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Random Graphs from a Minor-Closed Class.

Abstract:

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

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Publication status:
Published

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Publisher copy:
10.1017/S0963548309009717

Authors


Journal:
Combinatorics, Probability and Computing
Volume:
18
Issue:
4
Pages:
583-599
Publication date:
2009-01-01
DOI:
EISSN:
1469-2163
ISSN:
0963-5483
URN:
uuid:85743fad-0945-4861-9716-03bf232bbd56
Source identifiers:
102283
Local pid:
pubs:102283
Language:
English

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