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Testing Bipartiteness in the Dense-Graph Model

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 75 Accesses

Years and Authors of Summarized Original Work

  • 1998; Goldreich, Goldwasser, Ron

  • 2002; Alon, Krivelevich

Problem Definition

A graph is bipartite (or 2-colorable) if its vertices can be partitioned into two sets such that there are no edges between pairs of vertices that reside in the same set.

Given a (simple) graph, the task is to determine whether it is bipartite or is “far” from being bipartite. Thus, the standard decision problem is relaxed by allowing any answer when the graph is not bipartite but is “close” to some bipartite graph. We focus on dense graphs (i.e., for which the number of edges is quadratic in the number of vertices) and wish to solve the aforementioned “approximate decision” problem in constant time, given access to a data structure that answers adjacency queries in unit time.

To complete the formulation of the problem, we need to define the distance between graphs and describe how the graph is accessed. The distance between the graphs G1 = (V, E1) and G2 = (V, E2)...

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Recommended Reading

  1. Alon N, Krivelevich M (2002) Testing k-colorability. SIAM J Discret Math 15:211–227

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Author information

Authors and Affiliations

  1. Department of Computer Science, Weizmann Institute of Science, Rehovot, Israel

    Oded Goldreich

  2. School of Electrical Engineering, Tel-Aviv University, Ramat-Aviv, Israel

    Dana Ron

Authors
  1. Oded Goldreich
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  2. Dana Ron
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Corresponding author

Correspondence to Oded Goldreich .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Goldreich, O., Ron, D. (2016). Testing Bipartiteness in the Dense-Graph Model. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_702

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