Ramanujan Hypergraphs and Ramanujan Geometries

* Final gross prices may vary according to local VAT.

Get Access

Abstract

Ramanujan hypergraphs or bigraphs (bipartite biregular graphs) are to the biregular tree what Ramanujan graphs are to the homogeneous tree. A survey of the known constructions is given. Of special interest is the case when the bidegree (k, l) is non-symmetric, i.e. kl. The case of r—partite graphs is sketched out and a connection with buildings and chamber systems is looked at. The concept of universal cover of a family of finite graphs by an infinite locally finite graph is emphasized.