# Testing k-Connectivity and Bipartiteness in Bounded-degree / Sparse Graphs

@inproceedings{2008TestingKA, title={Testing k-Connectivity and Bipartiteness in Bounded-degree / Sparse Graphs}, author={}, year={2008} }

Recall that the connectivity (1-connectivity) testing algorithm is based on the observation that if a graph is far from being connected then it contains many small connected components. As mentioned in the last lecture, there is a generalization to k > 1. What can be shown is that if a graph is far from being k-connected then it contains many subsets C that are small and such that: (1) (C,C) = ` < k; (2) for every C ′ ⊂ C, (C ′, C ′) > `. We say in this case the C is `-extreme. As in the case… CONTINUE READING