Minimal coloring numbers on minimal diagrams of torus links

Kazuhiro Ichihara; Katsumi Ishikawa; Eri Matsudo

Minimal coloring numbers on minimal diagrams of torus links

Geometric Topology 2019-08-05 v1

Authors: Kazuhiro Ichihara , Katsumi Ishikawa , Eri Matsudo

Abstract

We determine the minimal number of colors for non-trivial $\mathbb{Z}$ -colorings on the standard minimal diagrams of $\mathbb{Z}$ -colorable torus links. Also included are complete classifications of such $\mathbb{Z}$ -colorings and of such $\mathbb{Z}$ -colorings by only four colors, which are shown by using rack colorings on link diagrams.

Keywords

torus links minimal diagrams z-colorings minimal number of colors rack colorings link diagrams

Cite

@article{arxiv.1908.00857,
  title  = {Minimal coloring numbers on minimal diagrams of torus links},
  author = {Kazuhiro Ichihara and Katsumi Ishikawa and Eri Matsudo},
  journal= {arXiv preprint arXiv:1908.00857},
  year   = {2019}
}

Comments

16 pages, 18 figures

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