Not Every Uniform Tree Covers Ramanujan Graphs

Alexander Lubotzky*, Tatiana Nagnibeda

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

The notion of Ramanujan graph has been extended to not necessarily regular graphs by Y. Greenberg. We construct infinite trees with infinitely many finite quotients, none of which is Ramanujan. We give a sufficient condition for a finite graph to be covered by such a tree.

Original languageEnglish
Pages (from-to)202-212
Number of pages11
JournalJournal of Combinatorial Theory. Series B
Volume74
Issue number2
DOIs
StatePublished - Nov 1998

Keywords

  • Covering tree
  • Minimal graph
  • Ramanujan graph
  • Spectral radius

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