Xiao-Dong Zhang

works on

Berge hypergraphs 1 extremal combinatorics 1 hypergraph Turán problems 1 matching number 1 uniform hypergraphs 1

From the 1 of 7 linked papers with an AI index.

activity

20242026

collaborators

7 papers

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

Hypergraph Turan with bounded matching number

Yue Xu, Jiasheng Zeng, Xiao-Dong Zhang

The paper determines the exact maximum number of edges in 3‑uniform and 4‑uniform Berge‑K₃‑free hypergraphs whose matching number is bounded by s, providing precise Turán numbers a…

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 $I^»_{1} (G) \geq I^»_{2} (G) \geq \dots \geq I^»_{n} (G)$ be its eigenvalues. For an integer $p…

math.CO2026

TurÃ¡n extremal graphs vs. Signless Laplacian spectral TurÃ¡n extremal graphs

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

Let $F$ be a graph with chromatic number $I ¨ (F) = r + 1$ . Denote by $e x (n, F)$ and $E x (n, F)$ the TurÃ¡n 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 TurÃ¡n 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…