11-Colored knot diagram with five colors-Reference-Cited by-同舟云学术

11-Colored knot diagram with five colors

Published:2016-04 Issue:04 Volume:25 Page:1650017
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Nakamura T.¹,Nakanishi Y.²,Satoh S.²

Affiliation:

1. Department of Engineering Science, Osaka Electro-Communication University, Hatsu-cho 18-8, Neyagawa 572-8530, Japan

2. Department of Mathematics, Kobe University, Rokkodai-cho 1-1, Nada-ku, Kobe 657-8501, Japan

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216516500176

Reference16 articles.

1. Mathematical Surveys and Monographs;Carter J. S.,1998

2. Any 11-Colorable knot can be colored with at most six colors

3. Knots and Graphs I—Arc Graphs and Colorings

4. On the minimum number of colors for knots

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