Fox coloring and the minimum number of colors

Elhamdadi, Mohamed; Kerr, Jeremy

doi:10.2140/involve.2017.10.291

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Fox coloring and the minimum number of colors

Mohamed Elhamdadi and Jeremy Kerr

Vol. 10 (2017), No. 2, 291–316

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.

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

Vol. 10, No. 2, 2017