• Corpus ID: 246015818

Independent sets in random subgraphs of the hypercube

  title={Independent sets in random subgraphs of the hypercube},
  author={Gal Kronenberg and Yinon Spinka},
Let Qd,p be the random subgraph of the d-dimensional hypercube {0, 1} , where each edge is retained independently with probability p. We study the asymptotic number of independent sets in Qd,p as d → ∞ for a wide range of parameters p, including values of p tending to zero as fast as C log d d1/3 , constant values of p, and values of p tending to one. The results extend to the hardcore model on Qd,p, and are obtained by studying the closely related antiferromagnetic Ising model on the hypercube… 


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