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Efficient Testing of Hypergraphs

Extended Abstract
  • Yoshiharu Kohayakawa
  • Brendan Nagle
  • Vojtěch Rödl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2380)

Abstract

We investigate a basic problem in combinatorial property testing, in the sense of Goldreich, Goldwasser, and Ron [9,10], in the context of 3-uniform hypergraphs, or 3-graphs for short. As customary, a 3-graph F is simply a collection of 3-element sets. Let Forbind(n, F) be the family of all 3-graphs on n vertices that contain no copy of F as an induced subhypergraph. We show that the property “H ∈ Forbind(n, F)” is testable, for any 3-graph F. In fact, this is a consequence of a new, basic combinatorial lemma, which extends to 3-graphs a result for graphs due to Alon, Fischer, Krivelevich, and Szegedy [2,3].

Indeed, we prove that if more than ξn 3 (V > 0) triples must be added or deleted from a 3-graph H on n vertices to destroy all induced copies of F, then H must contain ≥ cn |V(F)| induced copies of F, as long as nn 0(ξ, F). Our approach is inspired in [2,3], but the main ingredients are recent hypergraph regularity lemmas and counting lemmas for 3-graphs.

Keywords

Bipartite Graph Triple System Arithmetic Progression Property Testing Large Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Yoshiharu Kohayakawa
    • 1
  • Brendan Nagle
    • 2
    • 3
  • Vojtěch Rödl
    • 4
  1. 1.Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Department of MathematicsUniversity of NevadaRenoUSA
  4. 4.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA

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