A proof of the Kauffman-Harary Conjecture

Abstract

We prove the Kauffman-Harary Conjecture, posed in 1999: given a reduced, alternating diagram D of a knot with prime determinant p, every non-trivial Fox p-coloring of D will assign different colors to different arcs.

v2: Simplification of argument in Section 3; 10 pages and 3 figures

Cited by in corpus (4)

• Orderability of link quandles
• Positive quandle homology and its applications in knot theory
• The Generalized Kauffman-Harary Conjecture is True
• Knot Theory and Error-Correcting Codes