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A Helly theorem in weakly modular space

✍ Scribed by Hans-Jürgen Bandelt; Victor Chepoi

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
772 KB
Volume
160
Category
Article
ISSN
0012-365X

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✦ Synopsis

The d-convex sets in a metric space are those subsets which include the metric interval between any two of its elements. Weak modularity is a certain interval property for triples of points. The d-convexity of a discrete weakly modular space X coincides with the geodesic convexity of the graph formed by the two-point intervals in X. The Helly number of such a space X turns out to be the same as the clique number of the associated graph. This result thus entails a Helly theorem for quasi-median graphs, pseudo-modular graphs, and bridged graphs.

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