Maximum of Seven Colors Needed for Proper Vertex Coloring on Torus
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Theorem
Let $G$ be a graph embedded on the surface of a torus.
$G$ can be assigned a proper vertex $k$-coloring such that $k \le 7$.
Proof
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Historical Note
This result was known before the Four Color Theorem, its counterpart for planar graphs.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $7$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $7$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): four-colour problem
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): four-colour problem