Example
The torus has g = 1, so χ = 0. Therefore, as the formula states, any subdivision of the torus into regions can be colored using at most seven colors. The illustration shows a subdivision of the torus in which each of seven regions are adjacent to each other region; this subdivision shows that the bound of seven on the number of colors is tight for this case. The boundary of this subdivision forms an embedding of the Heawood graph onto the torus.
Read more about this topic: Heawood Conjecture
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