8 papers
Proving a conjecture concerning chromatic number, size and least eigenvalue
Leyou Xu, Bo Zhou
Let be a simple nonempty graph with size , chromatic number , and least eigenvalue . 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…
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 of order satisfying contains at least two cycles…
On -connected vertex-pancyclic graphs without pancyclic edges
Leyou Xu, Bo Zhou
An edge of a graph of order is pancyclic if it lies in a cycle of every length . A graph of order is vertex-pancyclic if every vertex lies in a cycle of every l…
Extremal -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 -index. We determine the unique graph that maximizes the -index amo…
Girth and Laplacian eigenvalue distribution
Leyou Xu, Bo Zhou
Let be a connected graph of order with girth . For , let be the number of Laplacian eigenvalues (counting multiplicities) of tha…
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…