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STICK NUMBERS OF 2-BRIDGE KNOTS AND LINKS
- Authors
- Huh, Youngsik; No, Sungjong; Oh, Seungsang
- Issue Date
- 11월-2011
- Publisher
- AMER MATHEMATICAL SOC
- Keywords
- Knot; stick number; 2-bridge
- Citation
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.139, no.11, pp.4143 - 4152
- Indexed
- SCIE
SCOPUS
- Journal Title
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
- Volume
- 139
- Number
- 11
- Start Page
- 4143
- End Page
- 4152
- ISSN
- 0002-9939
- 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) <= 2c(K). Furthermore, McCabe proved that s(K) <= 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.
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