Shengtong Zhang

collaborators

16 papers

math.CO2026

A positive square-energy strengthening of TurÃ¡n's theorem

Yinchen Liu, Quanyu Tang, Shengtong Zhang

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

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

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

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

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…