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While the minimal forbidden induced subgraphs for comparability graphs are completely characterized, the corresponding characterization for word-representable graphs remains open.\n  In this paper, we precisely determine which minimal non-comparability graph","authors_text":"Benny George Kenkireth, Gopalan Sajith, Sreyas Sasidharan","cross_cats":[],"headline":"Word-representable graphs on n vertices exist whose cover number by comparability graphs is Omega(log n).","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2025-02-10T19:18:42Z","title":"Word-representability and comparability: Minimal forbidden induced subgraphs and cover number bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06979","kind":"arxiv","version":4},"verdict":{"created_at":"2026-05-23T03:37:08.294882Z","id":"268675f4-2edf-490f-b24c-ca1af03a9915","model_set":{"reader":"grok-4.3"},"one_line_summary":"Classifies minimal non-comparability graphs by word-representability and shows the cover number by comparability graphs is Θ(log n) for some word-representable graphs on n vertices.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Word-representable graphs on n vertices exist whose cover number by comparability graphs is Omega(log n).","strongest_claim":"We demonstrate the existence of word-representable graphs on n vertices whose cover number by comparability graphs is Ω(log n), which establishes that the universal O(log n) upper bound is asymptotically tight for the class of word-representable graphs.","weakest_assumption":"The explicit constructions used to achieve the Ω(log n) lower bound on cover number produce graphs that are word-representable (i.e., admit semi-transitive orientations)."}},"verdict_id":"268675f4-2edf-490f-b24c-ca1af03a9915"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5cf8141e98cf7a23a0015742d3b74c0765b27c3c8ace0039fd13681c23727967","target":"record","created_at":"2026-06-19T16:11:09Z","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":"25236240ffdce6996b70b93ab2717ce178bd7060833581c1d6cb00a25cdffab9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2025-02-10T19:18:42Z","title_canon_sha256":"08ee80f62c1bea86632f814bd879f667abb97b92ac7c760f4744dec0becc08e8"},"schema_version":"1.0","source":{"id":"2502.06979","kind":"arxiv","version":4}},"canonical_sha256":"2da063480c2f64a87a8aa79506bf88dcf94b8bb2ddae583dd387050282ffac00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2da063480c2f64a87a8aa79506bf88dcf94b8bb2ddae583dd387050282ffac00","first_computed_at":"2026-06-19T16:11:09.929307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:09.929307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bAtfZmpWU+o+2oEY51T5Id0w3s6dGQ+daBPFK1AuSfs5hB02dZwNN6RfNkyvrriFCSuqyBDqBtm2Tr1vrx0OCA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:09.929767Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.06979","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cf8141e98cf7a23a0015742d3b74c0765b27c3c8ace0039fd13681c23727967","sha256:8f1099170d941e5747ee38b4259cc75c37d1e73203e6db9cba8fa7d2581cc422"],"state_sha256":"d0e70fe2cd97de06b756873d14c516e75d26a55dcf60056d1c048d509728c9e8"}