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6

RSA
2010

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Vertices of given degree in series-parallel graphs

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Vertices of given degree in series-parallel graphs

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We show that the number of vertices of a given degree k in several kinds of series-parallel labelled graphs of size n satisfy a central limit theorem with mean and variance proportional to n, and quadratic exponential tail estimates. We further prove a corresponding theorem for the number of nodes of degree two in labelled planar graphs. The proof method is based on generating functions and singularity analysis. In particular we need systems of equations for multivariate generating functions and transfer results for singular representations of analytic functions.

Michael Drmota, Omer Giménez, Marc Noy

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Added	30 Jan 2011
Updated	30 Jan 2011
Type	Journal
Year	2010
Where	RSA
Authors	Michael Drmota, Omer Giménez, Marc Noy

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