Shoujun Xu

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20242026

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6 papers · 1 filter

math.CO2026

Resolving the KlavÅ¾ar-KovÅ¡e conjecture on opposite semicube isomorphisms in partial cubes and its extension

Zhaoman Huang, Yan-Ting Xie, Shou-Jun Xu

Partial cubes are a fundamental class of graphs that admit isometric embeddings into hypercubes. KlavÅ¾ar and KovÅ¡e [Ars Combin. 93 (2009), 77--86] observed that the opposite semi…

math.CO2026

Resolving problems on the polynomial identity characterization of daisy cubes

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 $I (x, 0^{n})$ …

math.CO2025

Characterizing simplex graphs

Yan-Ting Xie, Shou-Jun Xu

The simplex graph $S (G)$ of a graph $G$ is defined as the graph whose vertices are the cliques of $G$ (including the empty set), with two vertices being adjacent if, as cliques of…

math.CO2024

A characterization of regular partial cubes whose all convex cycles have the same lengths

Yan-Ting Xie, Yong-De Feng, Shou-Jun Xu

Partial cubes are graphs that can be isometrically embedded into hypercubes. Convex cycles play an important role in the study of partial cubes. In this paper, we prove that a regu…

math.CO2024

Ultra log-concavity and real-rootedness of dependence polynomials

Yan-Ting Xie, Shou-Jun Xu

For some positive integer $m$ , a real polynomial $P (x) = k = 0 \sum m a_{k} x^{k}$ with $a_{k} ⩾ 0$ is called log-concave (resp. ultra log-concave) if $a_k^2\geqslant a_{k-1}a_…

math.CO2024

A relation between the cube polynomials of partial cubes and the clique polynomials of their crossing graphs

Yan-Ting Xie, Yong-De Feng, Shou-Jun Xu

Partial cubes are the graphs which can be embedded into hypercubes. The {\em cube polynomial} of a graph $G$ is a counting polynomial of induced hypercubes of $G$ , which is defined…