UNKNOTTING NUMBERS OF DIAGRAMS OF A GIVEN NONTRIVIAL KNOT ARE UNBOUNDED(Knots and soft-matter physics: Topology of polymers and related topics in physics, mathematics and biology)

@inproceedings{Taniyama2008UNKNOTTINGNO,
  title={UNKNOTTING NUMBERS OF DIAGRAMS OF A GIVEN NONTRIVIAL KNOT ARE UNBOUNDED(Knots and soft-matter physics: Topology of polymers and related topics in physics, mathematics and biology)},
  author={Kouki Taniyama},
  year={2008}
}
We show that for any nontrivial knot K and any natural number n, there is a diagram D of K such that the unknotting number of D is greater than or equal to n. It is well-known that twice the unknotting number of K is less than or equal to the crossing number of K minus one. We show that the equality holds only when K is a (2, p)-torus knot. 

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