Chromatic Numbers of Spaces with Forbidden Monochromatic Triangles
Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 117-126.

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New lower estimates for chromatic numbers of Euclidean spaces with forbidden monochromatic isosceles triangles are obtained.
Keywords: space coloring, chromatic number of space, forbidden distance.
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A. M. Raigorodskii; D. V. Samirov. Chromatic Numbers of Spaces with Forbidden Monochromatic Triangles. Matematičeskie zametki, Tome 93 (2013) no. 1, pp. 117-126. http://geodesic.mathdoc.fr/item/MZM_2013_93_1_a11/

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

[2] P. Frankl, R. Wilson, “Intersection theorems with geometric consequences”, Combinatorica, 1:4 (1981), 357–368 | DOI | MR | Zbl

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

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

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

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

[7] A. M. Raigorodskii, I. M. Shitova, “O khromaticheskikh chislakh veschestvennykh i ratsionalnykh prostranstv s veschestvennymi ili ratsionalnymi zapreschennymi rasstoyaniyami”, Matem. sb., 199:4 (2008), 107–142 | DOI | MR | Zbl

[8] E. S. Gorskaya, I. M. Mitricheva, V. Yu. Protasov, A. M. Raigorodskii, “Otsenka khromaticheskikh chisel evklidova prostranstva metodami vypukloi minimizatsii”, Matem. sb., 200:6 (2009), 3–22 | DOI | MR

[9] Z. Füredi, J.-H. Kang, “Distance graphs on $\mathbb Z^n$ with $l_1$-norm”, Theoretical Comp. Sci., 319:1-3 (2004), 357–366 | MR | Zbl

[10] N. G. Moschevitin, A. M. Raigorodskii, “O raskraskakh prostranstva $\mathbb R^n$ s neskolkimi zapreschennymi rasstoyaniyami”, Matem. zametki, 81:5 (2007), 733–743 | DOI | MR | Zbl

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

[12] R. L. Graham, B. L. Rothschild, J. H. Spencer, Ramsey Theory, Wiley-Intersci. Ser. Discrete Math. Optim., John Wiley Sons, New York, 1990 | MR | Zbl

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

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

[15] J. Pach, P. K. Agarwal, Combinatorial Geometry, Wiley-Intersci. Ser. Discrete Math. Optim., John Wiley Sons, New York, 1995 | MR | Zbl

[16] V. Klee, S. Wagon, Old and New Unsolved Problems in Plane Geometry and Number Theory, Dolciani Math. Exp., 11, Math. Association of America, Washington, DC, 1991 | MR | Zbl

[17] A. Soifer, “Khromaticheskoe chislo ploskosti: ego proshloe, nastoyaschee i buduschee”, Matem. prosveschenie, 8, MTsNMO, M., 2004, 185–221

[18] L. A. Székely, “Erdős on unit distances and the Szemerédi–Trotter theorems”, Paul Erdős and his Mathematics, II (Budapest, 1999), Bolyai Soc. Math. Stud., 11, János Bolyai Math. Soc., Budapest, 2002, 649–666 | MR | Zbl

[19] A. E. Guterman, V. K. Lyubimov, A. M. Raigorodskii, S. A. Usachev, “O chislakh nezavisimosti grafov rasstoyanii s vershinami v $\{-1,0,1\}^n$: otsenki, gipotezy i prilozheniya k zadacham Nelsona–Erdesha–Khadvigera i Borsuka”, Sovremennaya matematika i ee prilozheniya, 65 (2009), 82–100