2021/06/01 by Qiyao Chen, Chen, Qiyao, Yi‐Chao Chen +1
Engineering · Computer Science · Mathematics · #graph theory and CDMA systems #Coding theory and cryptography #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2106.00381
Recently, Gross, Mansour and Tucker introduced the partial-twuality polynomials. 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-orientable partial-Petrial polynomial of an arbitrary ribbon graph even-interpolating? In addition, we also find a counterexample to the conjecture 8.1 of Gross, Mansour and Tucker: If the partial-dual genus polynomial is neither an odd nor an even polynomial, then it is interpolating.