Bo Ning

activity

20232026

most citedVariants of spectral Turán theorems and eigenvectors of graphs

1 citations · 2 across the 14 of their papers we have counts for

collaborators

15 papers

math.CO2026

The spectral Erdős book theorem: sharp bounds and stability

Lele Liu, Yongtao Li, Bo Ning

The booksize $bk (G)$ of a graph $G$ is the largest number of triangles sharing a common edge. A classical theorem of Edwards, conjectured by Bollobás and Erdős, states tha…

math.CO2026

A complete solution to the Boots-Royle/Cao-Vince conjecture

Lele Liu, Bo Ning, Yi Wang

Boots and Royle, and independently Cao and Vince, conjectured that the join of an edge and a path on $n - 2$ vertices is the unique planar graph of maximum adjacency spectral radius…

math.CO2026

The largest Laplacian eigenvalue of induced- $K_{1, r}$ -free graphs

Lele Liu, Bo Ning

Let $G$ be a simple graph of maximum degree $d$ , and let $μ (G)$ denote the largest eigenvalue of its Laplacian matrix. For a fixed integer $k \geq 2$ , Aharoni, Alon, and Berger (201…

math.CO2026

An exponentially small gap of the Perron vector on independent sets

Hongzhang Chen, Jianxi Li, Yongtao Li +2

A classical result of Cioabă states that if $G$ is a connected graph with the unit Perron vector $x$ , then any independent set $S$ of $G$ satisfies $\sum_{v\in S} x_v^2 \l…

math.CO2026

A short proof of a perturbation inequality for the spectral radius

Lele Liu, Bo Ning

Let $G$ be a simple graph, and denote by $λ (G)$ its spectral radius. Sun and Das (2020) established that for any non-isolated vertex $v$ with degree $d (v)$ , \[ λ(G)\leq \sqrt{λ(G-v…

math.CO2026

An Improved Interpolation Theorem and Disproofs of Two Conjectures on 2-Connected Subgraphs

Haiyang Liu, Bo Ning

We prove that any $2$-connected graph $G$ on $n$ vertices with minimum degree $δ(G) \ge \frac{n}{4}+2$ contains a $2$-connected subgraph of order $k$ for every integer…

math.CO2025

Exact Turán numbers of two vertex-disjoint paths

Miao Dong, Bo Ning, Long-Tu Yuan +1

The Turán number of a graph $H$ is the maximum number of edges in any graph of order $n$ that does not contain $H$ as a subgraph. In 1959, Erd\H os and Gallai obtained a sharp uppe…

math.CO2025

Two conjectures on vertex-disjoint rainbow triangles

Xu Liu, Bo Ning, Yuting Tian

In 1963, Dirac proved that every $n$ -vertex graph has $k$ vertex-disjoint triangles if $n \geq 3 k$ and minimum degree $δ (G) \geq \frac{n + k}{2}$ . The base case $n = 3 k$ can be reduced t…

math.CO2025

A new spectral Turán theorem for weighted graphs and consequences

Lele Liu, Bo Ning

Confirming a conjecture of Elphick and Edwards and strengthening a spectral theorem of Wilf, Nikiforov proved that for any $K_{r + 1}$ -free graph $G$ , $λ (G)^{2} \leq 2 (1 - 1/ r) m$ , wh…

math.CO2025

The stability of independence polynomials of complete bipartite graphs

Guo Chen, Bo Ning, Jianhua Tu

The independence polynomial of a graph is termed {\it stable} if all its roots are located in the left half-plane ${z \in C : Re (z) \leq 0}$ , and the graph itse…

math.CO2024★ 1 cited

The number of edges in graphs with bounded clique number and circumference

Chunyang Dou, Bo Ning, Xing Peng

Let $H$ be a family of graphs. The Turán number $ex (n, H)$ is the maximum possible number of edges in an $n$ -vertex graph which does not contain any member of $\ca…

math.CO2024

The generalized Tur'{a}n number of long cycles in graphs and bipartite graphs

Changchang Dong, Mei Lu, Jixiang Meng +1

Given a graph $T$ and a family of graphs $F$ , the maximum number of copies of $T$ in an $F$ -free graph on $n$ vertices is called the generalized Turán number, d…

math.CO2024

On degree power sum in $P_{k}$ -free graphs

Jiangdong Ai, Fankang He, Yihang Liu +1

Let $G$ be a graph on $n$ vertices with degree sequence $(d_{1}, d_{2} ...... d_{n})$ . For a real $p \geq 1$ , let $D_{p} (G) = \sum_{i = 1}^{n} d_{i}^{p}$ . A Turán-type problem of degree power sum was in…

math.CO2024

Graph operations and a unified method for kinds of Turán-type problems on paths, cycles and matchings

Jiangdong Ai, Hui Lei, Bo Ning +1

Let $G$ be a connected graph and $P (G)$ a graph parameter. We say that $P (G)$ is feasible if $P (G)$ satisfies the following properties: (I) $\mathcal{…

math.CO2023★ 1 cited

Variants of spectral Turán theorems and eigenvectors of graphs

Lele Liu, Bo Ning

In 2002, Nikiforov proved that for an $n$ -vertex graph $G$ with clique number $ω$ and edge number $m$ , the spectral radius $λ (G)$ satisfies $λ (G) \leq 2 (1 - 1/ ω) m$ , which c…

The spectral Erdős book theorem: sharp bounds and stability

A complete solution to the Boots-Royle/Cao-Vince conjecture

The largest Laplacian eigenvalue of induced-K1,r​-free graphs

An exponentially small gap of the Perron vector on independent sets

A short proof of a perturbation inequality for the spectral radius

An Improved Interpolation Theorem and Disproofs of Two Conjectures on 2-Connected Subgraphs

Exact Turán numbers of two vertex-disjoint paths

Two conjectures on vertex-disjoint rainbow triangles

A new spectral Turán theorem for weighted graphs and consequences

The stability of independence polynomials of complete bipartite graphs

The number of edges in graphs with bounded clique number and circumference

The generalized Tur'{a}n number of long cycles in graphs and bipartite graphs

On degree power sum in Pk​-free graphs

Graph operations and a unified method for kinds of Turán-type problems on paths, cycles and matchings

Variants of spectral Turán theorems and eigenvectors of graphs

The largest Laplacian eigenvalue of induced- $K_{1, r}$ -free graphs

On degree power sum in $P_{k}$ -free graphs