The 6- and 8-palette numbers of links

For an effectively n-colorable link L, Cn⁎(L) stands for the minimum number of distinct colors used over all effective n-colorings of L. It is known that Cn⁎(L)≥1+log2⁡n for any effectively n-colorable link L with non-zero determinant. The aim of this paper is to prove that C6⁎(L)=4 and C8⁎(L)=5 for...

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Bibliographic Details
Published in:Topology and its applications 2017-05, Vol.222, p.200-216
Main Authors: Nakamura, Takuji, Nakanishi, Yasutaka, Saito, Masahico, Satoh, Shin
Format: Article
Language:English
Subjects:
Coloring
Diagram
Knot
Palette number
Ribbon 2-knot
Virtual knot
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Summary:For an effectively n-colorable link L, Cn⁎(L) stands for the minimum number of distinct colors used over all effective n-colorings of L. It is known that Cn⁎(L)≥1+log2⁡n for any effectively n-colorable link L with non-zero determinant. The aim of this paper is to prove that C6⁎(L)=4 and C8⁎(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 C13⁎(L)=5 for n=13.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2017.02.080