The palette numbers of 2-bridge knots-Reference-Cited by-同舟云学术

The palette numbers of 2-bridge knots

Published:2017-04-20 Issue:08 Volume:26 Page:1750047
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Nakamura Takuji¹,Nakanishi Yasutaka²,Saito Masahico³,Satoh Shin²

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

3. Department of Mathematics, University of South Florida, Tampa, Florida 33620, USA

Abstract

We prove that for any odd [Formula: see text], the [Formula: see text]-palette number of any effectively [Formula: see text]-colorable [Formula: see text]-bridge knot is equal to [Formula: see text]. Namely, there is an effectively [Formula: see text]-colored diagram of the [Formula: see text]-bridge knot such that the number of distinct colors that appeared in the diagram is exactly equal to [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021821651750047X

Reference9 articles.

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

2. Fox coloring and the minimum number of colors

3. Monograph in Japanese;Kawauchi A.,2007

4. On effective 9-colorings for knots

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