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Asymptotic properties of the connectivity number of random railways

Part of: Graph theory Combinatorial probability Limit theorems

Published online by Cambridge University Press:  01 July 2016

Hans Garmo
Hans Garmo*
Affiliation:
Uppsala University
*
∗ Postal address: Department of Mathematics, Uppsala University, Box 480, S75106 Uppsala, Sweden.
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Abstract

In a cubic multigraph certain restrictions on the paths are made to define what is called a railway. On the tracks in the railway (edges in the multigraph) an equivalence relation is defined. The number of equivalence classes induced by this relation is investigated for a random railway achieved from a random cubic multigraph, and the asymptotic distribution of this number is derived as the number of vertices tends to infinity.

Keywords

Random railwayconnectivity numberbinary branching processcubic multigraph

MSC classification

Primary: 60F05: Central limit and other weak theorems 05C40: Connectivity 05C80: Random graphs
Secondary: 60C05: Combinatorial probability 05C38: Paths and cycles
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 31 , Issue 3 , September 1999 , pp. 720 - 741
Copyright
Copyright © Applied Probability Trust 1999 

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References

Bender, E. A. and Canfield, E. R. (1978). The asymptotic number of labelled graphs with given degree sequences. J. Combin. Theory A, 24, 296–307.CrossRefGoogle Scholar
Billingsley, P. (1968). Convergence of Probability Measures. Wiley, New York.Google Scholar
Bollobás, B., (1980). A probabilistic proof of an asymptotic formula for the number of labelled regular graphs. Eur. J. Combinatorics 1, 311–316.CrossRefGoogle Scholar
Bollobás, B., (1985). Random Graphs. Academic Press, London.Google Scholar
Feller, W. (1950). An Introduction to Probability Theory and its Applications. Wiley, New York.Google Scholar
Garmo, H. (1996). Random railways modeled as random 3-regular graphs. Random Struct. Alg. 9, 113–136.3.0.CO;2-#>CrossRefGoogle Scholar
Gondran, M. and Minoux, M. (1984). Graphs and Algorithms. Wiley, New York.Google Scholar
Wormald, N. C. (1978). Some problems in the enumeration of labelled graphs. , Newcastle University.Google Scholar