Tight bounds for testing bipartiteness in general graphs

Tali Kaufman*, Michael Krivelevich, Dana Ron

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


In this paper we consider the problem of testing bipartiteness of general graphs. The problem has previously been studied in two models, one most suitable for dense graphs, and one most suitable for bounded-degree graphs. Roughly speaking, dense graphs can be tested for bipartiteness with constant complexity, while the complexity of testing bounded-degree graphs is θ̃(√n), where n is the number of vertices in the graph. Thus there is a large gap between the complexity of testing in the two cases. In this work we bridge the gap described above. In particular, we study the problem of testing bipartiteness in a model that is suitable for all densities. We present an algorithm whose complexity is Õ(min(√n,n2/m)) where m is the number of edges in the graph, and match it with an almost tight lower bound.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization : Algorithms and Techniques
Subtitle of host publication6th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2003 and 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003, Princeton, NJ, USA, August 24-26, 2003. Proceedings
EditorsSanjeev Asora, Klaus Jansen, Jose D.P. Rolim, Amit Sahai
Place of PublicationBerlin Heidelberg
PublisherSpringer Verlag
Number of pages13
ISBN (Electronic)978-3-540-45198-3
ISBN (Print)3540407707, 9783540407706
StatePublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


  • Average degree
  • Regular graph
  • query complexity
  • testing algorithm


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