A Proof of the Kauffman–harary Conjecture
نویسنده
چکیده
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.
منابع مشابه
On the Harary-kauffman Conjecture and Turk’s Head Knots
Abstract. The m, n Turk’s Head Knot, THK(m, n), is an “alternating (m, n) torus knot.” We prove the Harary-Kauffman conjecture for all THK(m, n) except for the case where m ≥ 5 is odd and n ≥ 3 is relatively prime to m. We also give evidence in support of the conjecture in that case. Our proof rests on the observation that none of these knots have prime determinant except for THK(m, 2) when Pm ...
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