Kauffman–Harary conjecture for alternating virtual knots
2015 ◽
Vol 24
(08)
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pp. 1550046
In 1999, Kauffman–Harary conjectured that every non-trivial Fox p-coloring of a reduced, alternating knot diagram with prime determinant p is heterogeneous. Ten years later this conjecture was proved by Mattman and Solis. Williamson generalized this conjecture to alternating virtual knots and proved it for certain families of alternating virtual knots. In this paper, by studying the coloring matrices and the determinants of alternating virtual knot diagrams we give an affirmative answer to the Kauffman–Harary conjecture for alternating virtual knots.
2020 ◽
Vol 29
(02)
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pp. 2040004
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2017 ◽
Vol 26
(13)
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pp. 1750090
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2013 ◽
Vol 22
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pp. 1350073
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Vol 15
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pp. 327-338
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2014 ◽
Vol 23
(06)
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pp. 1450031
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2002 ◽
Vol 11
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pp. 311-322
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Vol 18
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pp. 757-772
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2018 ◽
Vol 27
(04)
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pp. 1850024
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