TY - CHAP

T1 - Tight bounds for testing bipartiteness in general graphs

AU - Kaufman, Tali

AU - Krivelevich, Michael

AU - Ron, Dana

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=26944436398&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-45198-3_29

DO - 10.1007/978-3-540-45198-3_29

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AN - SCOPUS:26944436398

SN - 3540407707

SN - 9783540407706

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 341

EP - 353

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Asora, Sanjeev

A2 - Sahai, Amit

A2 - Jansen, Klaus

A2 - Rolim, Jose D.P.

PB - Springer Verlag

ER -