Analytic combinatorics of non-crossing configurations
Discrete Mathematics - Special issue on selected papers in honor of Henry W. Gould
On the Number of Edges in Random Planar Graphs
Combinatorics, Probability and Computing
Analytic Combinatorics
Generating unlabeled connected cubic planar graphs uniformly at random
Random Structures & Algorithms
Series-Parallel Automata and Short Regular Expressions
Fundamenta Informaticae
Random graphs from a minor-closed class
Combinatorics, Probability and Computing
Growth constants of minor-closed classes of graphs
Journal of Combinatorial Theory Series B
Degree distribution in random planar graphs
Journal of Combinatorial Theory Series A
Asymptotic Study of Subcritical Graph Classes
SIAM Journal on Discrete Mathematics
Series-Parallel Automata and Short Regular Expressions
Fundamenta Informaticae
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We show that the number g"n of labelled series-parallel graphs on n vertices is asymptotically g"n~g@?n^-^5^/^2@c^nn!, where @c and g are explicit computable constants. We show that the number of edges in random series-parallel graphs is asymptotically normal with linear mean and variance, and that it is sharply concentrated around its expected value. Similar results are proved for labelled outerplanar graphs and for graphs not containing K"2","3 as a minor.