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

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 (Gross et al., 2021): Is the restricted-orientable partial-Petrial polynomial o...

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Bibliographic Details
Published inEuropean journal of combinatorics Vol. 102; p. 103492
Main Authors Chen, Qiyao, Chen, Yichao
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.05.2022
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Summary: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 (Gross et al., 2021): 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.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2021.103492