Unknotting numbers of diagrams of a given nontrivial knot are unbounded

Kouki Taniyama*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1049-1063
Number of pages15
JournalJournal of Knot Theory and its Ramifications
Issue number8
Publication statusPublished - 2009 Aug


  • Crossing number.
  • Knot
  • Unknotting number
  • Unknotting number of diagram

ASJC Scopus subject areas

  • Algebra and Number Theory


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