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Bibliographic Details
Main Authors:	Kauffman, Louis H., Silver, Daniel S., Williams, Susan G.
Format:	Preprint
Published:	2026
Subjects:	Geometric Topology Primary 05C15, secondary 57M15
Online Access:	https://arxiv.org/abs/2604.16635
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Table of Contents:

For any cubic graph in a closed orientable surface and a perfect matching, the Penrose-Kauffman polynomial is a sum of chromatic polynomials of a collection of associated graphs. A knot-theoretic perspective affords elementary proofs of old and new results about the polynomial. The Four Color Theorem is shown to be equivalent to a statement about 3-coloring alternating link diagrams in the plane that are reduced and have no bigon regions.