On balanced CSPs with high treewidth
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Finding Planted Partitions in Random Graphs with General Degree Distributions
SIAM Journal on Discrete Mathematics
On laplacians of random complexes
Proceedings of the twenty-eighth annual symposium on Computational geometry
Loose laplacian spectra of random hypergraphs
Random Structures & Algorithms
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We investigate the Laplacian eigenvalues of sparse random graphsGnp. We show that in the case that the expected degree d= (n-1)p is bounded, the spectral gap of thenormalized Laplacian ℒ(Gn,p) iso(1). Nonetheless, w.h.p. G = Gnp has a largesubgraph core(G) such that the spectral gap ofℒ(core(G)) is as large as 1-O(d1/2). We derive similar results regarding the spectrumof the combinatorial Laplacian L(Gnp). Thepresent paper complements the work of Chung, Lu and Vu [8] on theLaplacian spectra of random graphs with given expected degreesequences. Applied to Gnp, their results imply that inthe dense case d ≥ ln2n the spectral gap ofℒ(Gn,p)is 1-O(d1/2) w.h.p.