Journal article
Antipodal metrics and split systems
No matching items found.
Research Areas
No matching items found.
Publication Details
Author list: Huber, K. T.;Moulton, Vincent
Publication year: 2002
Start page: 187
End page: 200
Number of pages: 14
ISSN: 0195-6698
DOI: http://dx.doi.org/10.1006/eujc.2001.0556
View additional information: View in Web of Science™
Abstract
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.
Projects
No matching items found.
Keywords
No matching items found.
Documents
No matching items found.