A. E. Zvonarev, A. M. Raigorodskii, D. V. Samirov, A. A. Kharlamova, “On the chromatic number of a space with forbidden equilateral triangle”, Mat. Sb., 2014, Volume 205, Number 9,Pages <nobr>97

This article is cited in 18 papers

On the chromatic number of a space with forbidden equilateral triangle

A. E. Zvonarev^ab, A. M. Raigorodskii^ab, D. V. Samirov^b, A. A. Kharlamova^a

^a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Department of Innovations and High Technology, Moscow Institute of Physics and Technology

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.

UDC: 517.538

MSC: Primary 05C65; Secondary 05C15, 05D10

Received: 12.12.2013 and 14.04.2014

DOI: 10.4213/sm8312