Research PaperNo Access

Minimal coloring number for $ℤ$ -colorable links II

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

https://doi.org/10.1142/S0218216519500470Cited by:1 (Source: Crossref)

Abstract

The minimal coloring number of a $ℤ$ -colorable link is defined as the minimum number of colors for nontrivial $ℤ$ -colorings on diagrams of the link. In this paper, we show that the minimal coloring number of any nonsplittable $ℤ$ -colorable links is four.

Keywords:

AMSC: 57M25

References

1. R. H. Fox, A quick trip through knot theory, in Topology of 3-Manifolds and Related Topics (Proc. The Univ. of Georgia Institute, 1961), (Prentice Hall, Englewood Cliffs, NJ, 1962), pp. 120–167. Google Scholar
2. F. Harary and L. H. Kauffman, Knots and graphs. I. Arc graphs and colorings, Adv. Appl. Math. 22(3) (1999) 312–337. Web of Science, Google Scholar
3. K. Ichihara and E. Matsudo, Minimal coloring number for Z-colorable links, J. Knot Theory Ramifications 26(4) (2017) 1750018, 23 pp. Link, Web of Science, Google Scholar
4. M. Zhang, X. Jin and Q. Deng, The minimal coloring number of any non-splittable $ℤ$ -colorable link is four, J. Knot Theory Ramifications 26(13) (2017) 1750084, 18. Link, Web of Science, Google Scholar