English

Connectivity of chamber graphs of buildings and related complexes

Combinatorics 2012-07-24 v1

Abstract

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

Keywords

Cite

@article{arxiv.0907.0325,
  title  = {Connectivity of chamber graphs of buildings and related complexes},
  author = {Anders Björner and Kathrin Vorwerk},
  journal= {arXiv preprint arXiv:0907.0325},
  year   = {2012}
}

Comments

14 pages, 9 figures