Multi angle Random cubic planar graphs revisited
Auteurs : Rué, Juanjo (Auteur de la Conférence)
CIRM (Editeur )
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Résumé : We analyze random labelled cubic planar graphs according to the uniform distribution. This model was analyzed first by Bodirsky et al. in a paper from 2007. Here we revisit and extend their work. The motivation for this revision is twofold. First, some proofs where incomplete with respect to the singularity analysis and we provide full proofs. Secondly, we obtain new results that considerably strengthen those known before. For instance, we show that the number of triangles in random cubic planar graphs is asymptotically normal with linear expectation and variance, while formerly it was only known that it is linear with high probability.Codes MSC :
This is based on a joint work with Marc Noy (UPC) and Clément Requilé (FU Berlin - BMS).
05A16 - Asymptotic enumeration
05C10 - Planar graphs; geometric and topological aspects of graph theory
05C80 - Random graphs
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