Geodesic
Properties of Random Graphs via Boltzmann Samplers
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) (2007).

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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. 
@article{DMTCS_2007_special_253_a34,
     author = {Panagiotou, Konstantinos and Wei{\ss}l, Andreas},
     title = {Properties of {Random} {Graphs} via {Boltzmann} {Samplers}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07)},
     year = {2007},
     doi = {10.46298/dmtcs.3552},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3552/}
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Panagiotou, Konstantinos; Weißl, Andreas. Properties of Random Graphs via Boltzmann Samplers. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) (2007). doi : 10.46298/dmtcs.3552. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3552/

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