New lower bound for the chromatic number of a rational space with one and two forbidden distances

DOI10.1134/S0001434615010265zbMath1317.05064MaRDI QIDQ2353733

E. I. Ponomarenko, Andrei M. Raigorodskii

Publication date: 16 July 2015

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

chromatic numberStirling's formulaNelson-Hadwiger problemindependence number of a graphrational space with forbidden distances

Mathematics Subject Classification ID

Coloring of graphs and hypergraphs (05C15) Distance in graphs (05C12) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (11)

On a bound in extremal combinatorics ⋮ On the chromatic numbers of rational spaces ⋮ On the chromatic number of an infinitesimal plane layer ⋮ Turán-type bounds for distance graphs ⋮ Unnamed Item ⋮ Lower bound for the chromatic number of a rational space with metric \(l_u\) and with one forbidden distance ⋮ Chromatic numbers of spheres ⋮ Distance graphs with large chromatic number and without cliques of given size in the rational space ⋮ Chromatic numbers of distance graphs without short odd cycles in rational spaces ⋮ 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

Cites Work

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• On the chromatic number of a space with two forbidden distances
• Fourier analysis, linear programming, and densities of distance avoiding sets in \(\mathbb R^n\)
• On the chromatic number of with an arbitrary norm
• Borsuk's problem and the chromatic numbers of some metric spaces
• Coloring Distance Graphs and Graphs of Diameters
• Research Problems in Discrete Geometry
• The Mathematical Coloring Book
• Chromatic numbers of real and rational spaces with real or rational forbidden distances
• Estimating the chromatic numbers of Euclidean space by convex minimization methods
• On the chromatic number of a space
• The realization of distances within sets in Euclidean space

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