Mingqing Zhai

collaborators

9 papers

math.CO2026

Edge-spectral supersaturation for tripartite color-critical graphs

Longfei Fang, Huiqiu Lin, Mingqing Zhai

We study edge-spectral supersaturation for two families of color-critical graphs with chromatic number three. For an integer $r \geq 1$ , we define the spectral threshold \[ g_r(m):=…

math.CO2026

Nikiforov's spectral consecutive cycle problem and the connected-matching method

Bo Ning, Mingqing Zhai

Let $I ¨ (G)$ denote the adjacency spectral radius of a graph $G$ of order $n$ . We determine the sharp constant in an open problem of Nikiforov (2008) on cycles of consecutive length…

math.CO2026

Spectral extremal graphs on closed surfaces of fixed Euler genus

Mingqing Zhai, Longfei Fang, Huiqiu Lin

Graph theory on surfaces extends classical graph structures to topological surfaces, providing a theoretical foundation for characterizing the embedding properties of complex netwo…

math.CO2026

A spectral threshold for triangle counting

Yuhan Zhang, Mingqing Zhai

The 1970 spectral extension of Mantel's theorem, proved by Nosal, states that every graph with $m$ edges and spectral radius $I ¨ _{1} > m$ contains at least one triangle. Its qua…

math.CO2026

The spectral TurÃ¡n problem: Characterizing spectral-consistent graphs

Longfei Fang, Sergey Goryainov, Denis Krotov +2

Let $EX (n, H)$ and $SPEX (n, H)$ denote the families of $n$ -vertex $H$ -free graphs with the maximum size and the maximum spectral radius, respectively. A graph $H$ is said…

math.CO2026

Extremal eigenvalues with respect to graph minors

Mingqing Zhai, Longfei Fang, Huiqiu Lin

Let $s p e x (n, H_{min or})$ denote the maximum spectral radius of $n$ -vertex $H$ -minor free graphs. The problem on determining this extremal value can be dated back to the early 1990s.…