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COLORING LINKS BY THE SYMMETRIC GROUP OF DEGREE THREE
Kazuhiro Ichihara,Eri Matsudo Korean Mathematical Society 2023 대한수학회논문집 Vol.38 No.3
We consider the number of colors for colorings of links by the symmetric group S<sub>3</sub> of degree 3. For knots, such a coloring corresponds to a Fox 3-coloring, and thus the number of colors must be 1 or 3. However, for links, there are colorings by S<sub>3</sub> with 4 or 5 colors. In this paper, we show that if a 2-bridge link admits a coloring by S<sub>3</sub> with 5 colors, then the link also admits such a coloring with only 4 colors.