Le Xu

activity

20232026

most citedSpectral conditions for the existence of chorded cycles in graphs with fixed size

1 citations · 2 across the 18 of their papers we have counts for

collaborators

20 papers

math.CO2026

Positive discrepancy of graphs far from Turán graphs

Leyou Xu, Bo Zhou

We prove that, for every $\eps>0$, any $n$ -vertex graph that needs at least $\eps n^2$ edge changes to become a Turán graph has positive discrepancy at least $c_\eps n^{5/4}$. Cons…

math.CO2026

Proving a conjecture concerning chromatic number, size and least eigenvalue

Leyou Xu, Bo Zhou

Let $G$ be a simple nonempty graph with size $m$ , chromatic number $χ$ , and least eigenvalue $λ$ . We prove that \[ χ(χ-1) \le (m+1-λ^2)+\sqrt{(m+1-λ^2)^2-4(λ^2-1)(λ^2-m)} \] with e…

math.CO2026

The number of cycles of a given length in dense hamiltonian graphs: proving Hilton's conjecture

Chengli Li, Leyou Xu, Bo Zhou

A classical theorem of Sheehan in 1977 states that every hamiltonian graph $G$ of order $n$ satisfying $e (G) > ⌊ \frac{n ^{2}}{4} ⌋ + 1$ contains at least two cycles…

math.CO2026

On $k$ -connected vertex-pancyclic graphs without pancyclic edges

Leyou Xu, Bo Zhou

An edge of a graph of order $n$ is pancyclic if it lies in a cycle of every length $3, \dots, n$ . A graph of order $n$ is vertex-pancyclic if every vertex lies in a cycle of every l…

math.CO2026

Extremal $Q$ -index problem in outerplanar graphs

Jin Cai, Leyou Xu, Bo Zhou

Outerplanar Turán problem has received considerable attention recently. We study the spectral version via $Q$ -index. We determine the unique graph that maximizes the $Q$ -index amon…

math.CO2025

Girth and Laplacian eigenvalue distribution

Leyou Xu, Bo Zhou

Let $G$ be a connected graph of order $n$ with girth $g$ . For $k = 1, \dots, min {g - 1, n - g}$ , let $n (G, k)$ be the number of Laplacian eigenvalues (counting multiplicities) of $G$ tha…

math.CO2025

Cycles and paths through specified vertices in graphs with a given clique number

Chengli Li, Leyou Xu

B. Bollobás and G. Brightwell and independently R. Shi proved the existence of a cycle through all vertices whose degrees at least $\frac{n}{2}$ in any $2$ -connected graph of order…

math.CO2024

Spectral conditions implying the existence of doubly chorded cycles without or with constraints

Leyou Xu, Bo Zhou

What spectral conditions imply a graph contains a chorded cycle? This question was asked by R.J. Gould in 2022. We answer two modified versions of Gould's question by giving tight…

math.CO2024★ 1 cited

Spectral conditions for the existence of chorded cycles in graphs with fixed size

Jin Cai, Leyou Xu, Bo Zhou

A chorded cycle is a cycle with at least one chord. Gould asked in [Graphs Comb. 38 (2022) 189] the question: What spectral conditions imply a graph contains a chorded cycle? For a…

math.CO2024

Diameter vs Laplacian eigenvalue distribution

Leyou Xu, Bo Zhou

Let $G$ be a simple graph of order $n$ . It is known that any Laplacian eigenvalue of $G$ belongs to the interval $[0, n]$ . For an interval $I \subseteq [0, n]$ , denote by $m_{G} I$ the…

math.CO2023

Answers to Gould's question concerning the existence of chorded cycles

Leyou Xu, Bo Zhou

Answers are offered to the Gould's question to find spectral sufficient conditions for a graph to have a chorded cycle via signless Laplacian spectral radius. The conditions are ti…

math.CO2023

Distribution of signless Laplacian eigenvalues and graph invariants

Leyou Xu, Bo Zhou

For a simple graph on $n$ vertices, any of its signless Laplacian eigenvalues is in the interval $[0, 2 n - 2]$ . In this paper, we give relationships between the number of signless La…

