Random graphs with bounded maximum degree: asymptotic structure and a logical limit law

Details Random graphs with bounded maximum degree: asymptotic structure and a logical limit law Random graphs with bounded maximum degree: asymptotic structure and a logical limit law

2012-04-11

arxiv.org/abs/1204.2446v1

Mathematics

Combinatorics

Scientific paper

For any fixed integer $R \geq 2$ we characterise the typical structure of
undirected graphs with vertices $1, ..., n$ and maximum degree $R$, as $n$
tends to infinity. The information is used to prove that such graphs satisfy a
labelled limit law for first-order logic. If $R \geq 5$ then also an unlabelled
limit law holds.

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