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

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

2010-08-31

arxiv.org/abs/1008.5361v1

Mathematics

Combinatorics

38 pages

Scientific paper

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.

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