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An upper bound of arc index of links

Published online by Cambridge University Press:  17 January 2001

YONGJU BAE  and
CHAN-YOUNG PARK
YONGJU BAE
Affiliation:
Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, Korea; e-mail: ybae@kyungpook.ac.kr, chnypark@kyungpook.ac.kr
CHAN-YOUNG PARK
Affiliation:
Department of Mathematics, College of Natural Sciences, Kyungpook National University, Taegu 702-701, Korea; e-mail: ybae@kyungpook.ac.kr, chnypark@kyungpook.ac.kr
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Abstract

In 1996, Cromwell and Nutt [7] found an upper bound on the arc index which is related to the minimal crossing number and conjectured that the upper bound achieves the lowest possible index for alternating links.

CONJECTURE. Let L be any prime link. Then α(L) [les ] c(L)+2. Moreover this inequality is strict if and only if L is not alternating.

In this paper, we define a new diagram, called a wheel diagram, of a link and use it to prove this conjecture.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 129 , Issue 3 , November 2000 , pp. 491 - 500
Copyright
© 2000 Cambridge Philosophical Society

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