11-colored knot diagram with five colors

Takuji Nakamura; Yasutaka Nakanishi; Shin Satoh

11-colored knot diagram with five colors

Geometric Topology 2015-05-13 v1

Authors: Takuji Nakamura , Yasutaka Nakanishi , Shin Satoh

Abstract

We prove that any $11$ -colorable knot is presented by an $11$ -colored diagram where exactly five colors of eleven are assigned to the arcs. The number five is the minimum for all non-trivially $11$ -colored diagrams of the knot. We also prove a similar result for any $11$ -colorable ribbon $2$ -knot.

Keywords

knot theory

Cite

@article{arxiv.1505.02980,
  title  = {11-colored knot diagram with five colors},
  author = {Takuji Nakamura and Yasutaka Nakanishi and Shin Satoh},
  journal= {arXiv preprint arXiv:1505.02980},
  year   = {2015}
}

Comments

20 pages, 27 figures. Submitted

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