Abstract
A simplicial complex Δ is called flag if all minimal nonfaces of Δ have at most two elements. The following are proved: First, if Δ is a flag simplicial pseudomanifold of dimension d−1, then the graph of Δ (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 Δ of dimension d−1 is minimized when Δ is the boundary complex of the d-dimensional cross-polytope.
Funding Statement
Supported by the 70/4/8755 ELKE Research Fund of the University of Athens.
Dedication
Dedicated to Anders Björner on the occasion of his sixtieth birthday.
Citation
Christos A. Athanasiadis. "Some combinatorial properties of flag simplicial pseudomanifolds and spheres." Ark. Mat. 49 (1) 17 - 29, April 2011. https://doi.org/10.1007/s11512-009-0106-4
Information