11-colored knot diagram with five colors

Takuji Nakamura, Yasutaka Nakanishi, Shin Satoh

Published 2015-05-12Version 1

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.