Largest random component of a k-cube

M. Ajtai, J. Komlós, E. Szemerédi

Research output: Contribution to journalArticle

72 Citations (Scopus)

Abstract

Let C k denote the graph with vertices (e{open} 1, ..., e{open} k ), e{open} i =0,1 and vertices adjacent if they differ in exactly one coordinate. We call C k the k-cube. Let G=G k, p denote the random subgraph of C k defined by letting {Mathematical expression} for all i, j ∈ C k and letting these probabilities be mutually independent. We show that for p=λ/k, λ>1, G k, p almost surely contains a connected component of size c2 k, c=c(λ). It is also true that the second largest component is of size o(2 k ).

Original languageEnglish
Pages (from-to)1-7
Number of pages7
JournalCombinatorica
Volume2
Issue number1
DOIs
Publication statusPublished - Mar 1982

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Regular hexahedron
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Connected Components
Subgraph
Adjacent
Graph in graph theory

Keywords

  • AMS subject classification (1980): 05C40, 60C05

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)

Cite this

Largest random component of a k-cube. / Ajtai, M.; Komlós, J.; Szemerédi, E.

In: Combinatorica, Vol. 2, No. 1, 03.1982, p. 1-7.

Research output: Contribution to journalArticle

Ajtai, M. ; Komlós, J. ; Szemerédi, E. / Largest random component of a k-cube. In: Combinatorica. 1982 ; Vol. 2, No. 1. pp. 1-7.
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