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On Stability of the Independence Number of a Certain Distance Graph

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Abstract

We study the asymptotic behavior of the independence number of a random subgraph of a certain (r, s)-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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Authors and Affiliations

  1. Department of Discrete Mathematics, Faculty of Innovation and High Technology, Moscow Institute of Physics and Technology (State University), Moscow, Russia

    P. A. Ogarok

  2. Phystech School of Applied Mathematics and Informatics and Laboratory of Advanced Combinatorics and Network Applications, Moscow Institute of Physics and Technology (State University), Moscow, Russia

    A. M. Raigorodskii

  3. Department of Mathematical Statistics and Random Processes, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    A. M. Raigorodskii

  4. Caucasus Mathematical Center, Adyghe State University, Maykop, Republic of Adygea, Russia

    A. M. Raigorodskii

  5. Institute of Mathematics and Computer Science, Buryat State University, Ulan-Ude, Russia

    A. M. Raigorodskii

Authors
  1. P. A. Ogarok
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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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  • DOI: https://doi.org/10.1134/S0032946020040055

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