Random graphs with bounded maximum degree: asymptotic structure and a logical limit law
Vera Koponen · Discrete Mathematics & Theoretical Computer Science · 2012
General 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.