Hongyuan Lai

activity

20142026

most citedCharacterizations of minimal graphs with equal edge connectivity and spanning tree packing number

2 citations · 6 across the 23 of their papers we have counts for

collaborators

24 papers

cond-mat.mtrl-sci2026

DiffGA: Steering Frozen Diffusion Models for Materials Design via Evolutionary Search

Shivang Agarwal, Rodrigo Wang, Kevin Ryczko +1

Steering candidate generation toward user-defined objectives is central to inverse materials design, yet remains difficult when objectives are black-box, changing, or non-different…

math.CO2026

On the Greedoid Tutte Polynomial for simple rooted graphs

Jianxuan Luo, Tingzeng Wu, Hong-Jian Lai

The Tutte polynomial, through its rank-generating formula, provides a unified framework for describing various combinatorial structures of graphs and matroids, and serves as an imp…

math.CO2025

On the characterizations of $D_{k} \ D_{k - 2}$

Jing Zeng, Lihua You, Xinghui Zhao +1

The determinant of a tournament $T$ , denoted by $det (T)$ , is defined as the determinant of the skew-adjacency matrix of $T$ . It is well-known that $det (T)$ is equal to $0$ if $n$ …

math.CO2025

Coefficients of univariate Tutte polynomials with one variable fixed

Tianlong Ma, Xiaxia Guan, Xian'an Jin +1

It is well known that the 2-variable Tutte polynomial of a graph $G$ includes chromatic polynomial and flow polynomial of $G$ , i.e. the cases of $y = 0$ and $x = 0$ . In 2013, Kálmán in…

math.CO2023

Square Coloring of Planar Graphs with Maximum Degree at Most Five

Jiani Zou, Miaomiao Han, Hong-Jian Lai

The \textit{square} of a graph $G$ , denoted by $G^{2}$ , is obtained from $G$ by adding an edge to connect every pair of vertices with a common neighbor in $G$ . In this paper we prove…

math.CO2023

No mixed graph with the nullity $η (G) = ∣ V (G) ∣ - 2 m (G) + 2 c (G) - 1$

Shengjie He, Rong-Xia Hao, Hong-Jian Lai +1

A mixed graph $G$ is obtained from a simple undirected graph $G$ , the underlying graph of $G$ , by orienting some edges of $G$ . Let $c (G) = ∣ E (G) ∣ - ∣ V (G) ∣ + ω (G)$ …

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.CO2021

Asymptotically sharpening the $s$ -Hamiltonian index bound

Sulin Song, Lan Lei, Yehong Shao +1

For a non-negative integer $s \leq ∣ V (G) ∣ - 3$ , a graph $G$ is $s$ -Hamiltonian if the removal of any $k \leq s$ vertices results in a Hamiltonian graph. Given a connected simple graph $G…

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…

math.CO2018

Unified spectral hamiltonian results of balanced bipartite graphs and complementary graphs

Muhuo Liu, Yang Wu, Hong-Jian Lai

There have been researches on sufficient spectral conditions for Hamiltonian properties and path-coverable properties of graphs. Utilizing the Bondy-Chvátal closure, we provide a u…

math.CO2018

Spanning tree packing, edge-connectivity and eigenvalues of graphs with given girth

Ruifang Liu, Hong-Jian Lai, Yingzhi Tian

Let $τ (G)$ and $κ^{'} (G)$ denote the edge-connectivity and the spanning tree packing number of a graph $G$ , respectively. Proving a conjecture initiated by Cioaba and Wong, Liu et al.…

math.CO2018

On the sizes of $(k, l)$ -edge-maximal $r$ -uniform hypergraphs

Yingzhi Tian, Hong-Jian Lai, Jixiang Meng +1

Let $H = (V, E)$ be a hypergraph, where $V$ is a set of vertices and $E$ is a set of non-empty subsets of $V$ called edges. If all edges of $H$ have the same cardinality $r$ , then $H$ …

math.CO2018

On the sizes of $k$ -edge-maximal $r$ -uniform hypergraphs

Yingzhi Tian, Liqiong Xu, Hong-Jian Lai +1

Let $H = (V, E)$ be a hypergraph, where $V$ is a set of vertices and $E$ is a set of non-empty subsets of $V$ called edges. If all edges of $H$ have the same cardinality $r$ , then $H$ …

math.CO2017

Nonseparating trees in 2-connected graphs and oriented trees in strongly connected digraphs

