Component Behaviour of Random Bipartite Graphs

Tuan Anh Do*, Joshua Erde, Mihyun Kang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We study the component behaviour of the binomial random bipartite graph G(n, n, p) near the critical point. We show that, as is the case in the binomial random graph G(n, p), for an appropriate range of p there is a unique ‘giant’ component of order at least n23 and determine asymptotically its order and excess. Our proofs rely on good enumerative estimates for the number of bipartite graphs of a fixed order, as well as probabilistic techniques such as the sprinkling method.

Original languageEnglish
Title of host publicationExtended Abstracts EuroComb 2021
PublisherSpringer
Pages325-330
Number of pages6
Volume14
DOIs
Publication statusPublished - 2021

Publication series

NameTrends in Mathematics
Volume14
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Keywords

  • Component behaviour
  • Critical point
  • Random bipartite graphs

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint

Dive into the research topics of 'Component Behaviour of Random Bipartite Graphs'. Together they form a unique fingerprint.

Cite this