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Dec 19, 2015 at 2:45 comment added Jan Kyncl Yes, it could. But the length will decrease, and there are only finitely many Hamiltonian cycles, so after a finite number of these operations we will get a noncrossing cycle. This might not be a very efficient algorithm though.
Dec 19, 2015 at 2:31 comment added JMP that might create a new crossing
Dec 19, 2015 at 2:24 history answered Jan Kyncl CC BY-SA 3.0