Largest random component of a k-cube

M. Ajtai, J. Komlós, E. Szemerédi

Research output: Contribution to journalArticle

72 Citations (Scopus)


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
Issue number1
Publication statusPublished - Mar 1 1982


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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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