Abstract:
We improve the Frankl-Rödl estimate for the product of the numbers of edges
in uniform hypergraphs with forbidden cardinalities of the intersection of
edges. By using this estimate, we
obtain explicit bounds for the chromatic number of a space
with forbidden monochromatic equilateral triangles.
Bibliography: 31 titles.
Keywords:
hypergraph, systems of sets with forbidden intersections,
Euclidean Ramsey theory, chromatic number of a space.
Citation:
A. E. Zvonarev, A. M. Raigorodskii, D. V. Samirov, A. A. Kharlamova, “On the chromatic number of a space with forbidden equilateral triangle”, Sb. Math., 205:9 (2014), 1310–1333
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\paper On the chromatic number of a~space with forbidden equilateral triangle
\jour Sb. Math.
\yr 2014
\vol 205
\issue 9
\pages 1310--1333
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Linking options:
https://www.mathnet.ru/eng/sm8312
https://doi.org/10.1070/SM2014v205n09ABEH004419
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This publication is cited in the following 17 articles:
A. A. Sagdeev, “On a Frankl–Wilson Theorem”, Problems Inform. Transmission, 55:4 (2019), 376–395
A. A. Sagdeev, A. M. Raigorodskii, “On a Frankl-Wilson theorem and its geometric corollaries”, Acta Math. Univ. Comen., 88:3 (2019), 1029–1033
R. I. Prosanov, “Upper Bounds for the Chromatic Numbers of Euclidean Spaces with Forbidden Ramsey Sets”, Math. Notes, 103:2 (2018), 243–250
A. A. Sagdeev, “Improved Frankl–Rödl theorem and some of its geometric consequences”, Problems Inform. Transmission, 54:2 (2018), 139–164
A. Sagdeev, “On the Frankl–Rödl theorem”, Izv. Math., 82:6 (2018), 1196–1224
A. A. Sagdeev, “Exponentially Ramsey sets”, Problems Inform. Transmission, 54:4 (2018), 372–396
A. Sagdeev, “Lower Bounds for the Chromatic Numbers of Distance Graphs with Large Girth”, Math. Notes, 101:3 (2017), 515–528
A. M. Raigorodskii, A. A. Sagdeev, “On the chromatic number of a space with a forbidden regular simplex”, Dokl. Math., 95:1 (2017), 15–16
A. Sagdeev, “The Chromatic Number of Space with Forbidden Regular Simplex”, Math. Notes, 102:4 (2017), 541–546
R. I. Prosanov, A. M. Raigorodskii, A. A. Sagdeev, “Improvements of the Frankl-Rodl theorem and geometric consequences”, Dokl. Math., 96:1 (2017), 336–338
A. V. Bobu, A. E. Kupriyanov, A. M. Raigorodskii, “On the number of edges of a uniform hypergraph with a range of allowed intersections”, Problems Inform. Transmission, 53:4 (2017), 319–342
A.A. Sagdeev, “On a Frankl–Rödl theorem and its geometric corollaries”, Electronic Notes in Discrete Mathematics, 61 (2017), 1033
A. V. Bobu, A. E. Kupriyanov, “On chromatic numbers of close-to-Kneser distance graphs”, Problems Inform. Transmission, 52:4 (2016), 373–390
A. M. Raigorodskii, “Combinatorial geometry and coding theory*”, Fund. Inform., 145:3 (2016), 359–369
A. E. Zvonarev, 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”, Proc. Steklov Inst. Math., 288 (2015), 94–104
M. M. Pyaderkin, “On the stability of the Erdős-Ko-Rado theorem”, Dokl. Math., 91:3 (2015), 290–293
D. V. Samirov, A. M. Raigorodskii, “Ob odnoi zadache, svyazannoi s optimalnoi raskraskoi prostranstva bez odnotsvetnykh ravnobedrennykh treugolnikov”, Trudy Moskovskogo fiziko-tekhnicheskogo instituta, 7 (2015), 39–50
Citation in format AMSBIB
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