On Ramanujan graphs and their girth

Yair Glasner
University of Illinois
Mathematics, Statistics, and Computer Science

I will show how to construct Ramanujan graphs with small girth. The focus of the talk would be on towers of Ramanujan graphs, i.e. infinite sequence of graphs covering each other:
... X_n --> X_n-1 --> ... --> X_0.

I will address the question:
what are the possible (infinite) graphs that can cover such a tower?

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