On the query complexity of testing orientations for being Eulerian

Eldar Fischer, Oded Lachish, Arie Matsliah, Ilan Newman, Orly Yahalom

Research output: Contribution to journalArticlepeer-review


We consider testing directed graphs Eulerianity in the orientation model introduced in Halevy et al. [2005]. Despite the local nature of the Eulerian property, it turns out to be significantly harder to test than other properties studied in the orientation model. We show a nonconstant lower bound on the query complexity of 2-sided tests and a linear lower bound on the query complexity of 1-sided tests for this property. On the positive side, we give several 1-sided and 2-sided tests, including a sublinear query complexity 2-sided test, for general graphs. For special classes of graphs, including bounded-degree graphs and expander graphs, we provide improved results. In particular, we give a 2-sided test with constant query complexity for dense graphs, as well as for expander graphs with a constant expansion parameter.

Original languageEnglish
Article number15
JournalACM Transactions on Algorithms
Issue number2
StatePublished - Apr 2012


  • Eulerian orientations
  • Graph algorithms
  • Massively parameterized
  • Property testing

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)


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