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11-Colored knot diagram with five colors

T. Nakamura

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

E-mail Address: n-takuji@isc.osakac.ac.jp

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Y. Nakanishi

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

E-mail Address: nakanisi@math.kobe-u.ac.jp

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, and

S. Satoh

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

E-mail Address: shin@math.kobe-u.ac.jp

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https://doi.org/10.1142/S0218216516500176Cited by:6 (Source: Crossref)

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:

AMSC: 57M25, 57Q45

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