A proof of the Kauffman–Harary Conjecture

Mattman, Thomas W; Solis, Pablo

doi:10.2140/agt.2009.9.2027

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A proof of the Kauffman–Harary Conjecture

Thomas W Mattman and Pablo Solis

Algebraic & Geometric Topology 9 (2009) 2027–2039

DOI: 10.2140/agt.2009.9.2027

Abstract

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

Keywords

Kauffman–Harary Conjecture, Fox coloring, alternating knot

Mathematical Subject Classification 2000

Primary: 57M25

References

Publication

Received: 14 February 2008

Revised: 17 July 2009

Accepted: 31 August 2009

Published: 9 October 2009

Authors

Thomas W Mattman
Department of Mathematics and Statistics California State University, Chico Chico, CA 95929-0525 USA

Pablo Solis
Department of Mathematics University of California Berkeley, CA USA

Volume 9, issue 4 (2009)