Xuan Zheng

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20242026

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3 papers · 1 filter

math.CO2026

The polynomial characterization of tope graphs of the lopsided sets

Xuan Zheng, Yan-Ting Xie, Shou-Jun Xu

The cube polynomial $C_{G} (x)$ generates the number of $k$ -cubes on a graph $G$ . As a subclass of partial cubes, the tope graphs of lopsided sets (LOPs) generalize daisy cubes and me…

math.CO2026

Resolving problems on polynomial characterizations of daisy cubes and extensions

Xuan Zheng, Yan-Ting Xie, Shou-Jun Xu

Let $X \subseteq {0, 1}^{n}$ be a set of binary strings of length $n$ . The daisy cube $Q_{n} (X)$ is the subgraph of the hypercube $Q_{n}$ induced by the union of the intervals $I (0^{n}, x)$ …

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…