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Independence numbers and chromatic numbers of some distance graphs

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Abstract

We study a family of distance graphs in ℝn. We present bounds for independence numbers which are asymptotically tight as n → ∞. We substantially improve upper bounds on chromatic numbers of these graphs, and in a number of cases we give explicit constructions of independence sets.

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Authors and Affiliations

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

    A. V. Bobu, O. A. Kostina & A. E. Kupriyanov

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  1. A. V. Bobu
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  2. O. A. Kostina
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  3. A. E. Kupriyanov
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Original Russian Text © A.V. Bobu, O.A. Kostina, A.E. Kupriyanov, 2015, published in Problemy Peredachi Informatsii, 2015, Vol. 51, No. 2, pp. 86–98.

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Bobu, A.V., Kostina, O.A. & Kupriyanov, A.E. Independence numbers and chromatic numbers of some distance graphs. Probl Inf Transm 51, 165–176 (2015). https://doi.org/10.1134/S0032946015020076

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