72 citations · 146 across the 10 of their papers we have counts for
4 papers · 1 filter
Eigenvalue bounds, spectral partitioning, and metrical deformations via flows
Punyashloka Biswal, James R. Lee, Satish Rao
We present a new method for upper bounding the second eigenvalue of the Laplacian of graphs. Our approach uses multi-commodity flows to deform the geometry of the graph; we embed t…
Eigenvectors of random graphs: Nodal domains
Yael Dekel, James R. Lee, Nathan Linial
We initiate a systematic study of eigenvectors of random graphs. Whereas much is known about eigenvalues of graphs and how they reflect properties of the underlying graph, relative…
Eigenvalue multiplicity and volume growth
James R. Lee, Yury Makarychev
Let be a finite group with symmetric generating set , and let be the doubling constant of the corresponding Cayley graph, where deno…
Coarse differentiation and multi-flows in planar graphs
James R. Lee, Prasad Raghavendra
We show that the multi-commodity max-flow/min-cut gap for series-parallel graphs can be as bad as 2, matching a recent upper bound Chakrabarti, Jaffe, Lee, and Vincent for this cla…