Yingzhi Tian, Hong-Jian Lai, Liqiong Xu +1

Mader [J. Graph Theory 65 (2010) 61-69] conjectured that for every positive integer $k$ and every finite tree $T$ with order $m$ , every $k$ -connected, finite graph $G$ with $δ(G)\g…

math.CO2017★ 1 cited

Connectivity keeping stars or double-stars in 2-connected graphs

Yingzhi Tian, Jixiang Meng, Hong-Jian Lai +1

In [W. Mader, Connectivity keeping paths in $k$ -connected graphs, J. Graph Theory 65 (2010) 61-69.], Mader conjectured that for every positive integer $k$ and every finite tree $T$ …

math.CO2017★ 1 cited

A note on edge degree and spanning trail containing given edges

Weihua Yang, Hong-jian Lai, Baoyindureng Wu

Let $G$ be a simple graph with $n \geq 4$ vertices and $d (x) + d (y) \geq n + k$ for each edge $x y \in E (G)$ . In this work we prove that $G$ either contains a spanning closed trail containi…

math.CO2016

Nowhere-zero $3$ -flow and $Z_{3}$ -connectedness in Graphs with Four Edge-disjoint Spanning Trees

Miaomiao Han, Hong-Jian Lai, Jiaao Li

Given a zero-sum function $β : V (G) \to Z_{3}$ with $\sum_{v \in V (G)} β (v) = 0$ , an orientation $D$ of $G$ with $d_{D}^{+} (v) - d_{D}^{-} (v) = β (v)$ in $Z_{3}$ for every ver…

math.CO2016

On the permanental nullity and matching number of graphs

Tingzeng Wu, Hong-Jian Lai

For a graph $G$ with $n$ vertices, let $ν (G)$ and $A (G)$ denote the matching number and adjacency matrix of $G$ , respectively. The permanental polynomial of $G$ is defined as $π(G,…

math.CO2014★ 2 cited

Characterizations of minimal graphs with equal edge connectivity and spanning tree packing number

Xiaofeng Gu, Hong-Jian Lai, Ping Li +1

With graphs considered as natural models for many network design problems, edge connectivity $κ^{'} (G)$ and maximum number of edge-disjoint spanning trees $τ (G)$ of a graph $G$ have b…

math.CO2014★ 1 cited

Realizing degree sequences as $Z_{3}$ -connected graphs

Fan Yang, Xiangwen Li, Hong -Jian Lai

An integer-valued sequence $π = (d_{1}, \dots, d_{n})$ is {\em graphic} if there is a simple graph $G$ with degree sequence of $π$ . We say the $π$ has a realization $G$ . Let $Z_{3}$ be a…

DiffGA: Steering Frozen Diffusion Models for Materials Design via Evolutionary Search

On the Greedoid Tutte Polynomial for simple rooted graphs

On the characterizations of Dk​\Dk−2​

Coefficients of univariate Tutte polynomials with one variable fixed

Square Coloring of Planar Graphs with Maximum Degree at Most Five

No mixed graph with the nullity η(G)=∣V(G)∣−2m(G)+2c(G)−1

Gallai-Ramsey numbers involving a rainbow 4-path

Asymptotically sharpening the s-Hamiltonian index bound

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

Unified spectral hamiltonian results of balanced bipartite graphs and complementary graphs

Spanning tree packing, edge-connectivity and eigenvalues of graphs with given girth

On the sizes of (k,l)-edge-maximal r-uniform hypergraphs

On the sizes of k-edge-maximal r-uniform hypergraphs

Nonseparating trees in 2-connected graphs and oriented trees in strongly connected digraphs

Connectivity keeping stars or double-stars in 2-connected graphs

A note on edge degree and spanning trail containing given edges

Nowhere-zero 3-flow and Z3​-connectedness in Graphs with Four Edge-disjoint Spanning Trees

On the permanental nullity and matching number of graphs

Characterizations of minimal graphs with equal edge connectivity and spanning tree packing number

Realizing degree sequences as Z3​-connected graphs

On the characterizations of $D_{k} \ D_{k - 2}$

No mixed graph with the nullity $η (G) = ∣ V (G) ∣ - 2 m (G) + 2 c (G) - 1$

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

Asymptotically sharpening the $s$ -Hamiltonian index bound

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

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

On the sizes of $(k, l)$ -edge-maximal $r$ -uniform hypergraphs

On the sizes of $k$ -edge-maximal $r$ -uniform hypergraphs

Nowhere-zero $3$ -flow and $Z_{3}$ -connectedness in Graphs with Four Edge-disjoint Spanning Trees

Realizing degree sequences as $Z_{3}$ -connected graphs