The 6-and 8-palette numbers of links

摘要

For an effectively n-colorable link L, C-n*(L) stands for the minimum number of distinct colors used over all effective n-colorings of L. It is known that C-n* (L) >= 1 + log(2) n for any effectively n-colorable link L with non-zero determinant. The aim of this paper is to prove that C-6*(L) = 4 and C-8*(L) = 5 for any effectively 6- and 8-colorable link L, respectively. For ribbon 2-links, we prove the same equalities for n = 6 and 8, and C-13* (L) = 5 for n = 13. (C) 2017 Elsevier B.V. All rights reserved.