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Minimal coloring number for $ℤ$ -colorable links

Department of Mathematics, College of Humanities and Sciences, Nihon University, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156-8550, Japan

E-mail Address: ichihara@math.chs.nihon_u.ac.jp

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and

Eri Matsudo

Graduate School of Integrated Basic Sciences, Nihon University, 3-25-40 Sakurajosui, Setagaya-ku, Tokyo 156-8550, Japan

E-mail Address: cher16001@g.nihon-u.ac.jp

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https://doi.org/10.1142/S0218216517500183Cited by:4 (Source: Crossref)

Abstract

For a link with zero determinants, a $ℤ$ -coloring is defined as a generalization of Fox coloring. We call a link having a diagram which admits a non-trivial $ℤ$ -coloring a $ℤ$ -colorable link. The minimal coloring number of a $ℤ$ -colorable link is the minimal number of colors for non-trivial $ℤ$ -colorings on diagrams of the link. We give sufficient conditions for non-splittable $ℤ$ -colorable links to have the least minimal coloring number.

Keywords:

AMSC: 57M25

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