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STICK NUMBERS OF 2-BRIDGE KNOTS AND LINKS

Authors
Huh, YoungsikNo, SungjongOh, 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
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/111189
DOI
10.1090/S0002-9939-2011-10832-3
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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