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Combinatorics, Complexity, and ChanceA Tribute to Dominic Welsh$
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Geoffrey Grimmett and Colin McDiarmid

Print publication date: 2007

Print ISBN-13: 9780198571278

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198571278.001.0001

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RANDOM PLANAR GRAPHS AND THE NUMBER OF PLANAR GRAPHS

RANDOM PLANAR GRAPHS AND THE NUMBER OF PLANAR GRAPHS

Chapter:
(p.213) 14 RANDOM PLANAR GRAPHS AND THE NUMBER OF PLANAR GRAPHS
Source:
Combinatorics, Complexity, and Chance
Author(s):

Marc Noy

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198571278.003.0014

This chapter surveys recent progress on the enumeration of labelled planar graphs and on the distribution of several parameters in random planar graphs. It shows how to use generating functions to obtain asymptotic estimates and limit probability laws. Emphasis is made on presenting the main ideas while keeping technical details to a minimum.

Keywords:   planar graphs, generating functions, asymptotic estimates, limit probability laws

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