The Generalized Kauffman-Harary Conjecture is True

Rhea Palak Bakshi; Huizheng Guo; Gabriel Montoya-Vega; Sujoy Mukherjee; Józef H. Przytycki

doi:10.2140/agt.2025.25.2067

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arXiv · 2301.02645

The Generalized Kauffman-Harary Conjecture is True

Rhea Palak Bakshi·Huizheng Guo·Gabriel Montoya-Vega·Sujoy Mukherjee·Józef H. Przytycki

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Abstract

For a reduced alternating diagram of a knot with a prime determinant $p,$ the Kauffman-Harary conjecture states that every non-trivial Fox $p$-coloring of the knot assigns different colors to its arcs. In this paper, 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 $\delta,$ there exists a Fox $\delta$-coloring that distinguishes them.

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Rhea Palak Bakshi, Huizheng Guo, Gabriel Montoya-Vega, Sujoy Mukherjee, Józef H. Przytycki. 2023-01-06. The Generalized Kauffman-Harary Conjecture is True. https://doi.org/10.2140/agt.2025.25.2067

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