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arXiv · 2405.09489

Evolution of locally dependent random graphs

Joshua Brody·Pat Devlin·Aditi Dudeja·Emmi Rivkin
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Abstract

In this paper we study $d$-dependent random graphs -- introduced by Brody and Sanchez -- which are the family of random graph distributions where each edge is present with probability $p$, and each edge is independent of all but at most $d$ other edges. For this random graph model, we analyze degree sequences, jumbledness, connectivity, and subgraph containment. Our results mirror those of the classical Erd\H{o}s--R\'enyi random graph, which are recovered by specializing our problem to $d=0$, although we show that in many regards our setting is appreciably more nuanced. We survey what is known for this model and conclude with a variety of open questions.

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Joshua Brody, Pat Devlin, Aditi Dudeja, Emmi Rivkin. 2024-05-15. Evolution of locally dependent random graphs. https://arxiv.org/abs/2405.09489

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