Kauffman-Harary conjecture for alternating virtual knots

Abstract

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 W. Mattman and P. Solis. Mathew Williamson generalized this conjecture to alternating virtual knots and proved it for certain families of virtual knots. In the present note, we use the methods of W. Mattman and P. Solis to give an affirmative answer to the Kauffman-Harary conjecture for alternating virtual knots.

8 pages, 5 figures

References in corpus (2)

• On Alexander-Conway Polynomials for Virtual Knots and Links
• On the Harary-Kauffman Conjecture and Turk's Head Knots

Cited by in corpus (1)

• On possible existence of HOMFLY polynomials for virtual knots