2014/11/19 by Nicolau C. Saldanha, Saldanha, Nicolau C., Márcio Telles +1 · 1 citation
Computer Science · Mathematics · #05C65 (Secondary) #05C80 (Primary) 60C05 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Stochastic processes and statistical mechanics #math.CO #msc:05C65 #msc:05C80 #msc:60C05
paper · pdf · doi:10.48550/arxiv.1411.5290
57 pages
openalex publication_date 2014/11/19 · arxiv created 2015/04/10 · arxiv updated 2015/04/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
This is an extended version of the thesis presented to the Programa de Pós-Graduação em Matemática of the Departamento de Matemática, PUC-Rio, in September 2013, incorporating some suggestions from the examining commission. Random graphs (and more generally hypergraphs) have been extensively studied, including their first order logic. In this work we focus on certain specific aspects of this vast theory. We consider the binomial model Gd+1(n,p) of the random (d+1)-uniform hypergraph on n vertices, where each edge is present, independently of one another, with probability p=p(n). We are particularly interested in the range p(n) ∼ Clog(n)/nd, after the double jump and near connectivity. We prove several zero-one, and, more generally, convergence results and obtain combinatorial applications of some