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On the realization of subgraphs of a random graph by diameter graphs in Euclidean spaces

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Abstract

The present paper is motivated by Borsuk’s classical problem of the partition of sets in spaces into parts of smaller diameter. We obtain sharp estimates for the maximal number of vertices of the induced subgraph of a random graph that, with high probability, is isomorphic to the diameter graph with given chromatic number in a space of any fixed dimension.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow Region, Russia

    A. A. Kokotkin & A. M. Raigorodskii

  2. Lomonosov Moscow State University, Moscow, Russia

    A. M. Raigorodskii

Authors
  1. A. A. Kokotkin
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  2. A. M. Raigorodskii
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Correspondence to A. A. Kokotkin.

Additional information

Original Russian Text © A. A. Kokotkin, A. M. Raigorodskii, 2015, published in Matematicheskie Zametki, 2015, Vol. 97, No. 5, pp. 699–717.

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Kokotkin, A.A., Raigorodskii, A.M. On the realization of subgraphs of a random graph by diameter graphs in Euclidean spaces. Math Notes 97, 709–724 (2015). https://doi.org/10.1134/S0001434615050065

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