# The Parameterized Complexity of k-Biclique

@article{Lin2015ThePC, title={The Parameterized Complexity of k-Biclique}, author={Bingkai Lin}, journal={ArXiv}, year={2015}, volume={abs/1406.3700} }

Given a graph G and a parameter k, the k-Biclique problem asks whether G contains a complete bipartite subgraph Kk,k. This is one of the most easily stated problems on graphs whose parameterized complexity has been long unknown. We prove that k-Biclique is W[1]-hard by giving an fpt-reduction from k-Clique to k-Biclique, thus solving this longstanding open problem.
Our reduction uses a class of bipartite graphs with a certain threshold property, which might be of some independent interest…

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