A proof of the Kauffman–Harary Conjecture

2009/06/30 by Thomas W. Mattman, Thomas W Mattman, Pablo Solis · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Limits and Structures in Graph Theory #math.GT #msc:57M25

paper · pdf · doi:10.2140/agt.2009.9.2027

published as Algebr. Geom. Topol. 9 (2009) 2027-2039 · v2: Simplification of argument in Section 3; 10 pages and 3 figures

arxiv created 2009/07/17 · openalex publication_date 2009/10/09 · arxiv updated 2014/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• On the classification of rational tangles
• State models and the jones polynomial

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• List of unsolved problems in mathematics [wikipedia]