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Combinatorica

, Volume 24, Issue 3, pp 403–426 | Cite as

Triangle Factors In Sparse Pseudo-Random Graphs

  • Michael Krivelevich*
  • Benni Sudakov†
  • Tibor Szabó‡
Original Paper

The goal of the paper is to initiate research towards a general, Blow-up Lemma type embedding statement for pseudo-random graphs with sublinear degrees. In particular, we show that if the second eigenvalue λ of a d-regular graph G on 3n vertices is at most cd 3/n 2 log n, for some sufficiently small constant c > 0, then G contains a triangle factor. We also show that a fractional triangle factor already exists if λ < 0.1d 2/n. The latter result is seen to be best possible up to a constant factor, for various values of the degree d = d(n).

Mathematics Subject Classification (2000):

05C70 05C80 

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Copyright information

© János Bolyai Mathematical Society 2004

Authors and Affiliations

  • Michael Krivelevich*
    • 1
  • Benni Sudakov†
    • 2
    • 3
  • Tibor Szabó‡
    • 4
  1. 1.Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.Department of MathematicsPrinceton UniversityPrincetonUSA
  3. 3.Institute for Advanced StudyPrincetonUSA
  4. 4.Department of Computer ScienceETH ZürichZürichSwitzerland

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