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On Generalized Random Railways

Published online by Cambridge University Press:  19 January 2004

HANS GARMO ,
SVANTE JANSON  and
MICHAŁ KAROŃSKI
HANS GARMO
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden (e-mail: hans.garmo@math.uu.se) http://www.math.uu.se/~svante
SVANTE JANSON
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden (e-mail: svante.janson@math.uu.se) http://www.math.uu.se/~svante
MICHAŁ KAROŃSKI
Affiliation:
Department of Discrete Mathematics, Adam Mickiewicz University, Poznań, Poland (e-mail: karonski@amu.edu.pl) Department of Mathematics and Computer Science, Emory University, Atlanta, USA (e-mail: michal@mathcs.emory.edu) http://main.amu.edu.pl/~karonski
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Abstract

We consider a random generalized railway defined as a random 3-regular multigraph where some vertices are regarded as switches that only allow traffic between certain pairs of attached edges. It is shown that the probability that the generalized railway is functioning is linear in the proportion of switches. Thus there is no threshold phenomenon for this property.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 13 , Issue 1 , January 2004 , pp. 31 - 35
Copyright
© 2004 Cambridge University Press

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