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Nechushtan Graph


NechushtanGraph

The Nechushtan graph, illustrated above, is a 10-vertex 5-chromatic graph that is unit-distance in 3 dimensions. It was used by Nechushtan (2002) in the construction of of a 6-chromatic graph in 3 dimensions.

The Nechushtan graph consists of two copies of the tritetrahedral graph (de Grey and Haugstrup 2022) and is denoted G_1 in de Grey (2020) and G_6 in de Grey and Haugstrup (2022).

NechushtanGraph2D

The Nechushtan graph is illustrated above in several 2-dimensional embeddings.


See also

de Grey-Haugstrup Graphs, Tritetrahedral Graph, Unit-Distance Graph

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References

de Grey, A. "A Small 6-Chromatic Unit-distance Graph in R^3." Geocombinatorics 30, 5-13, 2020.de Grey, A. and Haugstrup, A. "Two Small 6-Chromatic Unit-Distance Graphs in R^3." Geocombinatorics 31, 110-115, 2022.Nechushtan, O. "On the Space Chromatic Number." Disc. Math. 256, 499-507, 2002.

Cite this as:

Weisstein, Eric W. "Nechushtan Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NechushtanGraph.html

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