Distance graphs with large chromatic number and without large cliques

DOI10.1134/S0001434610030119zbMath1206.05037MaRDI QIDQ1957062

O. I. Rubanov, Andrei M. Raigorodskii

Publication date: 24 September 2010

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

zbMATH Keywords

Euclidean spacechromatic numberdistance graphprobability spacecliquerandom variableexpectationStirling's formula

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 (8)

Lower bounds for the chromatic numbers of distance graphs with large girth ⋮ On the chromatic numbers of rational spaces ⋮ Chromatic numbers of distance graphs with several forbidden distances and without cliques of a given size ⋮ Obstructions to the realization of distance graphs with large chromatic numbers on spheres of small radii ⋮ The chromatic number of space with forbidden regular simplex ⋮ Distance graphs with large chromatic numbers and small clique numbers ⋮ 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

Cites Work

• Chromatic numbers of 3-dimensional distance graphs containing no tetrahedra
• On the space chromatic number
• Borsuk's problem and the chromatic numbers of some metric spaces
• Research Problems in Discrete Geometry
• On Ramsey Type Problems in Combinatorial Geometry
• On the chromatic number of a space
• The realization of distances within sets in Euclidean space
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