The arrow, twisted arrow, and loop arrow polynomials of knotoids are shown to be evaluations of Bollobás-Riordan polynomials of associated marked ribbon graphs.
Generalized duality for graphs on surfaces and the signed Bollob´ as- Riordan polynomial
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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.