Bo Zhou

collaborators

5 papers

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.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

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…

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

Girth and Laplacian eigenvalue distribution

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

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