Local connectivity of a random graph

P. Erdős, E. M. Palmer, R. W. Robinson

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

A graph is locally connected if for each vertex ν of degree ≧2, the subgraph induced by the vertices adjacent to ν is connected. In this paper we establish a sharp threshold function for local connectivity. Specifically, if the probability of an edge of a labeled graph of order n is p = ((3/2 +ϵn) log n/n)1/2 where ϵn = (log log n + log(3/8) + 2x)/(2 log n), then the limiting probability that a random graph is locally connected is exp(‐exp(‐x)).

Original languageEnglish
Pages (from-to)411-417
Number of pages7
JournalJournal of Graph Theory
Volume7
Issue number4
DOIs
Publication statusPublished - 1983

    Fingerprint

ASJC Scopus subject areas

  • Geometry and Topology

Cite this