On Generalized Random Railways

Authors:
Hans Garmo;Svante Janson;Michał Karoński
Affiliations:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden, hans.garmo@math.uu.se, http://www.math.uu.se/~svante;Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden, svante.janson@math.uu.se, http://www.math.uu.se/~svante;Dept. of Disc. Math., Adam Mickiewicz Univ., Poznań, Poland, karonski@amu.edu.pl and Dept. of Math. and Comp. Sci., Emory Univ., Atlanta, USA, michal@mathcs.emory.edu, http://main.amu.edu.pl/ ...
Venue:
Combinatorics, Probability and Computing
Year:
2004

Citing 2
Cited 0

Threshold functions

Combinatorica
Random railways modeled as random 3-regular graphs

Proceedings of the seventh international conference on Random structures and algorithms

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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.