{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TADG4EEB6UGGQRR6EFXODDQOF5","short_pith_number":"pith:TADG4EEB","schema_version":"1.0","canonical_sha256":"98066e1081f50c68463e216ee18e0e2f498d7e79cd15aae5a7e585ce33241ae1","source":{"kind":"arxiv","id":"1711.10647","version":1},"attestation_state":"computed","paper":{"title":"Split-Decomposition Trees with Prime Nodes: Enumeration and Random Generation of Cactus Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"J\\'er\\'emie Lumbroso, Maryam Bahrani","submitted_at":"2017-11-29T02:10:22Z","abstract_excerpt":"In this paper, we build on recent results by Chauve et al. (2014) and Bahrani and Lumbroso (2017), which combined the split-decomposition, as exposed by Gioan and Paul, with analytic combinatorics, to produce new enumerative results on graphs---in particular the enumeration of several subclasses of perfect graphs (distance-hereditary, 3-leaf power, ptolemaic). Our goal was to study a simple family of graphs, of which the split-decomposition trees have prime nodes drawn from an enumerable (and manageable!) set of graphs. Cactus graphs, which we describe in more detail further down in this paper"},"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":"1711.10647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-29T02:10:22Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"68e9b8a8697d76d2f7c53b2d8e9bdbc3dcaab27e9294d5529a59a40cf14613cf","abstract_canon_sha256":"e88f46989eb85d76474c0e51270270ba941681f8b4032bb1be8fd99eba636f92"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:17.428555Z","signature_b64":"ggX0RmWMu0CJ1NYPKG+WDOIZCygXJC67b/GTFhIE0AgioFkBLweZ4YpQ9iG0InfSrpO9PhwYa+TBb2bKdqUPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98066e1081f50c68463e216ee18e0e2f498d7e79cd15aae5a7e585ce33241ae1","last_reissued_at":"2026-05-18T00:29:17.427791Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:17.427791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Split-Decomposition Trees with Prime Nodes: Enumeration and Random Generation of Cactus Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"J\\'er\\'emie Lumbroso, Maryam Bahrani","submitted_at":"2017-11-29T02:10:22Z","abstract_excerpt":"In this paper, we build on recent results by Chauve et al. (2014) and Bahrani and Lumbroso (2017), which combined the split-decomposition, as exposed by Gioan and Paul, with analytic combinatorics, to produce new enumerative results on graphs---in particular the enumeration of several subclasses of perfect graphs (distance-hereditary, 3-leaf power, ptolemaic). Our goal was to study a simple family of graphs, of which the split-decomposition trees have prime nodes drawn from an enumerable (and manageable!) set of graphs. Cactus graphs, which we describe in more detail further down in this paper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10647","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":"1711.10647","created_at":"2026-05-18T00:29:17.427918+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.10647v1","created_at":"2026-05-18T00:29:17.427918+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10647","created_at":"2026-05-18T00:29:17.427918+00:00"},{"alias_kind":"pith_short_12","alias_value":"TADG4EEB6UGG","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"TADG4EEB6UGGQRR6","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"TADG4EEB","created_at":"2026-05-18T12:31:43.269735+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/TADG4EEB6UGGQRR6EFXODDQOF5","json":"https://pith.science/pith/TADG4EEB6UGGQRR6EFXODDQOF5.json","graph_json":"https://pith.science/api/pith-number/TADG4EEB6UGGQRR6EFXODDQOF5/graph.json","events_json":"https://pith.science/api/pith-number/TADG4EEB6UGGQRR6EFXODDQOF5/events.json","paper":"https://pith.science/paper/TADG4EEB"},"agent_actions":{"view_html":"https://pith.science/pith/TADG4EEB6UGGQRR6EFXODDQOF5","download_json":"https://pith.science/pith/TADG4EEB6UGGQRR6EFXODDQOF5.json","view_paper":"https://pith.science/paper/TADG4EEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.10647&json=true","fetch_graph":"https://pith.science/api/pith-number/TADG4EEB6UGGQRR6EFXODDQOF5/graph.json","fetch_events":"https://pith.science/api/pith-number/TADG4EEB6UGGQRR6EFXODDQOF5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TADG4EEB6UGGQRR6EFXODDQOF5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TADG4EEB6UGGQRR6EFXODDQOF5/action/storage_attestation","attest_author":"https://pith.science/pith/TADG4EEB6UGGQRR6EFXODDQOF5/action/author_attestation","sign_citation":"https://pith.science/pith/TADG4EEB6UGGQRR6EFXODDQOF5/action/citation_signature","submit_replication":"https://pith.science/pith/TADG4EEB6UGGQRR6EFXODDQOF5/action/replication_record"}},"created_at":"2026-05-18T00:29:17.427918+00:00","updated_at":"2026-05-18T00:29:17.427918+00:00"}