A calculus for the random generation of labelled combinatorial structures
Theoretical Computer Science
Boltzmann Samplers for the Random Generation of Combinatorial Structures
Combinatorics, Probability and Computing
Journal of Combinatorial Theory Series B
Random planar graphs with n nodes and a fixed number of edges
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On properties of random dissections and triangulations
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Analytic Combinatorics
Vertices of given degree in series-parallel graphs
Random Structures & Algorithms
Degree distribution in random planar graphs
Journal of Combinatorial Theory Series A
Asymptotic Study of Subcritical Graph Classes
SIAM Journal on Discrete Mathematics
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In this work we determine the expected number of vertices of degree k = k(n) in a graph with n vertices that is drawn uniformly at random from a subcritical graph class. Examples of such classes are outerplanar, series-parallel, cactus and clique graphs. Moreover, we provide exponentially small bounds for the probability that the quantities in question deviate from their expected values.