{"paper":{"title":"On some lower bounds on the number of bicliques needed to cover a bipartite graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dirk Oliver Theis","submitted_at":"2007-08-08T21:06:24Z","abstract_excerpt":"The biclique covering number of a bipartite graph G is the minimum number of complete bipartite subgraphs (bicliques) whose union contains every edge of G.\n  In this little note we compare three lower bounds on the biclique covering number: A bound jk(G) proposed by Jukna & Kulikov (Discrete Math. 2009); the well-known fooling set bound fool(G); the \"tensor-power\" fooling set bound fool^\\infty(G). We show jk \\le fool le fool^\\infty \\le min_Q (rk Q)^2, where the minimum is taken over all matrices with a certain zero/nonzero-pattern. Only the first inequality is really novel, the third one gener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.1174","kind":"arxiv","version":4},"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"}