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Colorings of spaces, and random graphs

Abstract

This work deals with some problems on the embeddings of finite geometric graphs into the random ones. In particular, we study here applications of the random graph theory to the Nelson-Erdös-Hadwiger problem on coloring spaces.

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Correspondence to A. M. Raigorodskii.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 131–141, 2005.

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Raigorodskii, A.M. Colorings of spaces, and random graphs. J Math Sci 146, 5723–5730 (2007). https://doi.org/10.1007/s10958-007-0388-7

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Keywords

  • Random Graph
  • Chromatic Number
  • Isoperimetric Inequality
  • Distance Graph
  • Geometric Graph