Tuesday, July 05, 2016

[ejovwvyz] Torus coloring

7 colors suffice to color any map on a torus.  This suggests interesting puzzles about whether it can be done with fewer than 7 for a given map.  For a plane, the only interesting number is 3, an NP-complete problem.

Draw a seven color tessellation on a plane and provide a rectangular (or parallelogram-shaped) unit cell which defines a flat torus with opposing edges glued together.

I think hexagons work, as well as diagonal strips truncated to the height.

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