Toroidal Complete Graphs

Probability Level 2

In the graphs above, only K4K_4 can be drawn on a plane without any edge crossings, as illustrated below:

This cannot be done with K5K_5, yet it can be drawn on a torus without any edge crossings:

Top view of the torus. The blue dotted line is on the bottom side. Top view of the torus. The blue dotted line is on the bottom side.

Can K6K_6 and K7K_7 be drawn on a torus without edge crossings?

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