{"paper":{"title":"Connectivity of chamber graphs of buildings and related complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anders Bj\\\"orner, Kathrin Vorwerk","submitted_at":"2009-07-02T09:53:45Z","abstract_excerpt":"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.\n  Similar results are proved for the chamber graphs of Coxeter complexes and for order complexes of geometric lattices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0325","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}