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The Size of a Maximum Subgraph of the Random Graph with a Given Number of Edges

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Abstract

We have proven that the maximum size k of an induced subgraph of the binomial random graph \(G(n,p)\) with a given number of edges \(e(k)\) (under certain conditions on this function), with asymptotic probability 1, has at most two values.

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REFERENCES

  1. B. Bollobás, Random Graphs, 2nd ed. (Cambridge Univ. Press, Cambridge, 2001).

    Book  Google Scholar 

  2. S. Janson, T. Łuczak, and A. Ruciński, Random Graphs (Wiley, New York, 2000).

    Book  Google Scholar 

  3. M. E. Zhukovskii and A. M. Raigorodskii, Russ. Math. Surv. 70 (1), 33–81 (2015). https://doi.org/10.1070/RM2015v070n01ABEH004936

    Article  Google Scholar 

  4. N. M. Derevyanko and S. G. Kiselev, Probl. Inf. Transm. 53 (4), 307–318 (2017). https://doi.org/10.1134/S0032946017040019

    Article  MathSciNet  Google Scholar 

  5. A. N. Egorova and M. E. Zhukovskii, Dokl. Math. 99 (1), 68–70 (2019). https://doi.org/10.1134/S1064562419010216

    Article  Google Scholar 

  6. L. B. Ostrovsky and M. E. Zhukovskii, Ann. Pure Appl. Logic 168 (11), 2087–2101 (2017). https://doi.org/10.1016/j.apal.2017.06.004

    Article  MathSciNet  Google Scholar 

  7. B. Bollobás and P. Erdős, Math. Proc. Cambridge Phil. Soc. 80, 419–427 (1976).

    Article  Google Scholar 

  8. G. R. Grimmett and C. J. H. McDiarmid, Math. Proc. Cambridge Phil. Soc. 77 (2), 313–324 (1975). https://doi.org/10.1017/S0305004100051124

    Article  Google Scholar 

  9. D. Matula, “The Employee Party Problem,” Not. Am. Math. Soc. 19 (2), A-382 (1972).

    Google Scholar 

  10. D. Matula, The Largest Clique Size in a Random Graph, Technical Report (Dept. Comput. Sci., Southern Methodist Univ., Dallas, Texas, 1976).

  11. M. Krivelevich, B. Sudakov, V. H. Vu, and N. C. Wormald, Random Struct. Algorithms 22 (1), 1–14 (2003). https://doi.org/10.1002/rsa.10063

    Article  Google Scholar 

  12. A. M. Raigorodskii, Dokl. Math. 96 (3), 628–630 (2017). https://doi.org/10.1134/S1064562417060266

    Article  MathSciNet  Google Scholar 

  13. N. Fountoulakis, R. J. Kang, and C. McDiarmid, Eur. J. Combin. 35, 232–244 (2014). https://doi.org/10.1016/j.ejc.2013.06.012

    Article  Google Scholar 

  14. B. Bollobás, Discrete Math. 32, 201–203 (1980).

    Article  MathSciNet  Google Scholar 

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Funding

This work was supported by the Russian Science Foundation, grant no. 16-11-10014.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (National Research University), 141700, Dolgoprudnyi, Moscow oblast, Russia

    N. M. Derevyanko & M. E. Zhukovskii

  2. Caucasus Mathematical Center, 385000, Maykop, Republic of Adygea, Russia

    M. E. Zhukovskii

  3. Russian Presidential Academy of National Economy and Public Administration, 119571, Moscow, Russia

    M. E. Zhukovskii

  4. University of Zurich, Zurich, Switzerland

    M. Rassias

  5. Adyghe State University, 385000, Maykop, Republic of Adygea, Russia

    A. Yu. Skorkin

Authors
  1. N. M. Derevyanko
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  2. M. E. Zhukovskii
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  3. M. Rassias
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  4. A. Yu. Skorkin
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Corresponding author

Correspondence to M. E. Zhukovskii.

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Translated by I. Ruzanova

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Derevyanko, N.M., Zhukovskii, M.E., Rassias, M. et al. The Size of a Maximum Subgraph of the Random Graph with a Given Number of Edges. Dokl. Math. 100, 478–479 (2019). https://doi.org/10.1134/S1064562419050223

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  • DOI: https://doi.org/10.1134/S1064562419050223

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