Annals of Combinatorics 1 (1997) 183-196

Coordinatizing R-Trees in Terms of Universal c-Trees

Werner F. Terhalle

Research Center for Interdisciplinary Studies on Structure Formation (FSPM) Bielefeld University, Postbox 10 01 31, 33501 Bielefeld, Germany

Received February 26, 1997

AMS Subject Classification: 05B35, 05C05

Abstract. A complete R-tree T will be constructed such that, for every x \in T, the cardinality of the set of connected components of T\{x} is the same and equals a pre-given cardinality c; by this construction simultaneously the valuated matroid of the ends of this R-tree is given. In addition, for any arbitrary R-tree, an embedding into such a universal c-tree (for suitable c) will be constructed.

Keywords: R-trees, valuated matroids


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