Short paths in quasi-random triple systems with sparse underlying graphs

Joanna Polcyn, Vojtech Rödl, Andrzej Ruciński, Endre Szemerédi

Research output: Contribution to journalArticle

7 Citations (Scopus)


The regularity lemma for 3-uniform hypergraphs asserts that every large hypergraph can be decomposed into a bounded number of quasi-random structures consisting of a sub-hypergraph and a sparse underlying graph. In this paper we show that in such a quasi-random structure most pairs of the edges of the graph can be connected by hyperpaths of length at most twelve. Some applications are also given.

Original languageEnglish
Pages (from-to)584-607
Number of pages24
JournalJournal of Combinatorial Theory. Series B
Issue number4
Publication statusPublished - Jul 1 2006



  • Paths
  • Quasi-randomness
  • Triple systems

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this