Graphs of Some CAT(0) Complexes

Author: Chepoi V.

Source: Advances in Applied Mathematics, Volume 24, Number 2, February 2000 , pp. 125-179(55)

Buy & download fulltext article:

Price: $52.63 plus tax (Refund Policy)

Abstract:

In this note, we characterize the graphs (1-skeletons) of some piecewise Euclidean simplicial and cubical complexes having nonpositive curvature in the sense of Gromov's CAT(0) inequality. Each such cell complex K is simply connected and obeys a certain flag condition. It turns out that if, in addition, all maximal cells are either regular Euclidean cubes or right Euclidean triangles glued in a special way, then the underlying graph G(K) is either a median graph or a hereditary modular graph without two forbidden induced subgraphs. We also characterize the simplicial complexes arising from bridged graphs, a class of graphs whose metric enjoys one of the basic properties of CAT(0) spaces. Additionally, we show that the graphs of all these complexes and some more general classes of graphs have geodesic combings and bicombings verifying the 1- or 2-fellow traveler property. Copyright 2000 Academic Press.

Language: English

Document Type: Research article

Affiliations: SFB343 Diskrete Strukturen in der Mathematik, Universität Bielefeld, Bielefeld, D-33615, Germany

Publication date: 2000-02-01