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Matematicheskie Zametki, 2015, Volume 97, Issue 5, Pages 699–717
DOI: https://doi.org/10.4213/mzm10559 (Mi mzm10559) 		 
On the Realization of Subgraphs of a Random Graph by Diameter Graphs in Euclidean Spaces

A. A. Kokotkina, A. M. Raigorodskiiab

a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
b Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm10559
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.
Keywords: random graph, diameter graph, Euclidean space, Borsuk problem, chromatic number, independence number.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00683
Ministry of Education and Science of the Russian Federation МД-6277.2013.1
НШ-2519.2012.1
This work was supported by the Russian Foundation for Basic Research (grant no. 12-01-00683), by the Grant of the President of the Russian Federation MD-6277.2013.1, and by the program “Leading Scientific Schools” (grant no. NSh-2519.2012.1).
Received: 25.05.2014
Revised: 26.10.2014
English version:
Mathematical Notes, 2015, Volume 97, Issue 5, Pages 709–724
DOI: https://doi.org/10.1134/S0001434615050065
Bibliographic databases:
Document Type: Article
UDC: 519.174
Language: Russian
Citation: A. A. Kokotkin, A. M. Raigorodskii, “On the Realization of Subgraphs of a Random Graph by Diameter Graphs in Euclidean Spaces”, Mat. Zametki, 97:5 (2015), 699–717; Math. Notes, 97:5 (2015), 709–724
Citation in format AMSBIB
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