The asymptotic probability that a random graph is a unit interval graph, indifference graph, or proper interval graph

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Abstract

Let G be a graph on v labelled vertices with E edges, without loops or multiple edges. Let v → ∞ and let E=E(v) be a function of v such that lim E(v)v23=c. The limit of the probability that a random graph is a unit interval graph, indifference graph or proper interval graph is exp(−43c3).

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