Not Every Uniform Tree Covers Ramanujan Graphs

Lubotzky, Alexander; Smirnova-Nagnibeda, Tatiana

doi:10.1006/jctb.1998.1843

Scientific article

English

Not Every Uniform Tree Covers Ramanujan Graphs

ContributorsLubotzky, Alexander; Smirnova-Nagnibeda, Tatiana

Published inJournal of combinatorial theory. Series B, vol. 74, no. 2, p. 202-212

Publication date1998

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.

Keywords

Ramanujan graph
Covering tree
Spectral radius
Mini- mal graph

Affiliation

Faculté des sciences / Section de mathématiques

Citation (ISO format)

LUBOTZKY, Alexander, SMIRNOVA-NAGNIBEDA, Tatiana. Not Every Uniform Tree Covers Ramanujan Graphs. In: Journal of combinatorial theory. Series B, 1998, vol. 74, n° 2, p. 202–212. doi: 10.1006/jctb.1998.1843

Article (Published version)

Identifiers

PID : unige:12428
DOI : 10.1006/jctb.1998.1843

Commercial URLhttp://linkinghub.elsevier.com/retrieve/pii/S0095895698918433

ISSN of the journal0095-8956

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Not Every Uniform Tree Covers Ramanujan Graphs

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.

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