@article{Dudek2015AlmostRamanujanGA,
title={Almost-Ramanujan graphs and prime gaps},
author={A. Dudek},
journal={Eur. J. Comb.},
year={2015},
volume={43},
pages={204-209}
}

The method of Murty and Cioab? shows how one can use results about gaps between primes to construct families of almost-Ramanujan graphs. In this paper we give a simpler construction which avoids the search for perfect matchings and thus eliminates the need for any computational effort. A couple of known bounds on the gap between consecutive primes are then used to give the construction of k -regular families with lower bounds on the spectral gaps. We then show that a result of Ben-Aroya and Ta… Expand