Shengtong Zhang

activity

20232026

most citedMore on Nosal's spectral theorem: Books and

4

-cycles

2 citations · 3 across the 18 of their papers we have counts for

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17 papers · 1 filter

math.CO2026

A positive square-energy strengthening of Turán's theorem

Yinchen Liu, Quanyu Tang, Shengtong Zhang

Let $G$ be an $n$ -vertex graph with clique number $ω (G)$ , and let $s^{+} (G)$ denote the sum of the squared positive adjacency eigenvalues. We prove that $$ \sqrt{s^+(G)}\le\left(1-\f…

math.CO2026

The positive and negative square-energy conjecture

Yinchen Liu, Quanyu Tang, Shengtong Zhang

Let $s^{+} (G)$ and $s^{-} (G)$ denote the sums of the squares of the positive and negative adjacency eigenvalues of a graph $G$ , respectively. We prove the conjecture of Elphick, Farber…

math.CO2026

Spectral Sidorenko inequalities and edge-spectral supersaturation

Yongtao Li, Wilson Lin, Hong Liu +1

We develop a spectral approach to Sidorenko-type inequalities and apply it to establish sharp edge-spectral supersaturation results. Let $H$ be a bipartite graph with $v$ vertices…

math.CO2026

Bounds on median eigenvalues of graphs of bounded degree

Hricha Acharya, Zilin Jiang, Shengtong Zhang

We prove that for every integer $d \geq 3$ , the median eigenvalues of any graph of maximum degree $d$ are bounded above by $d - 1$ . We also prove that, in three separate cases,…

math.CO2026

Chromatic thresholds for linear equations and recurrence

Hong Liu, Zhuo Wu, Ningyuan Yang +1

Motivated by classical problems in extremal graph theory, we study a chromatic analogue of Roth-type questions for linear equations over $F_{p}$ . Given a homogeneous equation…

math.CO2026

Large point-line matchings and small Nikodym sets

Zach Hunter, Cosmin Pohoata, Jacques Verstraete +1

For any integer $d \geq 2$ and prime power $q$ , we construct unexpectedly large induced matchings in the point-line incidence graph of $F_{q}^{d}$ by leveraging a new conn…

math.CO2025

Edge-spectral Turán theorems for color-critical graphs with applications

Yongtao Li, Hong Liu, Shengtong Zhang

A classical result of Nosal asserts that every $m$ -edge graph with spectral radius $λ (G) > m$ contains a triangle. A celebrated extension of Nikiforov [2002, CPC] states that…

math.CO2025

From small eigenvalues to large cuts, and Chowla's cosine problem

Zhihan Jin, Aleksa Milojević, István Tomon +1

We prove that every graph with average degree $d$ and smallest adjacency eigenvalue $∣ λ_{n} ∣ \leq d^{γ}$ contains a clique of size $d^{1 - O (γ)}$ . A simple corollary of this yields the fi…

math.CO2025

An edge-spectral Erdős-Stone-Simonovits theorem and its stability

Yongtao Li, Hong Liu, Shengtong Zhang

We study the extremal problem that relates the spectral radius $λ (G)$ of an $F$ -free graph $G$ to its number of edges. Firstly, we prove that for any graph $F$ with chromatic numbe…

math.CO2025★ 2 cited

More on Nosal's spectral theorem: Books and $4$ -cycles

Yongtao Li, Hong Liu, Shengtong Zhang

Spectral graph theory studies how the eigenvalues of a graph relate to the structural properties of a graph. In this paper, we solve three open problems in spectral extremal graph…

math.CO2025

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut

Shengtong Zhang

For any $ε > 0$ , we show that if $G$ is a regular graph on $n ≫_{ε} 1$ vertices that is $ε$ -far (differs by at least $ε n^{2}$ edges) from any Turán graph, then its second eigenvalue $λ…

math.CO2025

Inertia, Independence and Expanders

Quanyu Tang, Shengtong Zhang, Clive Elphick

Let $G$ be a graph on $n$ vertices, independence number $α (G)$ , Lovász theta function $ϑ (G)$ , and Shannon capacity $Θ (G)$ . We define $n_{\geq 0} (G)$ to be the minimum number…

math.CO2025

Refinement of a conjecture on positive square energy of graphs

Saieed Akbari, Hitesh Kumar, Bojan Mohar +2

Let $G$ be a simple graph of order $n$ with eigenvalues $λ_{1} (G) \geq \dots \geq λ_{n} (G)$ . Define \[s^+(G)=\sum_{λ_i >0} λ_i^2(G), \quad s^-(G)=\sum_{λ_i<0} λ_i^2(G).\] It was conjec…

math.CO2025

Colorful Helly via induced matchings

Cosmin Pohoata, Kevin Yang, Shengtong Zhang

We establish a theorem regarding the maximum size of an {\it{induced}} matching in the bipartite complement of the incidence graph of a set system $(X, F)$ . We show that t…

math.CO2024

Extremal values for the square energies of graphs

Shengtong Zhang

Let $G$ be a graph with $n$ non-isolated vertices and $m$ edges. The positive / negative square energies of $G$ , denoted $s^{+} (G)$ / $s^{-} (G)$ , are defined as the sum of squares of t…

math.CO2023★ 1 cited

Triangle Ramsey numbers of complete graphs

Jacob Fox, Jonathan Tidor, Shengtong Zhang

A graph is $H$ -Ramsey if every two-coloring of its edges contains a monochromatic copy of $H$ . Define the $F$ -Ramsey number of $H$ , denoted by $r_{F} (H)$ , to be the minimum number of…

math.CO2023

On the first two eigenvalues of regular graphs

Shengtong Zhang

Let $G$ be a regular graph with $m$ edges, and let $μ_{1}, μ_{2}$ denote the two largest eigenvalues of $A_{G}$ , the adjacency matrix of $G$ . We show that, if $G$ is not complete, then $…

A positive square-energy strengthening of Turán's theorem

The positive and negative square-energy conjecture

Spectral Sidorenko inequalities and edge-spectral supersaturation

Bounds on median eigenvalues of graphs of bounded degree

Chromatic thresholds for linear equations and recurrence

Large point-line matchings and small Nikodym sets

Edge-spectral Turán theorems for color-critical graphs with applications

From small eigenvalues to large cuts, and Chowla's cosine problem

An edge-spectral Erdős-Stone-Simonovits theorem and its stability

More on Nosal's spectral theorem: Books and 4-cycles

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut

Inertia, Independence and Expanders

Refinement of a conjecture on positive square energy of graphs

Colorful Helly via induced matchings

Extremal values for the square energies of graphs

Triangle Ramsey numbers of complete graphs

On the first two eigenvalues of regular graphs

More on Nosal's spectral theorem: Books and $4$ -cycles