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)

Abstract

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.

Keywords

Chromatic Number Constraint Satisfaction Problem Moment Method Truth Assignment Black Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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