Efficiently Constructible Huge Graphs That Preserve First Order Properties of Random Graphs

  title={Efficiently Constructible Huge Graphs That Preserve First Order Properties of Random Graphs},
  author={Moni Naor and Asaf Nussboim and Eran Tromer},
We construct efficiently computable sequences of randomlooking graphs that preserve properties of the canonical random graphs G(2, p(n)). We focus on first-order graph properties, namely properties that can be expressed by a formula φ in the language where variables stand for vertices and the only relations are equality and adjacency (e.g. having an isolated vertex is a first-order property ∃x∀y(¬edge(x, y))). Random graphs are known to have remarkable structure w.r.t. first order properties… CONTINUE READING
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