Vol. 10, No. 2, 2017

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Fox coloring and the minimum number of colors

Mohamed Elhamdadi and Jeremy Kerr

Vol. 10 (2017), No. 2, 291–316
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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Keywords
knots, fox colorings, minimum number of colors
Mathematical Subject Classification 2010
Primary: 57M25
Milestones
Received: 29 September 2015
Revised: 5 January 2016
Accepted: 24 January 2016
Published: 10 November 2016

Communicated by Kenneth S. Berenhaut
Authors
Mohamed Elhamdadi
Mathematics Department
University of South Florida
Tampa, FL 33620
United States
Jeremy Kerr
Mathematics Department
University of South Florida
Tampa, FL 33620
United States