An upper bound on stick number of knots

Youngsik Huh, Seungsang Oh

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


In 1991, Negami found an upper bound on the stick number s(K) of a nontrivial knot K in terms of crossing number c(K) which is s(K) ≤ 2c(K). In this paper we give a new upper bound in terms of arc index, and improve Negami's upper bound to s(K) ≤ 3/2 (c(K)+1). Moreover if K is a nonalternating prime knot, then s(K) ≤ 3/2 c(K).

Original languageEnglish
Pages (from-to)741-747
Number of pages7
JournalJournal of Knot Theory and its Ramifications
Issue number5
Publication statusPublished - 2011 May

Bibliographical note

Funding Information:
This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MOST) (No. R01-2007-000-20293-0). The second author was supported by a Korea University Grant.


  • Knot
  • stick number
  • upper bound

ASJC Scopus subject areas

  • Algebra and Number Theory


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