#### Volume 9, issue 4 (2009)

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A proof of the Kauffman–Harary Conjecture

### Thomas W Mattman and Pablo Solis

Algebraic & Geometric Topology 9 (2009) 2027–2039
##### Abstract

We prove the Kauffman–Harary Conjecture, posed in 1999: given a reduced, alternating diagram $\mathsc{D}$ of a knot with prime determinant $p$, every nontrivial Fox $p$–coloring of $\mathsc{D}$ will assign different colors to different arcs.

##### Keywords
Kauffman–Harary Conjecture, Fox coloring, alternating knot
Primary: 57M25