The evolution of uniform random planar graphs

Details The evolution of uniform random planar graphs The evolution of uniform random planar graphs

2011-01-26

arxiv.org/abs/1101.5110v1

Electronic Journal of Combinatorics 17(1), #R7 (2010)

Mathematics

Combinatorics

20 pages, 11 figures

Scientific paper

Let P_{n,m} denote the graph taken uniformly at random from the set of all
planar graphs on {1,2,..., n} with exactly m(n) edges. We use counting
arguments to investigate the probability that P_{n,m} will contain given
components and subgraphs, finding that there is different asymptotic behaviour
depending on the ratio m/n.

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