2 citations · 2 across the 16 of their papers we have counts for
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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…
New bounds for equiangular lines and Balla's conjecture
Chuanyuan Ge, Shiping Liu
Let denote the maximum number of equiangular lines in with common angle . Balla conjectured that, if the spectral radius order $κ_{\frac{1-α}{2α…
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…
On finiteness of spectral radius order
Yanlong Ding, Chuanyuan Ge, Shiping Liu
The concept of spectral radius order plays an crucial role in the breakthrough work on equiangular lines due to Jiang, Tidor, Yao, Zhang, and Zhao [Ann. of Math. (2) 194 (2021), no…
Edge-connectivity and non-negative Lin-Lu-Yau curvature
Shiping Liu, Qing Xia
By definition, the edge-connectivity of a connected graph is no larger than its minimum degree. In this paper, we prove that the edge connectivity of a finite connected graph with…
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…