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Fox coloring
and the minimum number of colors
Mohamed Elhamdadi and Jeremy Kerr
Vol. 10 (2017), No. 2, 291–316
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Abstract |
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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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Keywords
knots, fox colorings, minimum number of colors
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Mathematical Subject Classification 2010
Primary: 57M25
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Milestones
Received: 29 September 2015
Revised: 5 January 2016
Accepted: 24 January 2016
Published: 10 November 2016
Communicated by Kenneth S. Berenhaut
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Authors |
| Mohamed Elhamdadi | |
| Mathematics Department University of South Florida Tampa, FL 33620 United States |
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| Jeremy Kerr | |
| Mathematics Department University of South Florida Tampa, FL 33620 United States |
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