On Single-Distance Graphs on the Rational Points in Euclidean Spaces

DOI10.4153/S0008439520000181zbMath1461.05078OpenAlexW3045797350WikidataQ114021614 ScholiaQ114021614MaRDI QIDQ5858655

Matt Noble, Sheng Bau, Peter D. jun. Johnson

Publication date: 14 April 2021

Published in: Canadian Mathematical Bulletin (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4153/s0008439520000181

zbMATH Keywords

rational pointsclique numberregular simplexgraph isomorphismEuclidean distance graph

Mathematics Subject Classification ID

Distance in graphs (05C12) Power residues, reciprocity (11A15) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (4)

Embedding Euclidean distance graphs in \(\mathbb{R}^n\) and \(\mathbb{Q}^n\) ⋮ Unnamed Item ⋮ A triangle-free, 4-chromatic \(\mathbb{Q}^3\) Euclidean distance graph Scavenger hunt! ⋮ On distance graphs in rational spaces

Cites Work

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• Some analogues of the Borsuk problem in \(\mathbb Q^{n}\)
• Two-colorings of a dense subgroup of \({\mathbb{Q}}^ n\) that forbid many distances
• Unit-distance graphs in rational n-spaces
• Distances forbidden by two-colorings of \(\mathbb{Q}^ 3\) and \(A_ n\)
• Maximal dimension of unit simplices
• Research Problems in Discrete Geometry
• The Mathematical Coloring Book
• Chromatic numbers of real and rational spaces with real or rational forbidden distances
• Normal Completions of Incidence Matrices

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