Isometric Embeddings of Finite Metric Timber into (Rn,d1) and (Rn,d∞)
Authors: Asuman Güven Aksoy, Mehmet Kiliç, Sahin Koçak
Summary: We examine isometric embeddings of finite metric bushes into (Rn,d1) and (Rn,d∞). We show {that a} finite metric tree will be isometrically embedded into (Rn,d1) if and provided that the variety of its leaves is at most 2n. We present {that a} finite star tree with at most 2n leaves will be isometrically embedded into (Rn,d∞) and a finite metric tree with greater than 2n leaves can’t be isometrically embedded into (Rn,d∞). We conjecture that an arbitrary finite metric tree with at most 2n leaves will be isometrically embedded into (Rn,d∞)
