A Sublinear Bipartiteness Tester for Bounded Degree Graphs

, and the testing algorithm can perform queries of the form: ``who is the ith neighbor of vertex v''. The tester should determine with high probability whether the graph is bipartite or e-far from bipartite for any given distance parameter e. Distance between graphs is defined to be the fraction of entries on which the graphs differ in their incidence-lists representation. Our testing algorithm has query complexity and running time \(\) where N is the number of graph vertices. It was shown before that \(\) queries are necessary (for constant e), and hence the performance of our algorithm is tight (in its dependence on N), up to polylogarithmic factors.

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