On the 2-Colorability of Random Hypergraphs

  • Dimitris Achlioptas
  • Cristopher Moore
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2483)


A 2-coloring of a hypergraph is a mapping from its vertices to a set of two colors such that no edge is monochromatic. Let H k (n,m) be a random k-uniform hypergraph on n vertices formed by picking m edges uniformly, independently and with replacement. It is easy to show that if r ≥r c = 2k-1ln2-(ln2)/2, then with high probability H k (n,m = rn) is not 2-colorable. We complement this observation by proving that if r ≤r c - 1 then with high probability H k (n, m = rn) is 2-colorable.


Chromatic Number Constraint Satisfaction Problem Moment Method Truth Assignment Black Vertex 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Dimitris Achlioptas
    • 1
  • Cristopher Moore
    • 2
  1. 1.Microsoft ResearchRedmond
  2. 2.Computer Science DepartmentUniversity of New Mexico, Albuquerque and the Santa Fe InstituteSanta Fe

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