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math.CO2025
Characterizing circle graphs with binomial partial Petrial polynomials
Ruiqing Feng, Qi Yan, Xuan Zheng
The partial Petrial polynomial was first introduced by Gross, Mansour, and Tucker as a generating function that enumerates the Euler genera of all possible partial Petrials on a ri…
math.CO2025
Partial Petrial polynomials for complete graphs and paths
Qi Yan, Yuancheng Li
Recently, Gross, Mansour, and Tucker introduced the partial Petrial polynomial, which enumerates all partial Petrials of a ribbon graph by Euler genus. They provided formulas or re…
math.CO2025
On the constant partial-dual polynomials of hypermaps
Yibing Xiang, Qi Yan
In this paper, we introduce the partial-dual polynomial for hypermaps, extending the concept from ribbon graphs. We discuss the basic properties of this polynomial and characterize…