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Tree components in random distance graphs of special form

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Abstract

In this work, we consider the problem of distribution of the number of tree components with given number of vertices k(k ≥ 2) for a certain series of random distance graphs. Generalizations of the classical Erdős–Rényi results are obtained in the case of geometric graphs of special form.

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References

  1. N. Alon and J. Spencer, The Probabilistic Method [Russian translation], Binom, Moscow (2007).

    Google Scholar 

  2. B. Bollobas, Random Graphs, Academic Press, New York (1985).

    MATH  Google Scholar 

  3. P. Erdős and A. Rényi, “On random graphs, 1,” Publ. Math. Debrecen, 6, 290–297 (1959); Magyar Tud. Akad. Mat. Kutató Int. Közl., 5, 17–61 (1960).

  4. P. Erdős and A. Rényi, “On the evolution of random graphs,” Publ. Math. Inst. Hungar. Acad. Sci, 5, 17–61 (1960).

    Google Scholar 

  5. P. Erdős and A. Rényi,“On the strength of connectedness of a random graph,” Acta Math. Acad. Sci. Hungar, 12, 261–267(1961).

    Article  MathSciNet  Google Scholar 

  6. W. Feller, An Introduction to Probability Theory and Its Applications [Russian translation], Mir, Moscow (1964).

    Google Scholar 

  7. V. F. Kolchin, Random Graphs [in Russian], Fizmatlit, Moscow (2004).

    Google Scholar 

  8. A. M. Raigorodskii, Methods of Linear Algebra in Combinatorics [in Russian], Moscow (2007).

  9. A. M. Raigorodskii, “Borsuk problem and chromatic numbers of some metric spaces,” Usp. Mat. Nauk, 56, No. 1 (337), 107–146 (2001).

    MathSciNet  Google Scholar 

  10. A. R. Yarmukhamrtov, “On the connectedness of random distance graphs of special form,” Chebysh. Sb. (2010).

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, Russia

    A. R. Yarmukhametov

Authors
  1. A. R. Yarmukhametov
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Correspondence to A. R. Yarmukhametov.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 76, Geometry and Mechanics, 2012.

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Yarmukhametov, A.R. Tree components in random distance graphs of special form. J Math Sci 187, 360–373 (2012). https://doi.org/10.1007/s10958-012-1069-8

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  • DOI: https://doi.org/10.1007/s10958-012-1069-8

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