Journal of Mathematical Sciences

, Volume 187, Issue 3, pp 360–373 | Cite as

Tree components in random distance graphs of special form

  • A. R. Yarmukhametov


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.


Random Graph Tree Component Chromatic Number Induction Assumption Distinguished Vertex 
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  1. 1.
    N. Alon and J. Spencer, The Probabilistic Method [Russian translation], Binom, Moscow (2007).Google Scholar
  2. 2.
    B. Bollobas, Random Graphs, Academic Press, New York (1985).MATHGoogle Scholar
  3. 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).Google Scholar
  4. 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. 5.
    P. Erdős and A. Rényi,“On the strength of connectedness of a random graph,” Acta Math. Acad. Sci. Hungar, 12, 261–267(1961).MathSciNetCrossRefGoogle Scholar
  6. 6.
    W. Feller, An Introduction to Probability Theory and Its Applications [Russian translation], Mir, Moscow (1964).Google Scholar
  7. 7.
    V. F. Kolchin, Random Graphs [in Russian], Fizmatlit, Moscow (2004).Google Scholar
  8. 8.
    A. M. Raigorodskii, Methods of Linear Algebra in Combinatorics [in Russian], Moscow (2007).Google Scholar
  9. 9.
    A. M. Raigorodskii, “Borsuk problem and chromatic numbers of some metric spaces,” Usp. Mat. Nauk, 56, No. 1 (337), 107–146 (2001).MathSciNetGoogle Scholar
  10. 10.
    A. R. Yarmukhamrtov, “On the connectedness of random distance graphs of special form,” Chebysh. Sb. (2010).Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.M. V. Lomonosov Moscow State UniversityMoscowRussia

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