11 papers
An extremal theorem for graphs with non-negative Bakry--Émery curvature
Jiawei Xie, Zhe You
Recently, Chen, Liu, and You (An extremal theorem for positive curvature of graphs, arXiv:2607.02297) proved an extremal theorem for positive Lin--Lu--Yau curvature. They further p…
Bipartite graphs, random graphs, and Lin--Lu--Yau curvature
Huiqiu Lin, Zhe You, Da Zhao
Let be a bipartite graph with parts and where and . We show that every bipartite graph with more than edges has positive Lin--L…
An extremal theorem for positive curvature of graphs
Kaizhe Chen, Shiping Liu, Zhe You
We prove an extremal theorem for positive Ollivier/Lin--Lu--Yau curvature: every graph of order \(n\geq 8\) with more than \[ T(n)=\frac{n^2-3n}{2}-\left\lceil\frac{n}{2}\right\rce…
Krahn--Szegő type inequalities and nodal domain methods on graphs
Huiqiu Lin, Lianping Liu, Xilong Yin +1
We study discrete analogues of classical spectral geometric inequalities and extremal eigenvalue problems on graphs. The classical Krahn--Szegő inequality states that, among bounde…
A Faber--Krahn inequality for trees
Huiqiu Lin, Lianping Liu, Zhe You
The well-known Faber-Krahn theorem states that the ball has the lowest first Dirichlet eigenvalue among all domains of the same volume in . Leydold (Geom. Funct. Anal…
Estimates of the first Dirichlet eigenvalue of graphs
Huiqiu Lin, Lianping Liu, Zhe You +1
Inspired by the Li--Yau eigenvalue-diameter estimates, we investigate lower bounds for the first Dirichlet eigenvalue in terms of the diameter (or inscribed radius) of a graph. Let…
Halin graphs with positive Lin-Lu-Yau curvature
Kaizhe Chen, Huiqiu Lin, Shiping Liu +1
Halin graphs constitute an interesting class of planar and polyhedral graphs. A generalized Halin graph is obtained by connecting all leaves of a planar embedding of a tree via a c…
Connectivity versus Lin-Lu-Yau curvature
Kaizhe Chen, Shiping Liu, Zhe You
We explore the interaction between connectivity and Lin-Lu-Yau curvature of graphs systematically. The intuition is that connected graphs with large Lin-Lu-Yau curvature also have…
Upper bounds of Steklov eigenvalues on graphs
Huiqiu Lin, Lianping Liu, Zhe You +1
Let and be the maximum vertex degree and a subset of vertices in a graph respectively. In this paper, we study the first (non-trivial) Steklov eigenvalue of w…
Graphs with positive Lin-Lu-Yau curvature without quadrilaterals
Huiqiu Lin, Zhe You
The definition of Ricci curvature on graphs was given in Lin-Lu-Yau, Tohoku Math., 2011, which is a variation of Ollivier, J. Funct. Math., 2009. Recently, a powerful limit-free fo…
Graphs with nonnegative Bakry-Émery curvature without Quadrilateral
Huiqiu Lin, Zhe You
The definition of Ricci curvature on graphs in Bakry-Émery's sense based on curvature dimension condition was introduced by Lin and Yau [\emph{Math. Res. Lett.}, 2010]. Hua and Lin…