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On the spectra of first-order language properties for random graphs

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Abstract

We found the maximum and the minimum number in the spectra of the first-order formula with a quantifier depth of at most k. Moreover, we obtain the upper bounds on the mimimal limit points in the spectra and the lower bounds on the maximum limit points in the spectra.

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Authors and Affiliations

  1. Gourant Institute, Department of Computer Science and Department of Mathematics, New York University, New York, USA

    J. H. Spencer

  2. Department of Innovation and Higher Technology, Department of Discrete Mathematics, Moscow Institute of Physics and Technology (State University), Moscow, Russia

    M. E. Zhukovskii

Authors
  1. J. H. Spencer
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  2. M. E. Zhukovskii
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Corresponding author

Correspondence to M. E. Zhukovskii.

Additional information

Published in Russian in Doklady Akademii Nauk, 2015, Vol. 463, No. 6, pp. 642–645.

The article was translated by the authors.

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Spencer, J.H., Zhukovskii, M.E. On the spectra of first-order language properties for random graphs. Dokl. Math. 92, 503–506 (2015). https://doi.org/10.1134/S1064562415040304

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  • DOI: https://doi.org/10.1134/S1064562415040304

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