Distance graph on \(\mathbb Z^n\) with \(\ell_{1}\) norm

DOI10.1016/j.tcs.2004.02.010zbMath1043.05047OpenAlexW2577644185MaRDI QIDQ596065

Jeong-Hyun Kang, Zoltan Fueredi

Publication date: 10 August 2004

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.tcs.2004.02.010

zbMATH Keywords

Coloring metric spacesInteger gridUnit-distance graph

Mathematics Subject Classification ID

Coloring of graphs and hypergraphs (05C15) Distance in graphs (05C12)

Related Items (15)

On the chromatic numbers of integer and rational lattices ⋮ New directions in real algebraic geometry. Abstracts from the workshop held March 19--24, 2023 ⋮ Chromatic numbers of distance graphs with several forbidden distances and without cliques of a given size ⋮ Chromatic numbers of spaces with forbidden monochromatic triangles ⋮ On the chromatic number for a set of metric spaces ⋮ The chromatic number of the space $( {\mathbb R}^n, l_1)$ ⋮ Distance graphs on \(\mathbb R^n\) with 1-norm ⋮ Colorings of the space \(\mathbb R^{n}\) with several forbidden distances ⋮ On the chromatic number of a space with several forbidden distances ⋮ Around Borsuk's hypothesis ⋮ 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 ⋮ On the chromatic numbers of metric spaces with few forbidden distances ⋮ Borsuk's problem and the chromatic numbers of metric spaces ⋮ New lower bounds for the chromatic number of a space with forbidden isosceles triangles

Cites Work

• Intersection theorems with geometric consequences
• Distances realized by sets covering the plane
• Borsuk's problem and the chromatic numbers of some metric spaces
• The realization of distances within sets in Euclidean space
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