Connectivity of chamber graphs of buildings and related complexes
2010 (English)In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 31, no 8, 2149-2160 p.Article in journal (Refereed) Published
Let Delta be a thick and locally finite building with the property that no edge of the associated Coxerer diagram has label "infinity". 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. In the language of building theory this means that every pair of chambers of Delta is connected by q pairwise disjoint galleries. Similar results are proved for the chamber graphs of Coxeter complexes and for order complexes of geometric lattices.
Place, publisher, year, edition, pages
2010. Vol. 31, no 8, 2149-2160 p.
IdentifiersURN: urn:nbn:se:kth:diva-26645DOI: 10.1016/j.ejc.2010.06.005ISI: 000282674700017ScopusID: 2-s2.0-77956182341OAI: oai:DiVA.org:kth-26645DiVA: diva2:374282
QC 201012032010-12-032010-11-262014-01-22Bibliographically approved