{"paper":{"title":"Almost balanced ordered biclique covering of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anagh Indu Suresh, Anand Babu, Ervin Ranjan, Jatla Naga Sidhartha, Maddipati Deshith Sai, Sreedhara Vishwas","submitted_at":"2026-06-07T08:14:03Z","abstract_excerpt":"Let $f(n,k)$ be the minimum size of a collection of bicliques such that (i) every edge of the complete graph $K_n$ is covered by at least one and at most $k$ bicliques in the collection, and (ii) for each edge $\\{u,v\\}$, the number of bicliques in which $u$ appears in the first class and $v$ in the second class differs by at most one from the number of bicliques in which $u$ appears in the second class and $v$ in the first class.\n  For $k=1$, $f(n,k)$ reduces to the biclique partition number of $K_n$, and the Graham--Pollak theorem gives $f(n,1)=n-1$. For $k=2$, $f(n,k)$ is the ordered bicliqu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08506","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08506/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}