Hongzhang Chen

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9 papers · 1 filter

math.CO2026

Proofs of Li, Wang and Guo's conjectures on (signless) Laplacian spectral radius

Hongzhang Chen, Jianxi Li, Xiaoyun Lv

Let $μ (G)$ and $q (G)$ be the Laplacian and signless Laplacian spectral radii of a graph $G$ . Li, Wang and Guo (2026) conjectured that, if $H$ with $∣ V (H) ∣ \geq 1$ is an induced subg…

math.CO2026

Supersaturation in Nosal graphs: Triangles and books

Hongzhang Chen, Yongtao Li, Quanyu Tang

In this paper, we use the spectral surplus $λ (G) - m$ to measure how far $G$ lies above the Nosal threshold, and prove the following edge-spectral supersaturation results fo…

math.CO2026

An edge-spectral supersaturation of Mubayi's theorem for color-critical graphs

Hongzhang Chen, Yongtao Li

We study the supersaturation problem in its edge-spectral form. Let $λ (G)$ be the adjacency spectral radius of $G$ . Nikiforov proved that every $K_{r + 1}$ -free graph $G$ with $m$ ed…

math.CO2026

Spectral extremal graphs for even factors

Zeyuan Wu, Hongzhang Chen, Xinting Shi +1

An even factor of a graph $G$ is a spanning subgraph in which every vertex has positive even degree. It is known that the minimum degree $δ (G) \geq 2$ is a trivial necessary conditio…

math.CO2026

A non-hereditary Pollyanna class that is not strongly Pollyanna

Hongzhang Chen, Kaiyang Lan

Chudnovsky, Cook, Davies, and Oum introduced the notion of Pollyanna graph classes: a class $C$ is Pollyanna if for every $χ$ -bounded class $F$ , the intersectio…

math.CO2026

On two conjectures of Hoàng

Hongzhang Chen, Kaiyang Lan, Wenlong Zhong

A graph $G$ is said to be perfectly divisible if for every induced subgraph $H$ of $G$ with at least one edge, the vertex set $V (H)$ can be partitioned into two sets $A, B$ such th…

math.CO2026

Counterexamples to a conjecture on graph inertia

Hongzhang Chen, Jianxi Li

The inertia of a graph $G$ is $In (G) = (n^{+} (G), n^{0} (G), n^{-} (G))$ , where $n^{+} (G), n^{0} (G), n^{-} (G)$ are the numbers of positive, zero and negative eigenvalues of the ad…

math.CO2026

On a conjecture of distance spectral extremal problems

Hongzhang Chen, Jianxi Li, Yongtao Li

Brualdi and Hoffman proposed a well-known problem of determining the graph with maximum adjacency spectral radius among all graphs with given size $m$ . Early work by Friedland and…

math.CO2026

An exponentially small gap of the Perron vector on independent sets

Hongzhang Chen, Jianxi Li, Yongtao Li +2

A classical result of Cioabă states that if $G$ is a connected graph with the unit Perron vector $x$ , then any independent set $S$ of $G$ satisfies $\sum_{v\in S} x_v^2 \l…