Huiqiu Lin

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.SP2026

Minimally $(k, k)$ -edge-connected graphs via spectral radius

Yu Wang, Dan Li, Huiqiu Lin

For $l > 1$ , the $l$ -edge-connectivity $κ_{l}^{'} (G)$ of a connected graph $G$ is defined as the minimum number of edges whose removal leaves a graph with at least $l$ components. A gra…

Spectral extremal results for triangle-free graphs with chromatic number at least four

Yinfen Zhu, Huiqiu Lin

A graph is called $F$ -free if it does not contain a copy of $F$ . Let $G (r, s)$ denote a $K_{r + 1}$ -free graph of order $n$ with chromatic number at least $s$ that maximizes the spect…

Spectral radius, toughness and $k$ -factor of graphs

Yuanyuan Chen, Huiqiu Lin, Shucheng Li

A $k$ -regular spanning subgraph of $G$ is called a $k$ -factor. Fan, Lin and Lu [European J. Combin. 110 (2023) 103701] presented a tight sufficient condition in terms of the spectr…

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…

More on spectral supersaturation for the bowtie

Longfei Fang, Yongtao Li, Huiqiu Lin

A central topic in extremal graph theory is the supersaturation problem, which studies the minimum number of copies of a fixed substructure that must appear in any graph with more…

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…

Spectral supersaturation for color-critical graphs

Longfei Fang, Yongtao Li, Huiqiu Lin +1

A graph is color-critical if it contains an edge whose deletion reduces its chromatic number. This class of graphs, including cliques and odd cycles, plays a central role in extrem…

math.SP2025

A note on the spectral radius and $[a, b]$ -factor of graphs

Dandan Fan, Huiqiu Lin, Yinfen Zhu

The investigation of eigenvalue conditions for the existence of an $[a, b]$ -factor originates in the work of Brouwer and Haemers (2005) on perfect matchings. In the decades since, s…

Non-bipartite graphs without theta subgraphs

Longfei Fang, Huiqiu Lin

Fix a color-critical graph $H$ with $χ (H) = r + 1 \geq 3$ . Simonovits' chromatic critical edge theorem and Nikiforov's spectral chromatic critical edge theorem imply that $T_{n, r}$ is t…

On the Turán number of odd-ballooning of $3$ -chromatic graphs

Longfei Fang, Xueyi Huang, Huiqiu Lin +1

Given a graph $F$ , the Turán number $ex (n, F)$ is the maximum number of edges in any $n$ -vertex $F$ -free graph. The odd-ballooning of $F$ , denoted by $F^{o}$ , is a graph obtai…

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…

The existence of biregular spanning subgraphs in bipartite graphs via spectral radius

Dandan Fan, Xiaofeng Gu, Huiqiu Lin

Biregular bipartite graphs have been proven to have similar edge distributions to random bipartite graphs and thus have nice pseudorandomness and expansion properties. Thus it is q…

Long cycles and spectral radii in planar graphs

Ping Xu, Huiqiu Lin, Longfei Fang

There is a rich history of studying the existence of cycles in planar graphs. The famous Tutte theorem on the Hamilton cycle states that every 4-connected planar graph contains a H…

A unified approach to the spectral radius, connectivity and edge-connectivity of graphs

Yu Wang, Dan Li, Huiqiu Lin

For two integers $r \geq 2$ and $h \geq 0$ , the \emph{ $h$ -extra $r$ -component connectivity} $κ_{r}^{h} (G)$ of a graph $G$ is defined to be the minimum size of a subset of vertices whose…

Spectral expansion properties of pseudorandom bipartite graphs

Dandan Fan, Xiaofeng Gu, Huiqiu Lin

An $(a, b)$ -biregular bipartite graph is a bipartite graph with bipartition $(X, Y)$ such that each vertex in $X$ has degree $a$ and each vertex in $Y$ has degree $b$ . By the bipart…

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.…

On the spectral extremal problem of planar graphs

Xiaolong Wang, Xueyi Huang, Huiqiu Lin

The spectral extremal problem of planar graphs has aroused a lot of interest over the past three decades. In 1991, Boots and Royle [Geogr. Anal. 23(3) (1991) 276--282] (and Cao and…

Spectral extremal results on trees

Longfei Fang, Huiqiu Lin, Jinlong Shu +1

Let $spex (n, F)$ be the maximum spectral radius over all $F$ -free graphs of order $n$ , and $SPEX (n, F)$ be the family of $F$ -free graphs of order $n$ with spectral radius…

Eigenvalues and factors: a survey

Dandan Fan, Huiqiu Lin, Hongliang Lu +1

A factor of a graph is a spanning subgraph satisfying some given conditions. An earlier survey of factors can be traced back to the Akiyama and Kano [J. Graph Theory, 1985, 9: 1-42…

Toughness and spectral radius in graphs

Yuanyuan Chen, Dandan Fan, Huiqiu Lin

The Brouwer's toughness conjecture states that every $d$ -regular connected graph always has $t (G) > \frac{d}{λ} - 1$ where $λ$ is the second largest absolute eigenvalue of the adjacency…

Spectral extremal results on edge blow-up of graphs

Longfei Fang, Huiqiu Lin

Let $ex (n, F)$ and $spex (n, F)$ be the maximum size and maximum spectral radius of an $F$ -free graph of order $n$ , respectively. The value $spex (n, F)$ is called the…