Vertices of given degree in series-parallel graphs

Abstract

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… (More)
DOI: 10.1002/rsa.20290

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