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The generalized
Kauffman–Harary conjecture is true
Rhea Palak Bakshi, Huizheng Guo, Gabriel Montoya-Vega, Sujoy Mukherjee and Józef H Przytycki |
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Algebraic & Geometric Topology 25 (2025) 2067–2081
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Abstract |
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For a reduced alternating diagram of a knot with a prime determinant , the Kauffman–Harary conjecture states that every nontrivial Fox -coloring of the knot assigns different colors to its arcs. We prove a generalization of the conjecture, stated nineteen years ago by Asaeda, Przytycki and Sikora: for every pair of distinct arcs in the reduced alternating diagram of a prime link with determinant , there exists a Fox -coloring that distinguishes them. |
Keywords
determinants of links, double branched cover, Fox
colorings, Kauffman–Harary conjecture, knots and links,
pseudocolorings
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Mathematical Subject Classification
Primary: 57K10
Secondary: 57M12
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References |
Publication
Received: 13 January 2023
Revised: 24 November 2023
Accepted: 25 February 2024
Published: 11 August 2025
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Authors |
| Rhea Palak Bakshi | |
| Institute for Theoretical
Studies ETH Zurich Zurich Switzerland |
Department of Mathematics University of California, Santa Barbara Santa Barbara, CA United States |
| Huizheng Guo | |
| Department of Mathematics The George Washington University Washington, DC United States |
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| Gabriel Montoya-Vega | |
| Department of Mathematics The Graduate Center CUNY New York, NY United States |
Department of Mathematics University of Puerto Rico at Río Piedras San Juan, PR United States |
| Sujoy Mukherjee | |
| Department of Mathematics University of Denver Denver, CO United States |
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| Józef H Przytycki | |
| Department of Mathematics The George Washington University Washington, DC United States |
Department of Mathematics University of Gdańsk Gdańsk Poland |
| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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