On the chromatic number of with an arbitrary norm

DOI10.1016/j.disc.2010.12.005zbMath1235.05016OpenAlexW2213933826MaRDI QIDQ626862

Andrey B. Kupavskii

Publication date: 18 February 2011

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2010.12.005

zbMATH Keywords

coveringchromatic numbercentrally symmetric convex body

Mathematics Subject Classification ID

Partitions of sets (05A18) Coloring of graphs and hypergraphs (05C15) Combinatorial aspects of packing and covering (05B40)

Related Items (16)

On the chromatic numbers of low-dimensional spaces ⋮ Upper bounds for the chromatic numbers of Euclidean spaces with forbidden Ramsey sets ⋮ Chromatic numbers of distance graphs with several forbidden distances and without cliques of a given size ⋮ Two-colorings of normed spaces with no long monochromatic unit arithmetic progressions ⋮ Two-Colorings of Normed Spaces without Long Monochromatic Unit Arithmetic Progressions ⋮ Max-norm Ramsey theory ⋮ On the chromatic numbers corresponding to exponentially Ramsey sets ⋮ On the chromatic numbers of small-dimensional Euclidean spaces ⋮ Chromatic numbers of spheres ⋮ Exponentially Ramsey sets ⋮ A new proof of the Larman-Rogers upper bound for the chromatic number of the Euclidean space ⋮ A remark on lower bounds for the chromatic numbers of spaces of small dimension with metrics \(\ell_1\) and \(\ell_2\) ⋮ Refinement of lower bounds of the chromatic number of a space with forbidden one-color triangles ⋮ All finite sets are Ramsey in the maximum norm ⋮ New lower bound for the chromatic number of a rational space with one and two forbidden distances ⋮ New lower bounds for the chromatic number of a space with forbidden isosceles triangles

Cites Work

• Covering the \(n\)-space by convex bodies and its chromatic number
• On the packing densities of superballs and other bodies
• On the Minkowski-Hlawka theorem
• Borsuk's problem and the chromatic numbers of some metric spaces
• Research Problems in Discrete Geometry
• Estimating the chromatic numbers of Euclidean space by convex minimization methods
• Covering space with convex bodies
• The realization of distances within sets in Euclidean space
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