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…
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 Lichnerow…
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…
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 …
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…