Geodesic
The evolution of uniform random planar graphs
The electronic journal of combinatorics, Tome 17 (2010)
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Let $P_{n,m}$ denote the graph taken uniformly at random from the set of all planar graphs on $\{1,2, \ldots, n \}$ 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 ${m\over n}$.
DOI : 10.37236/279
Classification : 05C10, 05C80, 05C30
Mots-clés : Planar graphs, random graphs, isomorphic components, isomorphic subgraphs 
@article{10_37236_279,
     author = {Chris Dowden},
     title = {The evolution of uniform random planar graphs},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/279},
     zbl = {1189.05052},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/279/}
}
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Chris Dowden. The evolution of uniform random planar graphs. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/279

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