A triangle-free, 4-chromatic \(\mathbb{Q}^3\) Euclidean distance graph Scavenger hunt!

DOI10.1016/j.dam.2023.06.027zbMath1528.05018arXiv2303.09513OpenAlexW4383336654MaRDI QIDQ6064853

Jonathan Joe, Matt Noble

Publication date: 11 December 2023

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.09513

zbMATH Keywords

rational pointschromatic numbertriangle-free graphGrötzsch graphEuclidean distance graph

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Polyhedra and polytopes; regular figures, division of spaces (51M20) Coloring of graphs and hypergraphs (05C15) Distance in graphs (05C12)

Cites Work

• On the chromatic numbers of integer and rational lattices
• Two-colorings of a dense subgroup of \({\mathbb{Q}}^ n\) that forbid many distances
• Distances forbidden by two-colorings of \(\mathbb{Q}^ 3\) and \(A_ n\)
• Distances realized by sets covering the plane
• The Mathematical Coloring Book
• On Single-Distance Graphs on the Rational Points in Euclidean Spaces
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