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arXiv · 2008.13140

$\gamma$-variable first-order logic of uniform attachment random graphs

Yury Malyshkin·Maksim Zhukovskii
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Abstract

We study logical limit laws for uniform attachment random graphs. In this random graph model, vertices and edges are introduced recursively: at time $n+1$, the vertex $n+1$ is introduced together with $m$ edges joining the new vertex with $m$ different vertices chosen uniformly at random from $1,\ldots,n$. We prove that this random graph obeys convergence law for first-order sentences with at most $m-2$ variables.

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Yury Malyshkin, Maksim Zhukovskii. 2020-08-30. $\gamma$-variable first-order logic of uniform attachment random graphs. https://arxiv.org/abs/2008.13140

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