9 papers
Choquet-type extension theory of set-pair functions, and applications to graph limits, hypergraphs, Riemannian manifolds and metric measure spaces
Dong Zhang
We propose Choquet extension for set-pair functions, integration of Choquet extensions, and global extension constants, and apply these to investigate optimization problems a…
Graphon as a Bridge between Graphs and Manifolds
Dong Zhang
We show that there exist graphons that interpolate between Riemannian manifolds and weighted geometric graphs. Specifically, the graph-to-manifold approximation used in manifold le…
From the discrete to the continuous, from simplicial complexes to Riemannian manifolds. Approximating flows and cuts on manifolds by discrete versions
Marzieh Eidi, Juergen Jost, Dong Zhang
Many fundamental structures of Riemannian geometry have found discrete counterparts for graphs or combinatorial ones for simplicial complexes. These include those discussed in this…
Equivalent spectral theory for fundamental graph cut problems
Sihong Shao, Chuan Yang, Dong Zhang +1
We introduce and develop equivalent spectral graph theory for several fundamental graph cut problems including maxcut, mincut, Cheeger cut, anti-Cheeger cut, dual Cheeger problem a…
Combinatorial Courant-Fischer-Weyl Minimax Principle on Cheeger -constants of Weighted Forests
Zijun Meng, Dong Zhang
We establish novel max-min and minimax characterizations of Cheeger -constants in weighted forests, thereby providing the first combinatorial analogue of the Courant-Fischer-Wey…
Finite projective planes meet spectral gaps
Yuhan Guo, Dong Zhang
We show that for any connected graph with maximum degree , the spectral gap from with respect to the adjacency matrix is at most , with equality if and o…