Mathematics – Combinatorics
Scientific paper
2008-08-07
Electronic Journal of Combinatorics, Volume 15(1), R148 (2008)
Mathematics
Combinatorics
39 pages
Scientific paper
Tutte has described in the book "Connectivity in graphs" a canonical decomposition of any graph into 3-connected components. In this article we translate (using the language of symbolic combinatorics) Tutte's decomposition into a general grammar expressing any family of graphs (with some stability conditions) in terms of the 3-connected subfamily. A key ingredient we use is an extension of the so-called dissymmetry theorem, which yields negative signs in the grammar. As a main application we recover in a purely combinatorial way the analytic expression found by Gim\'enez and Noy for the series counting labelled planar graphs (such an expression is crucial to do asymptotic enumeration and to obtain limit laws of various parameters on random planar graphs). Besides the grammar, an important ingredient of our method is a recent bijective construction of planar maps by Bouttier, Di Francesco and Guitter.
Chapuy Guillaume
Fusy Eric
Kang Mihyun
Shoilekova Bilyana
No associations
LandOfFree
A Complete Grammar for Decomposing a Family of Graphs into 3-connected Components does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Complete Grammar for Decomposing a Family of Graphs into 3-connected Components, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Complete Grammar for Decomposing a Family of Graphs into 3-connected Components will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-29168