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

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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Vera Koponen. Random graphs with bounded maximum degree: asymptotic structure and a logical limit law. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2012, Vol. 14 no. 2 (2), pp.229--254. ⟨hal-00990599⟩

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