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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

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

Information

Received: 29 September 2015; Revised: 5 January 2016; Accepted: 24 January 2016; Published: 2017
First available in Project Euclid: 13 December 2017

zbMATH: 1358.57014
MathSciNet: MR3574302
Digital Object Identifier: 10.2140/involve.2017.10.291

Subjects:
Primary: 57M25

Keywords: fox colorings , knots , minimum number of colors

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.10 • No. 2 • 2017
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