Counterexamples to the interpolating conjecture on partial-dual genus polynomials of ribbon graphs

Gross, Mansour and Tucker introduced the partial-dual orientable genus polynomial Euler polynomial. They showed that for an ribbon graph is interpolating gave analogous conjecture: The Euler-genus any non-orientable interpolating. In this paper, we first give some counterexamples to conjecture. Then motivated by these counterexamples, further find two infinite classes of counterexamples.