On the Nelson--Erd\H{o}s--Hadwiger problem for a series of metric spaces
Čebyševskij sbornik, Tome 9 (2008) no. 1, pp. 158-168.

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A. M. Raǐgorodskiǐ; I. I. Timirova. On the Nelson--Erd\H{o}s--Hadwiger problem for a series of metric spaces. Čebyševskij sbornik, Tome 9 (2008) no. 1, pp. 158-168. http://geodesic.mathdoc.fr/item/CHEB_2008_9_1_a13/

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

[2] P. Frankl, R. Wilson, “Intersection theorems with geometric consequences”, Combinatorica, 1 (1981), 357–368 | DOI | MR

[3] J.-H. Kang, Z. Füredi, “Distance graphs on $ {\mathbb Z}^n $ with $ l_1 $-norm”, Theoretical Comp. Sci., 319:3 (2004), 357–366 | DOI | MR

[4] A. M. Raigorodskii, “O khromaticheskom chisle prostranstva”, Uspekhi matem. nauk, 55:2 (2000), 147–148 | MR

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

[6] A. M. Raigorodskii, “O khromaticheskom chisle prostranstva s metrikoi $ l_q $”, Uspekhi matem. nauk, 59:5 (2004), 161–162 | MR

[7] A. M. Raigorodskii, “O khromaticheskikh chislakh metricheskikh prostranstv”, Chebyshevskii sbornik, 5:1(9) (2004), 175–185 | MR

[8] A. M. Raigorodskii, “Problema Borsuka i khromaticheskie chisla metricheskikh prostranstv”, Uspekhi matem. nauk, 56:1 (2001), 107–146 | MR

[9] L. A. Székely, “Erdős on unit distances and the Szemerédi–Trotter theorems”, Paul Erdős and his Mathematics, Bolyai Society Mathematical Studies, 11, Springer, 2002, 649–666 | MR

[10] A. Soifer, “Khromaticheskoe chislo ploskosti: ego proshloe, nastoyaschee i buduschee”, Mat. prosveschenie, 2004, no. 8

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

[12] A. M. Raigorodskii, Khromaticheskie chisla, MTsNMO, M., 2003

[13] P. Brass, W. Moser, J. Pach, Research problems in discrete geometry, Springer, 2005 | MR

[14] V. Klee, S. Wagon, Old and new unsolved problems in plane geometry and number theory, Math. Association of America, 1991 | MR

[15] J. Pach, P. K. Agarwal, Combinatorial geometry, John Wiley and Sons Inc., New York, 1995 | MR

[16] F. Kharari, Teoriya grafov, Mir, M., 1973 | MR

[17] N. G. de Bruijn, P. Erdős, “A colour problem for infinite graphs and a problem in the theory of relations”, Proc. Koninkl. Nederl. Acad. Wet., Ser. A, 54:5 (1951), 371–373

[18] N. Alon, Dzh. Spenser, Veroyatnostnyi metod, Binom. Laboratoriya znanii, M., 2007

[19] B. Bollobás, Random Graphs, Second Edition, Cambridge Univ. Press, 2001 | MR

[20] K. Prakhar, Raspredelenie prostykh chisel, Mir, M., 1967 | MR

[21] A. M. Raigorodskii, I. M. Shitova, “O khromaticheskikh chislakh veschestvennykh i ratsionalnykh prostranstv s neskolkimi veschestvennymi ili neskolkimi ratsionalnymi zapreschennymi rasstoyaniyami”, Matem. sbornik, 199 (2008) | MR