The number of planar graphs and properties of random planar graphs

Omer Gimenez; Marc Noy

doi:10.46298/dmtcs.3354

Omer Gimenez ; Marc Noy - The number of planar graphs and properties of random planar graphs

dmtcs:3354 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms - https://doi.org/10.46298/dmtcs.3354

The number of planar graphs and properties of random planar graphsArticle

Authors: Omer Gimenez ^1,²; Marc Noy ^1,²

We show an asymptotic estimate for the number of labelled planar graphs on $n$ vertices. We also find limit laws for the number of edges, the number of connected components, and other parameters in random planar graphs.

https://doi.org/10.46298/dmtcs.3354

Source: HAL:hal-01184026v1

Volume: DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms

Section: Proceedings

Published on: January 1, 2005

Imported on: May 10, 2017

Keywords: limit law,asymptotic enumeration,analytic combinatorics,normal law,Planar graph,random graph,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG],[INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]

Bibliographic References

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Maher Afif Younan, 2014, Dynamics and combinatorics of 2 and 3 dimensional triangulations, 10.13097/archive-ouverte/unige:43269.

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Nicla Bernasconi;Konstantinos Panagiotou;Angelika Steger, Lecture notes in computer science, On the Degree Sequences of Random Outerplanar and Series-Parallel Graphs, pp. 303-316, 2008, 10.1007/978-3-540-85363-3_25.

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Omer Giménez;Marc Noy;Juan José Rué, 2007, Graph classes with given 3-connected components: asymptotic counting and critical phenomena, Electronic Notes in Discrete Mathematics, 29, pp. 521-529, 10.1016/j.endm.2007.07.080.

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