which is a subdivision
of the graph of the d-dimensional cross-polytope. Second, the h-vector of a flag simplicial homology
sphere of dimension d-1 is minimized when is the boundary complex of the d-dimensional
cross-polytope.
1. Introduction
We will be interested in finite simplicial complexes. Such a complex is called
flag if every set of vertices which are pairwise joined by edges in is a face of
. For instance, every order complex (meaning the simplicial complex of all chains
in a finite partially ordered set) is a flag complex. According to [11, p. 100], flag
complexes form a fascinating class of simplicial complexes which deserves further
study. The class of flag complexes coincides with that of clique complexes of finite

Source: Athanasiadis, Christos - Department of Mathematics, University of Athens

Collections: Mathematics