Geodesic
Covering sets in~$\mathbb{R}^m$
Sbornik. Mathematics, Tome 205 (2014) no. 8, pp. 1160-1200

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper investigates questions related to Borsuk's classical problem of partitioning a set in Euclidean space into subsets of smaller diameter, as well as to the well-known Nelson-Erdős-Hadwiger problem on the chromatic number of a Euclidean space. The results of the work are obtained using combinatorial and geometric methods alike. A new approach to the investigation of such problems is suggested; it leads to a collection of results which significantly improve all results known so far. Bibliography: 58 titles.
Keywords: chromatic number, Borsuk's problem, diameter of a set, covering of a plane set, universal covering sets and systems. 
@article{SM_2014_205_8_a4,
     author = {V. P. Filimonov},
     title = {Covering sets in~$\mathbb{R}^m$},
     journal = {Sbornik. Mathematics},
     pages = {1160--1200},
     publisher = {mathdoc},
     volume = {205},
     number = {8},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2014_205_8_a4/}
}
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V. P. Filimonov. Covering sets in~$\mathbb{R}^m$. Sbornik. Mathematics, Tome 205 (2014) no. 8, pp. 1160-1200. http://geodesic.mathdoc.fr/item/SM_2014_205_8_a4/