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Antipodal metrics and split systems
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
2002 (English)In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 23, no 2, p. 187-200Article in journal (Refereed) Published
Abstract [en]

Recall that a metric d on a finite set X is called antipodal if there exists a map sigma : X --> X: x --> (x) over bar so that d(x, (x) over bar) = d(x, y) + d(y, (x) over bar) holds for all x, y epsilon X. Antipodal metrics canonically arise as metrics induced on specific weighted graphs, although their abundance becomes clearer in light of the fact that any finite metric space can be isometrically embedded in a more or less canonical way into an antipodal metric space called its full antipodal extension. In this paper, we examine in some detail antipodal metrics that are, in addition, totally split decomposable. In particular, we give an explicit characterization of such metrics, and prove that-somewhat surprisingly-the full antipodal extension of a proper metric d on a finite set X is totally split decomposable if and only if d is linear or #X = 3 holds.

Place, publisher, year, edition, pages
2002. Vol. 23, no 2, p. 187-200
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-13674DOI: 10.1006/eujc.2001.0556ISI: 000173869900005Scopus ID: 2-s2.0-0036110215OAI: oai:DiVA.org:miun-13674DiVA, id: diva2:412185
Available from: 2011-04-21 Created: 2011-04-21 Last updated: 2017-12-11Bibliographically approved

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Huber, K. T.Moulton, Vincent

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