The maximum degree of planar graphs I. Series-parallel graphs

Michael Drmota; Omer Gimenez; Marc Noy

The maximum degree of planar graphs I. Series-parallel graphs

Combinatorics 2010-09-01 v1

Authors: Michael Drmota , Omer Gimenez , Marc Noy

Abstract

We prove that the maximum degree $\Delta_n$ of a random series-parallel graph with $n$ vertices satisfies $\Delta_n/\log n \to c$ in probability, and $\mathbb{E}\, \Delta_n \sim c \log n$ for a computable constant $c>0$ . The same result holds for outerplanar graphs.

Keywords

random graphs graph pebbling preferential attachment

Cite

@article{arxiv.1008.5361,
  title  = {The maximum degree of planar graphs I. Series-parallel graphs},
  author = {Michael Drmota and Omer Gimenez and Marc Noy},
  journal= {arXiv preprint arXiv:1008.5361},
  year   = {2010}
}

Comments

38 pages

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