Involve: A Journal of Mathematics

  • Involve
  • Volume 10, Number 2 (2017), 291-316.

Fox coloring and the minimum number of colors

Mohamed Elhamdadi and Jeremy Kerr

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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.

Article information

Involve, Volume 10, Number 2 (2017), 291-316.

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

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

knots fox colorings minimum number of colors


Elhamdadi, Mohamed; Kerr, Jeremy. Fox coloring and the minimum number of colors. Involve 10 (2017), no. 2, 291--316. doi:10.2140/involve.2017.10.291.

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