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A complete grammar for decomposing a family of graphs into 3-connected components

Abstract : In this article, we recover the results of Gimenez and Noy for the generating series counting planar graphs, via a different method. This is done thanks to a complete grammar, written in the language of symbolic combinatorics, for the decomposition of a family of graphs into 3-connected components, and thanks to a bijective derivation of the generating series counting labelled planar maps pointed in several ways. The main advantages of our method are: first, that all the calculations are simple (we do not need the two difficult integration steps as in [Gimenez-Noy]); second, that our grammar is general and also applies to other families of labelled graphs, and, hopefully, is a promising tool toward the enumeration of unlabelled planar graphs.
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https://hal.archives-ouvertes.fr/hal-00713485
Contributor : Guillaume Chapuy <>
Submitted on : Sunday, July 1, 2012 - 5:35:17 PM
Last modification on : Thursday, March 5, 2020 - 6:21:02 PM

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  • HAL Id : hal-00713485, version 1

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Guillaume Chapuy, Eric Fusy, Mihyun Kang, Bilyana Shoilekova. A complete grammar for decomposing a family of graphs into 3-connected components. The Electronic Journal of Combinatorics, Open Journal Systems, 2008, 15 (1), Research Paper 148. ⟨hal-00713485⟩

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