Hongyuan Lai

activity

20162021

most citedConnectivity keeping stars or double-stars in 2-connected graphs

1 citations · 3 across the 8 of their papers we have counts for

collaborators

14 papers

math.CO2021★ 1 cited

Gallai-Ramsey numbers involving a rainbow $4$ -path

Jinyu Zou, Zhao Wang, Hong-Jian Lai +1

Given two non-empty graphs $G, H$ and a positive integer $k$ , the Gallai-Ramsey number $gr_{k} (G : H)$ is defined as the minimum integer $N$ such that for all $n \geq N$ ,…

math.CO2020

Fractional matching number and spectral radius of nonnegative matrix of graphs

Ruifang Liu, Hong-Jian Lai, Litao Guo +1

A fractional matching of a graph $G$ is a function $f : E (G) \to [0, 1]$ such that for any $v \in V (G)$ , $\sum_{e \in E_{G} (v)} f (e) \leq 1$ where $E_{G} (v) = {e \in E (G) : e$ is incident wit…

math.CO2020

Connectivity and eigenvalues of graphs with given girth or clique number

Zhen-Mu Hong, Hong-Jian Lai, Zheng-Jiang Xia

Let $κ^{'} (G)$ , $κ (G)$ , $μ_{n - 1} (G)$ and $μ_{1} (G)$ denote the edge-connectivity, vertex-connectivity, the algebraic connectivity and the Laplacian spectral radius of $G$ , respectively.…

math.CO2020

Induced subgraphs of product graphs and a generalization of Huang's theorem

Zhen-Mu Hong, Hong-Jian Lai, Jian-Bing Liu

Recently, Huang showed that every $(2^{n - 1} + 1)$ -vertex induced subgraph of the $n$ -dimensional hypercube has maximum degree at least $n$ in [Annals of Mathematics, 190 (2019…

math.CO2019

Vertex-connectivity and $Q$ -index of graphs with fixed girth

Huicai Jia, Hong-Jian Lai, Ruifang Liu +1

Let $q (G)$ denote the $Q$ -index of a graph $G$ , which is the largest signless Laplacian eigenvalue of $G$ . We prove best possible upper bounds of $q (G)$ and best possible lower bou…

math.CO2018

A note on eigenvalues and Hamiltoinan properties of $k$ -connected graphs

Huicai Jia, Ruifang Liu, Hong-Jian Lai

Let $λ_{1} (G)$ and $μ_{1} (G)$ denote the spectral radius and the Laplacian spectral radius of a graph $G$ , respectively. Li in [Electronic J. Linear Algebra 34 (2018) 389-392] prov…

Gallai-Ramsey numbers involving a rainbow 4-path

Fractional matching number and spectral radius of nonnegative matrix of graphs

Connectivity and eigenvalues of graphs with given girth or clique number

Induced subgraphs of product graphs and a generalization of Huang's theorem

Vertex-connectivity and Q-index of graphs with fixed girth

A note on eigenvalues and Hamiltoinan properties of k-connected graphs

Gallai-Ramsey numbers involving a rainbow $4$ -path

Vertex-connectivity and $Q$ -index of graphs with fixed girth

A note on eigenvalues and Hamiltoinan properties of $k$ -connected graphs