Research ArticleNo Access

Arc presentations of Montesinos links

Department of Mathematics Education, Dongguk University-Gyeongju, 123 Dongdae-ro, Gyeongju 38066, Korea

https://doi.org/10.1142/S0218216521500474Cited by:0 (Source: Crossref)

Abstract

Let $L$ be a Montesinos link $M (- p, q, r)$ with positive rational numbers $p, q$ and $r$ , each less than 1, and $c (L)$ the minimal crossing number of $L$ . Herein, we construct arc presentations of $L$ with $c (L)$ , $c (L) - 1$ and $c (L) - 2$ arcs under some conditions for $p$ , $q$ and $r$ . Furthermore, we determine the arc index of infinitely many Montesinos links.

Keywords:

AMSC: 57K10

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