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Random Graphs from a Minor-Closed Class

Published online by Cambridge University Press:  01 July 2009

COLIN McDIARMID
COLIN McDIARMID*
Affiliation:
Department of Statistics, Oxford University (e-mail: cmcd@stats.ox.ac.uk)
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Abstract

A minor-closed class of graphs is addable if each excluded minor is 2-connected. We see that such a class of labelled graphs has smooth growth; and, for the random graph Rn sampled uniformly from the n-vertex graphs in , the fragment not in the giant component asymptotically has a simple ‘Boltzmann Poisson distribution’. In particular, as n → ∞ the probability that Rn is connected tends to 1/A(ρ), where A(x) is the exponential generating function for and ρ is its radius of convergence.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 18 , Issue 4 , July 2009 , pp. 583 - 599
Copyright
Copyright © Cambridge University Press 2009

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