3 citations · 10 across the 9 of their papers we have counts for
11 papers
Positively Lin-Lu-Yau curved graphs with no minor
Shuliang Bai, Xiaonan Liu, Zi-Xia Song
Let be a connected graph with minimum degree at least two, positive Lin-Lu-Yau Ricci curvature, and no minor, where is an integer. We first establish tight u…
Signed GLMY Homology of Signed Graphs via Double Covers
Shuliang Bai, Jingyan Li, Shing-Tung Yau
We define a signed GLMY chain complex over for signed digraphs using sheet-labelled regular paths. The complex is naturally isomorphic to the deck anti-invariant subco…
A Sharp Curvature Threshold for GLMY Path Homology
Shuliang Bai, Jingyan Li, Shing-Tung Yau
Let be a finite simple graph with at least one edge. We prove the sharp vanishing theorem \[ κ_{\min}^{\mathrm{LLY}}(G)>\frac12 \quad\Longrightarrow\quad \PathH_1(G;\R)=0. \] E…
Ricci-flat graphs with maximum degree at most 4
Shuliang Bai, Linyuan Lu, Shing-Tung Yau
A graph is called Ricci-flat if its Ricci curvatures vanish on all edges, here the definition of Ricci curvature on graphs was given by Lin-Lu-Yau. The authors in arXiv:1301.0102 a…
Turán Density of -edge-colored Bipartite Graphs with Application on -Hypergraphs
Shuliang Bai, Linyuan Lu
We consider the Turán problems of -edge-colored graphs. A -edge-colored graph is a triple consisting of the vertex set , the set of red edges and t…
Ollivier Ricci-flow on weighted graphs
Shuliang Bai, Yong Lin, Linyuan Lu +2
We study the existence of solutions of Ricci flow equations of Ollivier-Lin-Lu-Yau curvature defined on weighted graphs. Our work is motivated by\cite{NLLG} in which the discrete t…