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math.GT2009★ 14 cited
A proof of the Kauffman-Harary Conjecture
Thomas W. Mattman, Pablo Solis
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…
math.GT2008★ 9 cited
On the Harary-Kauffman Conjecture and Turk's Head Knots
Nicholas E. Dowdall, Thomas W. Mattman, Kevin Meek +1
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 \geq 5 is odd and n \…