Graphs with Bounded Maximum Degree : Asymptotic Structure and a Logical Limit Law

Abstract

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

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