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Recently, Gross, Mansour and Tucker introduced the partial-twualitypolynomials. In this paper, we find that when there are enough parallel edges,any multiple graph is a negative answer to the problem 8.7 in their paper[European J. Combin. 95 (2021), 103329]: Is the restricted-orientablepartial-Petrial polynomial of an arbitrary ribbon graph even-interpolating? Inaddition, we also find a counterexample to the conjecture 8.1 of Gross, Mansourand Tucker: If the partial-dual genus polynomial is neither an odd nor an evenpolynomial, then it is interpolating.

Parallel edges in ribbon graphs and interpolating behavior of partial-duality polynomials