Enumerative combinatorics
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
On the Degree Sequences of Random Outerplanar and Series-Parallel Graphs
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Analytic Combinatorics
On the Degree Sequences of Random Outerplanar and Series-Parallel Graphs
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
On the degree distribution of random planar graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
| Hi-index | 0.00 |
Let be a class of labeled connected graphs and let be the class of biconnected graphs in . In this paper we develop a general framework that allows us to derive mechanically the degree distribution of random graphs with nvertices from certain 'nice' classes as a function of the degree distribution of the graphs in that are drawn under a specific probabilistic model, namely the Boltzmann model. We apply this framework to obtain the degree distribution of a random outerplanar graph and a random series-parallel graph. For the latter we formulate a generic concentration result that allows us to make statements that are true with high probability for a large family of variables defined on random graphs drawn according to the Boltzmann distribution.