Measurable chromatic number of geometric graphs and sets without some distances in Euclidean space

DOI10.1007/BF02579223zbMath0558.05020OpenAlexW2044896787MaRDI QIDQ762489

László A. Székely

Publication date: 1984

Published in: Combinatorica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02579223

zbMATH Keywords

geometric graphindependent setsmeasurable chromatic numberLebesgue upper density

Mathematics Subject Classification ID

Coloring of graphs and hypergraphs (05C15) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Related Items (7)

Better bounds for planar sets avoiding unit distances ⋮ Fourier analysis, linear programming, and densities of distance avoiding sets in \(\mathbb R^n\) ⋮ Same graph, different universe ⋮ Geometrical sets with forbidden configurations ⋮ The fractional chromatic number of the plane ⋮ Winning Fast in Sparse Graph Construction Games ⋮ Bounds on the measurable chromatic number of \({\mathbb{R}}\)

Cites Work

• The realization of distances in measurable subsets covering \(R^ n\).
• Intersection theorems with geometric consequences
• Distances realized by sets covering the plane
• The realization of distances within sets in Euclidean space
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