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Antipodal metrics a...
Antipodal metrics and split systems
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Dress, A (författare)
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- Huber, K. T. (författare)
- Mittuniversitetet,Uppsala universitet,Centrum för bioinformatik,V,Moulton,Institutionen för teknik, fysik och matematik (-2008)
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- Moulton, Vincent (författare)
- Mittuniversitetet,Institutionen för teknik, fysik och matematik (-2008)
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(creator_code:org_t)
- Elsevier BV, 2002
- 2002
- Engelska.
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Ingår i: European Journal of Combinatorics. - : Elsevier BV. - 0195-6698 .- 1095-9971. ; 23:2, s. 187-200
- Relaterad länk:
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https://doi.org/10.1...
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https://urn.kb.se/re...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- decomposition
- graphs
- MATHEMATICS
- MATEMATIK
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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