Parallel edges in ribbon graphs and interpolating behavior of partial-duality polynomials
Combinatorics
2021-11-11 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2106.00381,
title = {Parallel edges in ribbon graphs and interpolating behavior of partial-duality polynomials},
author = {Qiyao Chen and Yichao Chen},
journal= {arXiv preprint arXiv:2106.00381},
year = {2021}
}