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 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