Connectivity of chamber graphs of buildings and related complexes

Let be a finite building (or, more generally, a thick spherical and locally finite building). The chamber graph G(), whose edges are the pairs of adjacent chambers in , is known to be q-regular for a certain number q = q(). Our main result is that G() 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.

• Type: Journal
• Year: 2010
• Where: EJC
• Authors: Anders Björner, Kathrin Vorwerk
• Keywords: Adjacent Chambers, Chamber Graphs, EJC 2007, EJC 2010, Finite Building