• Corpus ID: 11435821

Towards Constructing Ramanujan Graphs Using Shift Lifts

  title={Towards Constructing Ramanujan Graphs Using Shift Lifts},
  author={Karthekeyan Chandrasekaran and Ameya Velingker},
  journal={arXiv: Combinatorics},
In a breakthrough work, Marcus-Spielman-Srivastava recently showed that every $d$-regular bipartite Ramanujan graph has a 2-lift that is also $d$-regular bipartite Ramanujan. As a consequence, a straightforward iterative brute-force search algorithm leads to the construction of a $d$-regular bipartite Ramanujan graph on $N$ vertices in time $2^{O(dN)}$. Shift $k$-lifts studied by Agarwal-Kolla-Madan lead to a natural approach for constructing Ramanujan graphs more efficiently. The number of… 
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