Characterization of some subgraphs of point-collinearity graphs of building geometries

Authors:
Anna Kasikova
Affiliations:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States
Venue:
European Journal of Combinatorics
Year:
2007

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Abstract

Let B be a building over a type set I. Suppose J@?I meets every connected component of the diagram of B and let (P,L) be the point-line truncation of the J-Grassmann geometry of B. We present a theorem that allows one to identify shadows of apartments of residues of B in the point-collinearity graph of (P,L). Also, other results related to shadows of apartments of residues and shadows of residues are presented, including a proof of the fact that the shadow of every residue of B is a convex subspace of (P,L).