Antipodal Metrics and Split Systems

Dress A, Huber KT, Moulton V (2002)
European Journal of Combinatorics 23(2): 187-200.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Dress, AndreasUniBi; Huber, Katharina T.; Moulton, Vincent
Abstract / Bemerkung
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. (C) 2002 Academic Press.
Erscheinungsjahr
2002
Zeitschriftentitel
European Journal of Combinatorics
Band
23
Ausgabe
2
Seite(n)
187-200
ISSN
0195-6698
Page URI
https://pub.uni-bielefeld.de/record/1615283

Zitieren

Dress A, Huber KT, Moulton V. Antipodal Metrics and Split Systems. European Journal of Combinatorics. 2002;23(2):187-200.
Dress, A., Huber, K. T., & Moulton, V. (2002). Antipodal Metrics and Split Systems. European Journal of Combinatorics, 23(2), 187-200. https://doi.org/10.1006/eujc.2001.0556
Dress, A., Huber, K. T., and Moulton, V. (2002). Antipodal Metrics and Split Systems. European Journal of Combinatorics 23, 187-200.
Dress, A., Huber, K.T., & Moulton, V., 2002. Antipodal Metrics and Split Systems. European Journal of Combinatorics, 23(2), p 187-200.
A. Dress, K.T. Huber, and V. Moulton, “Antipodal Metrics and Split Systems”, European Journal of Combinatorics, vol. 23, 2002, pp. 187-200.
Dress, A., Huber, K.T., Moulton, V.: Antipodal Metrics and Split Systems. European Journal of Combinatorics. 23, 187-200 (2002).
Dress, Andreas, Huber, Katharina T., and Moulton, Vincent. “Antipodal Metrics and Split Systems”. European Journal of Combinatorics 23.2 (2002): 187-200.

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