cs.SI2023

Link residual closeness of graphs with fixed parameters

Leyou Xu, Chengli Li, Bo Zhou

Link residual closeness is a newly proposed measure for network vulnerability. In this model, vertices are perfectly reliable and the links fail independently of each other. It mea…

math.CO2023

Toughness and existence of $2$ -factors

Leyou Xu, Bo Zhou

A graph is $t$ -tough if the deletion of any set of, say, $m$ vertices from the graph leaves a graph with at most $\frac{m}{t}$ components. In 1973, Chvátal suggested the problem of…

math.CO2023

The Alon-Tarsi number of $K_{3, 3}$ -minor-free graphs

Leyou Xu, Bo Zhou

The well known Wagner's theorem states that a graph is a planar graph if and only if it is $K_{5}$ -minor-free and $K_{3, 3}$ -minor-free. Denote by $A T (G)$ the Alon-Tarsi number of a g…

math.CO2023★ 1 cited

Laplacain eigenvalue distribution and diameter of graphs

Leyou Xu, Bo Zhou

Let $G$ be a connected graph on $n$ vertices with diameter $d$ . It is known that if $2 \leq d \leq n - 2$ , there are at most $n - d$ Laplacian eigenvalues in the interval $[n - d + 2, n]$ . In…

math.CO2023

The generalized $4$ -connectivity of bubble-sort graphs

Leyou Xu, Bo Zhou

For $S \subseteq V (G)$ with $∣ S ∣ \geq 2$ , let $κ_{G} (S)$ denote the maximum number of internally disjoint trees connecting $S$ in $G$ . For $2 \leq k \leq n$ , the generalized $k$ -connectivi…

math.CO2023

Hamiltonicity of $1$ -tough $(P_{2} \cup k P_{1})$ -free graphs

Leyou Xu, Chengli Li, Bo Zhou

Given a graph $H$ , a graph $G$ is $H$ -free if $G$ does not contain $H$ as an induced subgraph. For a positive real number $t$ , a non-complete graph $G$ is said to be $t$ -tough if f…

math.CO2023

Normalized Laplacian eigenvalues of hypergraphs

Leyou Xu, Bo Zhou

In this paper, we give tight bounds for the normalized Laplacian eigenvalues of hypergraphs that are not necessarily uniform, and provide an edge version interlacing theorem, a Che…

math.CO2023

Proof of a conjecture on distribution of Laplacian eigenvalues and diameter, and beyond

Leyou Xu, Bo Zhou

Ahanjideh, Akbari, Fakharan and Trevisan proposed a conjecture in [Linear Algebra Appl. 632 (2022) 1--14] on the distribution of the Laplacian eigenvalues of graphs: for any connec…

Positive discrepancy of graphs far from Turán graphs

Proving a conjecture concerning chromatic number, size and least eigenvalue

The number of cycles of a given length in dense hamiltonian graphs: proving Hilton's conjecture

On k-connected vertex-pancyclic graphs without pancyclic edges

Extremal Q-index problem in outerplanar graphs

Girth and Laplacian eigenvalue distribution

Cycles and paths through specified vertices in graphs with a given clique number

Spectral conditions implying the existence of doubly chorded cycles without or with constraints

Spectral conditions for the existence of chorded cycles in graphs with fixed size

Diameter vs Laplacian eigenvalue distribution

Answers to Gould's question concerning the existence of chorded cycles

Distribution of signless Laplacian eigenvalues and graph invariants

Link residual closeness of graphs with fixed parameters

Toughness and existence of 2-factors

The Alon-Tarsi number of K3,3​-minor-free graphs

Laplacain eigenvalue distribution and diameter of graphs

The generalized 4-connectivity of bubble-sort graphs

Hamiltonicity of 1-tough (P2​∪kP1​)-free graphs

Normalized Laplacian eigenvalues of hypergraphs

Proof of a conjecture on distribution of Laplacian eigenvalues and diameter, and beyond

On $k$ -connected vertex-pancyclic graphs without pancyclic edges

Extremal $Q$ -index problem in outerplanar graphs

Toughness and existence of $2$ -factors

The Alon-Tarsi number of $K_{3, 3}$ -minor-free graphs

The generalized $4$ -connectivity of bubble-sort graphs

Hamiltonicity of $1$ -tough $(P_{2} \cup k P_{1})$ -free graphs