## Stick numbers of $2$-bridge knots and links

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- by Youngsik Huh, Sungjong No and Seungsang Oh PDF
- Proc. Amer. Math. Soc.
**139**(2011), 4143-4152 Request permission

## Abstract:

Negami found an upper bound on the stick number $s(K)$ of a nontrivial knot $K$ in terms of the minimal crossing number $c(K)$ of the knot, which is $s(K) \leq 2 c(K)$. Furthermore, McCabe proved that $s(K) \leq c(K) + 3$ for a $2$-bridge knot or link, except in the cases of the unlink and the Hopf link. In this paper we construct any $2$-bridge knot or link $K$ of at least six crossings by using only $c(K)+2$ straight sticks. This gives a new upper bound on stick numbers of $2$-bridge knots and links in terms of crossing numbers.## References

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## Additional Information

**Youngsik Huh**- Affiliation: Department of Mathematics, School of Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea
- Email: yshuh@hanyang.ac.kr
**Sungjong No**- Affiliation: Department of Mathematics, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul 136-701, Republic of Korea
- Email: blueface@korea.ac.kr
**Seungsang Oh**- Affiliation: Department of Mathematics, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul 136-701, Republic of Korea
- Email: seungsang@korea.ac.kr
- Received by editor(s): March 9, 2010
- Received by editor(s) in revised form: July 22, 2010, and September 16, 2010
- Published electronically: March 16, 2011
- Additional Notes: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (No. 2009-0074101).
- Communicated by: Daniel Ruberman
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**139**(2011), 4143-4152 - MSC (2010): Primary 57M25, 57M27
- DOI: https://doi.org/10.1090/S0002-9939-2011-10832-3
- MathSciNet review: 2823059