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de Grey-Haugstrup Graphs

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The de Grey-Haugstrup graphs are two 6-chromatic graphs on 47 and 48 vertices that are unit-distance in 3 dimensions (de Grey and Haugstrup 2020).

The 47-de Grey-Haugstrup graph was also used by Haugstrup (2026) in the construction of a the 21217-vertex Haugstrup graph.

The de Grey-Haugstrup graph on 47 vertices is implemented in the Wolfram Language as GraphData["DeGreyHaugstrupGraph47"].

See also

de Grey Graphs, Haugstrup Graphs, Unit-Distance Graph

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References

de Grey, A. and Haugstrup, A. "Two Small 6-Chromatic Unit-Distance Graphs in R^3." Geombinatorics 33, 110-115, 2022.Haugstrup, A. "A Tetrahedron-Free 6-Chromatic Unit-Distance Graph in Three-Dimensional Space." Geombinatorics 35, 2026.

Referenced on Wolfram|Alpha

de Grey-Haugstrup Graphs

Cite this as:

Weisstein, Eric W. "de Grey-Haugstrup Graphs." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/deGrey-HaugstrupGraphs.html

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