Ramanujan Graphs in Polynomial Time
Data Structures and Algorithms
2016-04-13 v1 Combinatorics
Abstract
The recent work by Marcus, Spielman and Srivastava proves the existence of bipartite Ramanujan (multi)graphs of all degrees and all sizes. However, that paper did not provide a polynomial time algorithm to actually compute such graphs. Here, we provide a polynomial time algorithm to compute certain expected characteristic polynomials related to this construction. This leads to a deterministic polynomial time algorithm to compute bipartite Ramanujan (multi)graphs of all degrees and all sizes.
Cite
@article{arxiv.1604.03544,
title = {Ramanujan Graphs in Polynomial Time},
author = {Michael B. Cohen},
journal= {arXiv preprint arXiv:1604.03544},
year = {2016}
}