1 citations · 1 across the 10 of their papers we have counts for
11 papers
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…
Criteria on forbidden subgraphs in the complements for positive Lin--Lu--Yau curvature
Kaizhe Chen, Shiping Liu, Zhe You
We investigate forbidden subgraph conditions in the complement of a graph that guarantee positive Lin--Lu--Yau curvature. In particular, we prove that every graph whose complement…
Books versus Triangles near the n/6 Threshold
Kaizhe Chen, Jie Ma, Tianhen Wang
The book number of a graph is the maximum number of triangles sharing a common edge. A strengthening of Mantel's theorem due to Rademacher states that every -vertex g…
On Lichnerowicz sharp distance-regular graphs
Kaizhe Chen, Shiping Liu, Heng Zhang
The first non-zero Laplacian eigenvalue of a finite graph is bounded below by its minimum Lin--Lu--Yau curvature . This is a discrete analogue of the classical Lichnerowic…
Edge-connectivity of graphs with non-negative Bakry-Émery curvature and amply regular graphs
Kaizhe Chen, Jack H. Koolen, Shiping Liu
We establish a sharp edge-connectivity estimate for graphs with non-negative Bakry-Émery curvature. This leads to a geometric criterion for the existence of a perfect matching. Pre…
Existence results for Tzitzéica equation via topological degree method on graphs
Kaizhe Chen, Heng Zhang
We derive some existence results for the solutions of the Tzitzéica equation \begin{equation*} -Δu + h_1(x)e^{Au} + h_2(x)e^{-Bu}=0 \end{equation*} and the generalized Tzitzéica eq…
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…
Diameter bounds for distance-regular graphs via long-scale Ollivier Ricci curvature
Kaizhe Chen, Shiping Liu
In this paper, we derive new sharp diameter bounds for distance regular graphs, which better answer a problem raised by Neumaier and Penji\' c in many cases. Our proof is built upo…
Ricci curvature, diameter and eigenvalues of amply regular graphs
Kaizhe Chen, Chunyang Hu, Shiping Liu +1
Amply regular graphs are graphs with local distance-regularity constraints. In this paper, we prove a weaker version of a conjecture proposed by Qiao, Park, and Koolen on diameter…
Curvature and local matchings of conference graphs and extensions
Kaizhe Chen, Shiping Liu, Heng Zhang
We prove a conjecture of Bonini et al. on the precise values of the Lin--Lu--Yau curvature of conference graphs, i.e., strongly regular graphs with parameters . Ou…