Chromatic numbers of spheres |
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| Authors: | Roman Prosanov |
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| Affiliation: | Université de Fribourg, Chemin du Musée 23, CH-1700 Fribourg, Switzerland;Moscow Institute Of Physics And Technology, Institutskiy per. 9, 141700, Dolgoprudny, Russia |
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| Abstract: | The chromatic number of a subset of Euclidean space is the minimal number of colors sufficient for coloring all points of this subset in such a way that any two points at the distance 1 have different colors. We give new upper bounds on chromatic numbers of spheres. This also allows us to give new upper bounds on chromatic numbers of any bounded subsets. |
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| Keywords: | Chromatic number Geometric covering |
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