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Evolution of locally dependent random graphs
- Publication Year :
- 2024
-
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.<br />Comment: 12 pages
- Subjects :
- Mathematics - Combinatorics
05C80 (primary)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.09489
- Document Type :
- Working Paper