{"paper":{"title":"The Parameterized Complexity of k-Biclique","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Bingkai Lin","submitted_at":"2014-06-14T08:20:39Z","abstract_excerpt":"Given a graph $G$ and a parameter $k$, the $k$-biclique problem asks whether $G$ contains a complete bipartite subgraph $K_{k,k}$. This is the most easily stated problem on graphs whose parameterized complexity is still unknown. We provide an fpt-reduction from $k$-clique to $k$-biclique, thus solving this longstanding open problem.\n  Our reduction use a class of bipartite graphs with a threshold property of independent interest. More specifically, for positive integers $n$, $s$ and $t$, we consider a bipartite graph $G=(A\\;\\dot\\cup\\;B, E)$ such that $A$ can be partitioned into $A=V_1\\;\\dot\\cu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3700","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}