Interlacing families I: Bipartite Ramanujan graphs of all degrees

ANNALS OF MATHEMATICS, pp. 307-325, 2015.

Cited by: 0|Bibtex|Views9|DOI:https://doi.org/10.4007/annals.2015.182.1.7

Abstract:

We prove that there exist infinite families of regular bipartite Ramanujan graphs of every degree bigger than 2. We do this by proving a variant of a conjecture of Bilu and Linial about the existence of good 2-lifts of every graph. We also establish the existence of infinite families of "irregular Ramanujan" graphs, whose eigenvalues are ...More

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