Almost-Ramanujan graphs and prime gaps

  title={Almost-Ramanujan graphs and prime gaps},
  author={A. Dudek},
  journal={Eur. J. Comb.},
  • A. Dudek
  • Published 2015
  • Computer Science, Mathematics
  • Eur. J. Comb.
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
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