{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:HHYCR4463XY4UT2CF2E26UKKZF","short_pith_number":"pith:HHYCR446","schema_version":"1.0","canonical_sha256":"39f028f39eddf1ca4f422e89af514ac97a3218272f783ef0e21632889af41e40","source":{"kind":"arxiv","id":"2310.02336","version":1},"attestation_state":"computed","paper":{"title":"Hereditary Nordhaus-Gaddum Graphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rebecca Whitman, Vaidy Sivaraman","submitted_at":"2023-10-03T18:15:22Z","abstract_excerpt":"Nordhaus and Gaddum proved in 1956 that the sum of the chromatic number $\\chi$ of a graph $G$ and its complement is at most $|G|+1$. The Nordhaus-Gaddum graphs are the class of graphs satisfying this inequality with equality, and are well-understood. In this paper we consider a hereditary generalization: graphs $G$ for which all induced subgraphs $H$ of $G$ satisfy $\\chi(H) + \\chi(\\overline{H}) \\le |H|$. We characterize the forbidden induced subgraphs of this class and find its intersection with a number of common classes, including line graphs. We also discuss $\\chi$-boundedness and algorithm"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2310.02336","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2023-10-03T18:15:22Z","cross_cats_sorted":[],"title_canon_sha256":"204f43d6f9a1b8c113907fde70ed57addcacd7ac0a6319373217ea4ce668679c","abstract_canon_sha256":"3f9e442eb5b64702ab8fda75b902def0e775020bf75a5c3dcb0bb3037e850feb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:56:55.678165Z","signature_b64":"S2IfNrjKsgASOQFQPCXeG2wdIxN9YzXJz7tR/A/I84iyYvj5CaoMBhqDjxR0YNLaxeahwZDgHzXQ4IMIa9RwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39f028f39eddf1ca4f422e89af514ac97a3218272f783ef0e21632889af41e40","last_reissued_at":"2026-07-05T06:56:55.677700Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:56:55.677700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hereditary Nordhaus-Gaddum Graphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rebecca Whitman, Vaidy Sivaraman","submitted_at":"2023-10-03T18:15:22Z","abstract_excerpt":"Nordhaus and Gaddum proved in 1956 that the sum of the chromatic number $\\chi$ of a graph $G$ and its complement is at most $|G|+1$. The Nordhaus-Gaddum graphs are the class of graphs satisfying this inequality with equality, and are well-understood. In this paper we consider a hereditary generalization: graphs $G$ for which all induced subgraphs $H$ of $G$ satisfy $\\chi(H) + \\chi(\\overline{H}) \\le |H|$. We characterize the forbidden induced subgraphs of this class and find its intersection with a number of common classes, including line graphs. We also discuss $\\chi$-boundedness and algorithm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.02336","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/2310.02336/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2310.02336","created_at":"2026-07-05T06:56:55.677758+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.02336v1","created_at":"2026-07-05T06:56:55.677758+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.02336","created_at":"2026-07-05T06:56:55.677758+00:00"},{"alias_kind":"pith_short_12","alias_value":"HHYCR4463XY4","created_at":"2026-07-05T06:56:55.677758+00:00"},{"alias_kind":"pith_short_16","alias_value":"HHYCR4463XY4UT2C","created_at":"2026-07-05T06:56:55.677758+00:00"},{"alias_kind":"pith_short_8","alias_value":"HHYCR446","created_at":"2026-07-05T06:56:55.677758+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.28860","citing_title":"Mechanistic origins of catastrophic forgetting: why RL preserves circuits better than SFT?","ref_index":5,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HHYCR4463XY4UT2CF2E26UKKZF","json":"https://pith.science/pith/HHYCR4463XY4UT2CF2E26UKKZF.json","graph_json":"https://pith.science/api/pith-number/HHYCR4463XY4UT2CF2E26UKKZF/graph.json","events_json":"https://pith.science/api/pith-number/HHYCR4463XY4UT2CF2E26UKKZF/events.json","paper":"https://pith.science/paper/HHYCR446"},"agent_actions":{"view_html":"https://pith.science/pith/HHYCR4463XY4UT2CF2E26UKKZF","download_json":"https://pith.science/pith/HHYCR4463XY4UT2CF2E26UKKZF.json","view_paper":"https://pith.science/paper/HHYCR446","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.02336&json=true","fetch_graph":"https://pith.science/api/pith-number/HHYCR4463XY4UT2CF2E26UKKZF/graph.json","fetch_events":"https://pith.science/api/pith-number/HHYCR4463XY4UT2CF2E26UKKZF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HHYCR4463XY4UT2CF2E26UKKZF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HHYCR4463XY4UT2CF2E26UKKZF/action/storage_attestation","attest_author":"https://pith.science/pith/HHYCR4463XY4UT2CF2E26UKKZF/action/author_attestation","sign_citation":"https://pith.science/pith/HHYCR4463XY4UT2CF2E26UKKZF/action/citation_signature","submit_replication":"https://pith.science/pith/HHYCR4463XY4UT2CF2E26UKKZF/action/replication_record"}},"created_at":"2026-07-05T06:56:55.677758+00:00","updated_at":"2026-07-05T06:56:55.677758+00:00"}