When can a link be obtained from another using crossing exchanges and smoothings?
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Let L be a fixed link. Given a link diagram D, is there a sequence of crossing exchanges and smoothings on D that yields a diagram of L? We approach this problem from the computational complexity point of view. It follows from work by Endo, Itoh, and Taniyama that if L is a prime link with crossing number at most 5, then there is an algorithm that answers this question in polynomial time. We show that the same holds for all torus links T 2,m and all twist knots. © 2019
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Graph minors; Knot diagrams; Knot projections; Partial order; Plane graphs; Smoothing order
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