Xiao-Dong Zhang

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20232026

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9 papers · 1 filter

math.CO2026

The Sharp Upper Bounds for the Median Eigenvalues of Graphs

Zhengbo Chen, Yuzhenni Wang, Xiao-Dong Zhang

Let $λ_{1} \geq λ_{2} \geq \dots \geq λ_{n}$ be the eigenvalues of a simple graph $G$ of order $n$ . The HL-index of $G$ is defined by $R (G) = max ∥ λ_{h} ∣, ∣ λ_{ℓ} ∣}$ with $h=\lfloor(n+1)/2\rfloo…

math.CO2026

Turán number of a matching and a Berge triangle

Yue Xu, Jiasheng Zeng, Xiao-Dong Zhang

For a fixed graph $G$ , an $r$ -uniform hypergraph is said to contain a Berge- $G$ if there exists a bijection $f : E (G) \to E (H)$ for some subhypergraph $H$ su…

math.CO2026

Sharp Bounds for Guiduli-Type Hereditary Spectral Problems

Dongxiu Cai, Jiasheng Zeng, Xiao-Dong Zhang

Guiduli asked in 1996 the following problem concerning the maximum spectral radius of a graph under hereditary density constraints. If an $n$ -vertex graph $G$ satisfies $e(H)\le c|…

math.CO2026

Positive and negative 3-energies of graphs

Zhengbo Chen, Zhouningxin Wang, Xiao-Dong Zhang

For a simple graph $G$ with $n$ vertices, let $A_{G}$ denote the adjacency matrix of $G$ , and let $λ_{1} (G) \geq λ_{2} (G) \geq \dots \geq λ_{n} (G)$ be its eigenvalues. For an integer $p \g…

math.CO2026

Turán extremal graphs vs. Signless Laplacian spectral Turán extremal graphs

Ming-Zhu Chen, Ya-Lei Jin, Peng-Li Zhang +1

Let $F$ be a graph with chromatic number $χ (F) = r + 1$ . Denote by $e x (n, F)$ and $E x (n, F)$ the Turán number and the set of all extremal graphs for $F$ , respectively. In addition, $…

math.CO2025

Generalized Turan number with given size

Yan Wang, Yue Xu, Jiasheng Zeng +1

Generalized Turán problem with given size, denoted as $mex (m, K_{r}, F)$ , determines the maximum number of $K_{r}$ -copies in an $F$ -free graph with $m$ edges. We prove that for…

math.CO2024

Dense halves in balanced 2-partition of K4-free graphs

Yue Xu, Xiao-Dong Zhang

A balanced 2-partition of a graph is a bipartition $A, A^{c}$ of $V (G)$ such that $∣ A ∣ = ∣ A^{c} ∣$ . Balogh, Clemen, and Lidický conjectured that for every $K_{4}$ -free graph on $n$ (even) ve…

math.CO2023

The spectral radius of minor free graphs

Ming-Zhu Chen, A-Ming Liu, Xiao-Dong Zhang

In this paper, we present a sharp upper bound for the spectral radius of an $n$ -vertex graph without $F$ -minor for sufficient large $n$ , where $F$ is obtained from the complete gra…

math.CO2023

A note on median eigenvalues of subcubic graphs

Yuzhenni Wang, Xiao-Dong Zhang

Let $G$ be an simple graph of order $n$ whose adjacency eigenvalues are $λ_{1} \geq \dots \geq λ_{n}$ . The HL--index of $G$ is defined to be $R (G) = max {∣ λ_{h} ∣, ∣ λ_{l} ∣}$ with $h=\left\lf…