{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:Q3MGFPOZ2FGQ56T6UTVMKXEUJW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e743c718fc70c22f42c180fc9e102276ed089f183756d227be8ef2a7cf2597b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-22T22:27:38Z","title_canon_sha256":"eb018640d48a384ef709eed910ad7b1cfa628827b64a5aeb657e2878bfa91c17"},"schema_version":"1.0","source":{"id":"1903.09725","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.09725","created_at":"2026-05-17T23:50:35Z"},{"alias_kind":"arxiv_version","alias_value":"1903.09725v1","created_at":"2026-05-17T23:50:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.09725","created_at":"2026-05-17T23:50:35Z"},{"alias_kind":"pith_short_12","alias_value":"Q3MGFPOZ2FGQ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"Q3MGFPOZ2FGQ56T6","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"Q3MGFPOZ","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:f9143d3f35445875a0c76d2b394d26f37c38c909e2b8ddab8ff15d1868bdd407","target":"graph","created_at":"2026-05-17T23:50:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For a bipartite graph G, let h(G) be the largest t such that either G or the bipartite complement of G contain K_{t,t}. For a class F of graphs, let h(F)= min {h(G): G\\in F}. We say that a bipartite graph H is strongly acyclic if neither H nor its bipartite complement contain a cycle. By Forb(n, H) we denote a set of bipartite graphs with parts of sizes n each, that do not contain H as an induced bipartite subgraph respecting the sides. One can easily show that h(Forb(n,H))= O(n^{1-s}) for a positive s if H is not strongly acyclic. Here, we prove that h(Forb(n, H)) is linear in n for all stron","authors_text":"Casey Tompkins, Lea Weber, Maria Axenovich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-22T22:27:38Z","title":"Large homogeneous subgraphs in bipartite graphs with forbidden induced subgraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09725","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c1e8f9125dc98c4432c1cb548cb4cdab7781f3ab2ac81e1c1c27d9f52da90a6a","target":"record","created_at":"2026-05-17T23:50:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e743c718fc70c22f42c180fc9e102276ed089f183756d227be8ef2a7cf2597b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-22T22:27:38Z","title_canon_sha256":"eb018640d48a384ef709eed910ad7b1cfa628827b64a5aeb657e2878bfa91c17"},"schema_version":"1.0","source":{"id":"1903.09725","kind":"arxiv","version":1}},"canonical_sha256":"86d862bdd9d14d0efa7ea4eac55c944da8ae05f21d4bb3fef0331080a4be7bdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86d862bdd9d14d0efa7ea4eac55c944da8ae05f21d4bb3fef0331080a4be7bdd","first_computed_at":"2026-05-17T23:50:35.686155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:35.686155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"re3sEBcKs5AeL4Ahp1jOlmu7fTeNWDbDDv5kECuGw6nOHsabKtvnQtVLCOOaEdcwbAXlF6gmjzrtmHfU92j5Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:35.686868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.09725","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1e8f9125dc98c4432c1cb548cb4cdab7781f3ab2ac81e1c1c27d9f52da90a6a","sha256:f9143d3f35445875a0c76d2b394d26f37c38c909e2b8ddab8ff15d1868bdd407"],"state_sha256":"d10768a1d9df8531a3ee8c9669bff0a523640054f8d996ff847284be5d15c3bb"}