Illinois Journal of Mathematics

A state calculus for graph coloring

Louis H. Kauffman

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This paper discusses reformulations of the problem of coloring plane maps with four colors. We give a number of alternate ways to formulate the coloring problem including a tautological expansion similar to the Penrose Bracket, and we give a simple extension of the Penrose Bracket that counts colorings of arbitrary cubic graphs presented as immersions in the plane.

Article information

Illinois J. Math., Volume 60, Number 1 (2016), 251-271.

Received: 12 November 2015
Revised: 1 August 2016
First available in Project Euclid: 21 June 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C15: Coloring of graphs and hypergraphs
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}


Kauffman, Louis H. A state calculus for graph coloring. Illinois J. Math. 60 (2016), no. 1, 251--271. doi:10.1215/ijm/1498032032.

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