Properties of Random Graphs via Boltzmann Samplers

Konstantinos Panagiotou (1) , Andreas Weissl (1)

1 Institute of Theoretical Computer Science [Zurich]

This work is devoted to the understanding of properties of random graphs from graph classes with structural constraints. We propose a method that is based on the analysis of the behaviour of Boltzmann sampler algorithms, and may be used to obtain precise estimates for the maximum degree and maximum size of a biconnected block of a "typical'' member of the class in question. We illustrate how our method works on several graph classes, namely dissections and triangulations of convex polygons, embedded trees, and block and cactus graphs.

Mots clés: Random graphs with structural constraints; Generating functions; Sampling algorithms

Domaines: Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]; Combinatoire [math.CO]; Géométrie algorithmique [cs.CG]

Konstantinos Panagiotou, Andreas Weissl. Properties of Random Graphs via Boltzmann Samplers. 2007 Conference on Analysis of Algorithms, AofA 07, 2007, Juan les Pins, France. pp.171-182, ⟨10.46298/dmtcs.3552⟩. ⟨hal-01184800⟩