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

*Vera Koponen*

#### Abstract

For any fixed integer R ≥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 ≥5 then also an unlabelled limit law
holds.

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