Geodesic
On the Frankl--R\"odl theorem
Izvestiya. Mathematics , Tome 82 (2018) no. 6, pp. 1196-1224

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In this paper we considerably strengthen the currently known explicit exponential lower bound for the chromatic number of a Euclidean space with a forbidden regular simplex. We also strengthen the exponential lower bound for the chromatic numbers of distance graphs with large girth.
Keywords: Frankl–Rödl theorem, Euclidean Ramsey theory, distance graph, chromatic number, girth. 
@article{IM2_2018_82_6_a4,
     author = {A. Sagdeev},
     title = {On the {Frankl--R\"odl} theorem},
     journal = {Izvestiya. Mathematics },
     pages = {1196--1224},
     publisher = {mathdoc},
     volume = {82},
     number = {6},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_6_a4/}
}
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A. Sagdeev. On the Frankl--R\"odl theorem. Izvestiya. Mathematics , Tome 82 (2018) no. 6, pp. 1196-1224. http://geodesic.mathdoc.fr/item/IM2_2018_82_6_a4/