Fox coloring and the minimum number of colors

Mohamed Elhamdadi; Jeremy Kerr

doi:10.2140/involve.2017.10.291

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Home > Journals > Involve > Volume 10 > Issue 2 > Article

2017 Fox coloring and the minimum number of colors

Mohamed Elhamdadi, Jeremy Kerr

Involve 10(2): 291-316 (2017). DOI: 10.2140/involve.2017.10.291

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Abstract

We study Fox colorings of knots that are 13-colorable. We prove that any 13-colorable knot has a diagram that uses exactly five of the thirteen colors that are assigned to the arcs of the diagram. Due to an existing lower bound, this gives that the minimum number of colors of any 13-colorable knot is 5.

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Mohamed Elhamdadi. Jeremy Kerr. "Fox coloring and the minimum number of colors." Involve 10 (2) 291 - 316, 2017. https://doi.org/10.2140/involve.2017.10.291