Interlacing families I: Bipartite Ramanujan graphs of all degrees
ANNALS OF MATHEMATICS, pp. 307-325, 2015.
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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