Arkiv för Matematik
- Ark. Mat.
- Volume 49, Number 1 (2011), 17-29.
Some combinatorial properties of flag simplicial pseudomanifolds and spheres
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.
Dedicated to Anders Björner on the occasion of his sixtieth birthday.
Supported by the 70/4/8755 ELKE Research Fund of the University of Athens.
Ark. Mat., Volume 49, Number 1 (2011), 17-29.
Received: 6 April 2009
First available in Project Euclid: 31 January 2017
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Athanasiadis, Christos A. Some combinatorial properties of flag simplicial pseudomanifolds and spheres. Ark. Mat. 49 (2011), no. 1, 17--29. doi:10.1007/s11512-009-0106-4. https://projecteuclid.org/euclid.afm/1485907125