Author

Shoujun Xu

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Preprint Sep 2026

The polynomial characterization of tope graphs of the lopsided sets

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 median graphs. In this paper, we prove that every tope graph of a LOP shares its cube polynomial with some daisy cube, thereby answering affir...

Xuan Zheng, Yan-Ping Xie, Shou-Jun Xu · 0 citations

Preprint Aug 2026

Cop numbers for subclasses of partial cubes

The game of Cops and Robbers is a classical pursuit--evasion game on graphs. For a graph $G$, the cop number $c(G)$ is the minimum number of cops needed to guarantee the capture of a robber on $G$. Although this parameter has been determined for several fundamental graph classes, comparatively few exact results are kno...

Zhaoman Huang, Yan-Ping Xie, Shou-Jun Xu · 0 citations