Mingqing Zhai

activity

20222026

most citedExtremal eigenvalues with respect to graph minors

2 citations · 2 across the 12 of their papers we have counts for

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12 papers · 1 filter

math.CO2026

Dense-core approach to the Brualdi--Hoffman--Turán problem on odd wheels

Longfei Fang, Mingqing Zhai, Yuhan Zhang

We present a unified presentation of the fixed-size adjacency-spectral extremal problem for odd wheels $W_{2 k + 1}$ , where $k \geq 2$ and $W_{2 k + 1} = K_{1} \lor C_{2 k}$ . The exceptional cas…

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 $ρ (G)$ 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 lengths…

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 $ρ_{1} > m$ contains at least one triangle. Its quan…

math.CO2026

Counting color-critical subgraphs under Nikiforov's condition

Longfei Fang, Huiqiu Lin, Mingqing Zhai

For a graph $G$ with $m$ edges, let $ρ (G)$ be its spectral radius, and let $N_{F} (G)$ denote the number of copies of $F$ in $G$ . Nikiforov [Combin. Probab.\,Comput., 2002] proved tha…

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

Advances on two spectral conjectures regarding booksize of graphs

Mingqing Zhai, Rui Li, Zhenzhen Lou

The booksize $bk (G)$ of a graph $G$ , introduced by Erdős, refers to the maximum integer $r$ for which $G$ contains the book $B_{r}$ as a subgraph. This paper investi…

math.CO2025

The spectral Turán problem: Characterizing spectral-consistent graphs

Longfei Fang, Sergey Goryainov, Denis Krotov +2

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

math.CO2024

Spectral Radius of Graphs with Size Constraints: Resolving a Conjecture of Guiduli

Rui Li, Anyao Wang, Mingqing Zhai

We resolve a problem posed by Guiduli (1996) on the spectral radius of graphs satisfying the Hereditarily Bounded Property $P_{t, r}$ , which requires that every subgraph $H$ with $|…

math.CO2024

Turán numbers for non-bipartite graphs and applications to spectral extremal problems

Longfei Fang, Michael Tait, Mingqing Zhai

Given a graph family $H$ with $min_{H \in H} χ (H) = r + 1 \geq 3$ . Let $ex (n, H)$ and $spex (n, H)$ be the maximum number of edges and th…

math.CO2024★ 2 cited

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.…

math.CO2022

Extremal problems on planar graphs without k edge-disjoint cycles

Zhai Mingqing, Liu Muhuo

In the 1960s, Erdős and his cooperators initiated the research of the maximum numbers of edges in a graph or a planar graph on $n$ vertices without $k$ edge-disjoint cycles. This p…