We introduce a new graph for all whose cartesian powers the vertex isoperimetric problem has nested solutions. This is the fourth kind of graphs with this property besides the wel...
We consider the vertex-isoperimetric problem for cartesian powers of a graph G. A total order on the vertex set of G is called isoperimetric if the boundary of sets of a given siz...
Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an alternate idea that finds partitions with a small isoperimetric constant, requiring ...
We consider an edge-isoperimetric problem (EIP) on the cartesian powers of graphs. One of our objectives is to extend the list of graphs for whose cartesian powers the lexicograph...
The spectral profile of a graph is a natural generalization of the classical notion of its Rayleigh quotient. Roughly speaking, given a graph G, for each 0 < < 1, the spect...
Prasad Raghavendra, David Steurer and Prasad Tetal...