Essentially Every Unimodular Matrix Defines an Expander

  • Jin-Yi Cai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1969)


We generalize the construction of Gabber and Galil to essentially every unimodular matrix in SL2(Z). It is shown that every parabolic or hyperbolic fractional linear transformation explicitly defines an expander of bounded degree and constant expansion. Thus all but a vanishingly small fraction of unimodular matrices define expanders.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Jin-Yi Cai
    • 1
    • 2
  1. 1.Department of Computer Science and EngineeringState University of New York at Buffalo
  2. 2.Computer Sciences DepartmentUniversity of WisconsinMadison

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