Tight bounds for testing bipartiteness in general graphs

Tali Kaufman, Michael Krivelevich, Dana Ron

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

10 Scopus citations

Abstract

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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsSanjeev Asora, Amit Sahai, Klaus Jansen, Jose D.P. Rolim
PublisherSpringer Verlag
Pages341-353
Number of pages13
ISBN (Print)3540407707, 9783540407706
DOIs
StatePublished - 2003
Externally publishedYes

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2764
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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