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This article is available for purchase or by subscription. See below.
Abstract
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We study the validity of the first-order zero-one law for the binomial
-partite
random graph in two settings: dense (the probability
of appearance of an edge is a constant) and sparse
(, where
is the
cardinality of each part of the graph). On the way, we prove that, for every rational
,
there exists a bipartite strictly balanced graph with density
.
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Keywords
zero-one laws, random graphs, strictly balanced bipartite
graphs, first-order properties
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Mathematical Subject Classification
Primary: 05C80
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Milestones
Received: 25 August 2021
Revised: 28 September 2021
Accepted: 20 October 2021
Published: 17 January 2022
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