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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The minimal spanning tree and the upper box dimension


Authors: Gady Kozma, Zvi Lotker and Gideon Stupp
Journal: Proc. Amer. Math. Soc. 134 (2006), 1183-1187
MSC (2000): Primary 68U05, 05C05
Published electronically: September 20, 2005
MathSciNet review: 2196055
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Abstract: We show that the $\alpha$-weight of an MST over $n$ points in a metric space with upper box dimension $d$ has a bound independent of $n$ if $\alpha>d$ and does not have one if $\alpha<d$.


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Additional Information

Gady Kozma
Affiliation: Institute for Advanced Study, 1 Einstein Drive, Princeton, New Jersey 08540
Email: gady@ias.edu

Zvi Lotker
Affiliation: Office Centrum voor Wiskunde en Informatica, Kruislaan, 413, NL-1098 SJ Amsterdam, The Netherlands
Email: zvilo@eng.tau.ac.il

Gideon Stupp
Affiliation: MIT Computer Science and Artificial Intelligence Laboratory, The Stata Center, 32 Vassar Street, Cambridge, Massachusetts 02139
Email: gstupp@theory.csail.mit.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08061-5
PII: S 0002-9939(05)08061-5
Received by editor(s): January 7, 2004
Received by editor(s) in revised form: October 25, 2004
Published electronically: September 20, 2005
Communicated by: John R. Stembridge
Article copyright: © Copyright 2005 American Mathematical Society