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- W2950644590 abstract "The method of Murty and Cioabu{a} 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 computation. A couple of recent explicit bounds on the gap between consecutive primes are then used to give the construction of $k$-regular families with explicit lower bounds on the spectral gaps. We then show that a result of Ben-Aroya and Ta-Shma can be improved using our simpler construction on the assumption of the Riemann Hypothesis, which sheds some more light on a question raised by Reingold, Vadhan and Widgerson." @default.
- W2950644590 created "2019-06-27" @default.
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- W2950644590 date "2014-02-04" @default.
- W2950644590 modified "2023-09-27" @default.
- W2950644590 title "Almost-Ramanujan Graphs and Prime Gaps" @default.
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