{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:EVRRNIACFPQJRQ6Y2IXTV6BB5C","short_pith_number":"pith:EVRRNIAC","schema_version":"1.0","canonical_sha256":"256316a0022be098c3d8d22f3af821e8a6f664f9632dd405d6ddb3c63d20f4fc","source":{"kind":"arxiv","id":"1506.03746","version":1},"attestation_state":"computed","paper":{"title":"Split Graphs and Nordhaus-Gaddum Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ann Trenk, Christine Cheng, Karen L. Collins","submitted_at":"2015-06-11T17:16:31Z","abstract_excerpt":"A graph G is an NG-graph if \\chi(G) + \\chi(G complement) = |V(G)| + 1. We characterize NG-graphs solely from degree sequences leading to a linear-time recognition algorithm. We also explore the connections between NG-graphs and split graphs. There are three types of NG-graphs and split graphs can also be divided naturally into two categories, balanced and unbalanced. We characterize each of these five classes by degree sequence. We construct bijections between classes of NG-graphs and balanced and unbalanced split graphs which, together with the known formula for the number of split graphs on "},"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":"1506.03746","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-11T17:16:31Z","cross_cats_sorted":[],"title_canon_sha256":"7cbfc034f4eebb2488a9d7bb99b61fda81a67af667e9cd90b8d01a3df653ba60","abstract_canon_sha256":"1a28d91363267147e80c0689f50d9cb80d7f8e6ace3970072a44537a78eed9ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:03.391912Z","signature_b64":"mgU4uKsSD7V6mYTQG55MAgNaSyXJjUiF1iYuHDQ8kQ3vJYRPpVZi3cX0APOZfZTisuvJw3+nMgZ4FrqGrjoZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"256316a0022be098c3d8d22f3af821e8a6f664f9632dd405d6ddb3c63d20f4fc","last_reissued_at":"2026-05-18T01:53:03.391456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:03.391456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Split Graphs and Nordhaus-Gaddum Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ann Trenk, Christine Cheng, Karen L. Collins","submitted_at":"2015-06-11T17:16:31Z","abstract_excerpt":"A graph G is an NG-graph if \\chi(G) + \\chi(G complement) = |V(G)| + 1. We characterize NG-graphs solely from degree sequences leading to a linear-time recognition algorithm. We also explore the connections between NG-graphs and split graphs. There are three types of NG-graphs and split graphs can also be divided naturally into two categories, balanced and unbalanced. We characterize each of these five classes by degree sequence. We construct bijections between classes of NG-graphs and balanced and unbalanced split graphs which, together with the known formula for the number of split graphs on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03746","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":""},"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":"1506.03746","created_at":"2026-05-18T01:53:03.391525+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.03746v1","created_at":"2026-05-18T01:53:03.391525+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03746","created_at":"2026-05-18T01:53:03.391525+00:00"},{"alias_kind":"pith_short_12","alias_value":"EVRRNIACFPQJ","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"EVRRNIACFPQJRQ6Y","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"EVRRNIAC","created_at":"2026-05-18T12:29:19.899920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EVRRNIACFPQJRQ6Y2IXTV6BB5C","json":"https://pith.science/pith/EVRRNIACFPQJRQ6Y2IXTV6BB5C.json","graph_json":"https://pith.science/api/pith-number/EVRRNIACFPQJRQ6Y2IXTV6BB5C/graph.json","events_json":"https://pith.science/api/pith-number/EVRRNIACFPQJRQ6Y2IXTV6BB5C/events.json","paper":"https://pith.science/paper/EVRRNIAC"},"agent_actions":{"view_html":"https://pith.science/pith/EVRRNIACFPQJRQ6Y2IXTV6BB5C","download_json":"https://pith.science/pith/EVRRNIACFPQJRQ6Y2IXTV6BB5C.json","view_paper":"https://pith.science/paper/EVRRNIAC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.03746&json=true","fetch_graph":"https://pith.science/api/pith-number/EVRRNIACFPQJRQ6Y2IXTV6BB5C/graph.json","fetch_events":"https://pith.science/api/pith-number/EVRRNIACFPQJRQ6Y2IXTV6BB5C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EVRRNIACFPQJRQ6Y2IXTV6BB5C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EVRRNIACFPQJRQ6Y2IXTV6BB5C/action/storage_attestation","attest_author":"https://pith.science/pith/EVRRNIACFPQJRQ6Y2IXTV6BB5C/action/author_attestation","sign_citation":"https://pith.science/pith/EVRRNIACFPQJRQ6Y2IXTV6BB5C/action/citation_signature","submit_replication":"https://pith.science/pith/EVRRNIACFPQJRQ6Y2IXTV6BB5C/action/replication_record"}},"created_at":"2026-05-18T01:53:03.391525+00:00","updated_at":"2026-05-18T01:53:03.391525+00:00"}