On Stability of the Independence Number of a Certain Distance Graph

Abstract

We study the asymptotic behavior of the independence number of a random subgraph of a certain (rs)-distance graph. We provide upper and lower bounds for the critical edge survival probability under which a phase transition occurs, i.e., large new independent sets appear in the subgraph, which did not exist in the original graph.

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Funding

The research was carried out at the expense of the Russian Science Foundation, project no. 16-11-10014.

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Ogarok, P., Raigorodskii, A. On Stability of the Independence Number of a Certain Distance Graph. Probl Inf Transm 56, 345–357 (2020). https://doi.org/10.1134/S0032946020040055

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Keywords

  • random graph
  • distance graph
  • independence number