The arrow, twisted arrow, and loop arrow polynomials of knotoids are shown to be evaluations of Bollobás-Riordan polynomials of associated marked ribbon graphs.
The Kauffman bracket of virtual links and the Bol- lob´ as-Riordan polynomial.Moscow Mathematical Journal , 7(3):409–418, 2007
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Thistlethwaite Theorems for Knotoids and Linkoids
The arrow, twisted arrow, and loop arrow polynomials of knotoids are shown to be evaluations of Bollobás-Riordan polynomials of associated marked ribbon graphs.