PRIME KNOTS WITH ARC INDEX UP TO 11 AND AN UPPER BOUND OF ARC INDEX FOR NON-ALTERNATING KNOTS

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Every knot can be embedded in the union of finitely many half planes with a common boundary line in such a way that the portion of the knot in each half plane is a properly embedded arc. The minimal number of such half planes is called the arc index of the knot. We have identified all prime knots with arc index up to 11. We also proved that the crossing number is an upperbound of arc index for non-alternating knots. As a result the arc index is determined for prime knots up to twelve crossings.
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Issue Date
2010-12
Language
English
Article Type
Article
Keywords

OPEN-BOOK; EMBEDDING KNOTS; LINKS

Citation

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.19, no.12, pp.1655 - 1672

ISSN
0218-2165
DOI
10.1142/S0218216510008595
URI
http://hdl.handle.net/10203/96838
Appears in Collection
MA-Journal Papers(저널논문)
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