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

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

preprint2010arXivOpen access
Michael DrmotaOmer GimenezMarc Noy
math.CO
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Open access3 authors1 topic
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Michael DrmotaOmer GimenezMarc Noy

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