Vol. 10, No. 4, 2021

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Zero-one laws for random $k$-partite graphs

Juan Carlos Buitrago Oropeza

Vol. 10 (2021), No. 4, 315–337
DOI: 10.2140/moscow.2021.10.315
Abstract

We study the validity of the first-order zero-one law for the binomial k-partite random graph in two settings: dense (the probability p of appearance of an edge is a constant) and sparse (p = nα , where n is the cardinality of each part of the graph). On the way, we prove that, for every rational ρ 1, there exists a bipartite strictly balanced graph with density ρ.

Keywords
zero-one laws, random graphs, strictly balanced bipartite graphs, first-order properties
Mathematical Subject Classification
Primary: 05C80
Milestones
Received: 25 August 2021
Revised: 28 September 2021
Accepted: 20 October 2021
Published: 17 January 2022
Authors
Juan Carlos Buitrago Oropeza
Department of Applied Mathematics and Informatics
Moscow Institute of Physics and Technology (National Research University)
Dolgoprudny
Russia