A. For a reduced alternating diagram of a knot with a prime determinant , the Kau man-Harary conj... more A. For a reduced alternating diagram of a knot with a prime determinant , the Kau man-Harary conjecture states that every non-trivial Fox-coloring of the knot assigns di erent 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 , there exists a Fox-coloring that distinguishes them. C 1. History of the alternation conjecture 1 2. Preliminaries 2 3. Proof of the generalized Kau man-Harary conjecture 3 4. Non-prime alternating links 6 5. Examples of Fox colorings 7 6. Odds and ends 8 6.1. Pseudo colorings 8 6.2. Future directions 12 Acknowledgements 13 References 13
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Papers by Gabriel Vega