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We prove that there exist bipartite, biregular Ramanujan graphs of every degree and every number of vertices provided that the cardinalities of the two sets of the bipartition divide each other.
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M. Morgenstern. Existence and Explicit Constructions of q + 1 q+1 Regular Ramanujan Graphs for Every Prime Power q q . Journal of Combinatorial Theory, Series B. 62: 44–62, 1994. doi:10.1006/jctb.1994.1054
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K. Feng, W.-C. W. Li. Spectra of hypergraphs and applications. J. of Number Theory, 60(1):1–22, 1996
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J. Friedman. A proof of Alon’s second eigenvalue conjecture and related problems. Memoirs of the AMS, Vol. 195 No. 910, 2008
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R. A. Horn, C. R. Johnson. Matrix analysis. Cambridge Univ. Press, 2012
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C. Ballantine, B. Feigon, R. Ganapathy, J. Kool, K. Maurischat, A. Wooding. Explicit construction of Ramanujan bigraphs. Women in Numbers Europe. Springer (2015)
2015
Cited alongside, same era.
A. W. Marcus, D. A. Spielman, N. Srivastava. Interlacing families I: bipartite Ramanujan graphs of all degrees Ann. of Math. 182-1:307-325, 2015
2015
Cited alongside, same era.
C. Hall, D. Puder, W. F. Sawin. Ramanujan Covering of Graphs. Proc. of 46th ACM STOC, 2016
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2016
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2018
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2019
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A. W. Marcus. A class of multivariate convolutions (and applications). arXiv:2010.08996 , 2020
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A. W. Marcus, D. A. Spielman, N. Srivastava. Interlacing families IV: bipartite Ramanujan graphs of All sizes. Proc. of 56th IEEE FOCS, 2015
2015
Cited alongside, same era.
2020
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