Upper Bounds for the Chromatic Numbers of Euclidean Spaces with Forbidden Ramsey Sets
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The chromatic number of a Euclidean space ℝ n with a forbidden finite set C of points is the least number of colors required to color the points of this space so that no monochromatic set is congruent to C. New upper bounds for this quantity are found.
KeywordsEuclidean Ramsey theory chromatic number of space
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- 3.A. M. Raigorodskii, “Cliques and cycles in distance graphs and graphs of diameters,” in Discrete Geometry and Algebraic Combinatorics, Contemp. Math. (Amer. Math. Soc., Providence, RI, 2014), Vol. 625, pp. 93–109.Google Scholar
- 14.A. E. Zvonarev and A. M. Raigorodskii, “Improvements of the Frankl–Rödl theorem on the number of edges of a hypergraph with forbidden intersections, and their consequences in the problem of finding the chromatic number of a space with forbidden equilateral triangle,” Trudy Mat. Inst. Steklov, Vol. 288: Geometry, Topology and Application (Nauka, Moscow, 2015), pp. 109–119 [Proc. Steklov Inst. Math. 288 (1), 94–104 (2015)].Google Scholar
- 17.A. A. Sagdeev, “On the chromatic number of space with a forbidden regular simplex,” Mat. Zametki (in press).Google Scholar
- 18.A. A. Sagdeev, “On a Frank–Rödl theorem and its geometric corollaries,” Electron. Notes in DiscreteMath. (in press).Google Scholar
- 23.A. B. Kupavskii, “On the chromatic number of Rn with an arbitrary norm,” DiscreteMath. 311 (6), 437–440 (2011).Google Scholar
- 26.A. B. Kupavskii, “On the chromatic number of Rn with a set of forbidden distances,” Dokl. Ross. Akad. Nauk 435 (6), 740–743 (2010) [Dokl. Math. 82 (3), 963–966 (2010)].Google Scholar
- 27.R. Prosanov, A New Proof of the Larman–Rogers Upper Bound for the Chromatic Number of the Euclidean Space, 1610.02846 (2016).Google Scholar