Lower Bound for the Chromatic Number of a Rational Space with Metric~$l_u$ and with One Forbidden Distance
Matematičeskie zametki, Tome 102 (2017) no. 4, pp. 532-548.

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New lower bounds for the chromatic number of the rational space in the Minkowski metric for certain irrational values of the forbidden distance are obtained.
Keywords: chromatic number of the rational space, graph, forbidden distance, Minkowski metric.
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Yu. A. Demidovich. Lower Bound for the Chromatic Number of a Rational Space with Metric~$l_u$ and with One Forbidden Distance. Matematičeskie zametki, Tome 102 (2017) no. 4, pp. 532-548. http://geodesic.mathdoc.fr/item/MZM_2017_102_4_a5/

[1] A. M. Raigorodskii, “O khromaticheskom chisle prostranstva”, UMN, 55:2 (332) (2000), 147–148 | DOI | MR | Zbl

[2] D. G. Larman, C. A. Rogers, “The realization of distances within sets in Euclidean space”, Mathematika, 19 (1972), 1–24 | DOI | MR | Zbl

[3] M. Benda, M. Perles, “Colorings of metric spaces”, Geombinatorics, 9:3 (2000), 113–126 | MR | Zbl

[4] E. I. Ponomarenko, A. M. Raigorodskii, “Novaya nizhnyaya otsenka khromaticheskogo chisla ratsionalnogo prostranstva s odnim i dvumya zapreschennymi rasstoyaniyami”, Matem. zametki, 97:2 (2015), 255–261 | DOI | MR | Zbl

[5] E. I. Ponomarenko, A. M. Raigorodskii, “Novaya nizhnyaya otsenka khromaticheskogo chisla ratsionalnogo prostranstva”, UMN, 68:5 (413) (2013), 183–184 | DOI | MR | Zbl

[6] A. M. Raigorodskii, “Problema Borsuka i khromaticheskie chisla nekotorykh metricheskikh prostranstv”, UMN, 56:1 (337) (2001), 107–146 | DOI | MR | Zbl

[7] L. A. Székely, “Erdős on unit distances and the Szemerédi–Trotter theorems”, Paul Erdős and His Mathematics, II, Bolyai Soc. Math. Stud., 11, János Bolyai Math. Soc., Springer, Budapest, 2002, 649–666 | MR | Zbl

[8] A. M. Raigorodskii, “Coloring distance graphs and graphs of diameters”, Thirty Essays on Geometric Graph Theory, Springer, New York, 2013, 429–460 | MR | Zbl

[9] A. M. Raigorodskii, Lineino-algebraicheskii metod v kombinatorike, MTsNMO, M., 2007

[10] P. Brass, W. Moser, J. Pach, Research Problems in Discrete Geometry, Springer, New York, 2005 | MR | Zbl

[11] A. Soifer, The Mathematical Coloring Book, Springer, New York, 2009 | MR | Zbl

[12] A. M. Raigorodskii, “O khromaticheskom chisle prostranstva s metrikoi $l_q$”, UMN, 59:5 (359) (2004), 161–162 | DOI | MR | Zbl