Golomb graph

Undirected unit-distance graph requiring four colors

In graph theory, the Golomb graph is a polyhedral graph with 10 vertices and 18 edges. It is named after Solomon W. Golomb, who constructed it as a unit distance graph that requires four colors in any graph coloring. Thus, like the simpler Moser spindle, it provides a lower bound for the Hadwiger–Nelson problem: coloring the points of the Euclidean plane so that each unit line segment has differently-colored endpoints requires at least four colors.

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