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arXiv · 0907.0325

Connectivity of chamber graphs of buildings and related complexes

Anders Björner·Kathrin Vorwerk
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Abstract

Let Δbe a finite building (or, more generally, a thick spherical and locally finite building). The chamber graph G(Δ), whose edges are the pairs of adjacent chambers in Δ, is known to be q-regular for a certain number q=q(Δ). Our main result is that G(Δ) is q-connected in the sense of graph theory. Similar results are proved for the chamber graphs of Coxeter complexes and for order complexes of geometric lattices.

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Anders Björner, Kathrin Vorwerk. 2009-07-02. Connectivity of chamber graphs of buildings and related complexes. https://arxiv.org/abs/0907.0325

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