{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:V5U7HFG3J5ODOGMKH326UZEJ7J","short_pith_number":"pith:V5U7HFG3","schema_version":"1.0","canonical_sha256":"af69f394db4f5c37198a3ef5ea6489fa4ddf249e3d913604eaa064f82e399749","source":{"kind":"arxiv","id":"1112.3254","version":1},"attestation_state":"computed","paper":{"title":"Recognizing [h,2,1] graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Liliana Alc\\'on, Mar\\'ia P\\'ia Mazzoleni, Marisa Gutierrez","submitted_at":"2011-12-14T15:47:43Z","abstract_excerpt":"An (h,s,t)-representation of a graph G consists of a collection of subtrees of a tree T, where each subtree corresponds to a vertex of G such that (i) the maximum degree of T is at most h, (ii) every subtree has maximum degree at mots s, (iii) there is an edge between two vertices in the graph G if and only if the corresponding subtrees have at least t vertices in common in T. The class of graphs that have an (h,s,t)-representation is denoted [h,s,t].\n  An undirected graph G is called a VPT graph if it is the vertex intersection graph of a family of paths in a tree. In this paper we characteri"},"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":"1112.3254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-14T15:47:43Z","cross_cats_sorted":[],"title_canon_sha256":"e41f7b809e39152732bc7276049b1ec9a17aa147102e2551cfe3e281c9530383","abstract_canon_sha256":"4b12521b35a8e4cbc82d4a95ceb0f6951b8beaae70f2360d5f90f066e504e90a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:19.672764Z","signature_b64":"kFxHjtfU4cP5s2FNc9ZB8rFMCk+hyiaUCubROiuwNDWnKInxT3cytHRysCHDFU3SvzJSLd3oTVbIyq6ylfOyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af69f394db4f5c37198a3ef5ea6489fa4ddf249e3d913604eaa064f82e399749","last_reissued_at":"2026-05-18T04:06:19.671959Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:19.671959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recognizing [h,2,1] graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Liliana Alc\\'on, Mar\\'ia P\\'ia Mazzoleni, Marisa Gutierrez","submitted_at":"2011-12-14T15:47:43Z","abstract_excerpt":"An (h,s,t)-representation of a graph G consists of a collection of subtrees of a tree T, where each subtree corresponds to a vertex of G such that (i) the maximum degree of T is at most h, (ii) every subtree has maximum degree at mots s, (iii) there is an edge between two vertices in the graph G if and only if the corresponding subtrees have at least t vertices in common in T. The class of graphs that have an (h,s,t)-representation is denoted [h,s,t].\n  An undirected graph G is called a VPT graph if it is the vertex intersection graph of a family of paths in a tree. In this paper we characteri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3254","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":"1112.3254","created_at":"2026-05-18T04:06:19.672091+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.3254v1","created_at":"2026-05-18T04:06:19.672091+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3254","created_at":"2026-05-18T04:06:19.672091+00:00"},{"alias_kind":"pith_short_12","alias_value":"V5U7HFG3J5OD","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"V5U7HFG3J5ODOGMK","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"V5U7HFG3","created_at":"2026-05-18T12:26:42.757692+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/V5U7HFG3J5ODOGMKH326UZEJ7J","json":"https://pith.science/pith/V5U7HFG3J5ODOGMKH326UZEJ7J.json","graph_json":"https://pith.science/api/pith-number/V5U7HFG3J5ODOGMKH326UZEJ7J/graph.json","events_json":"https://pith.science/api/pith-number/V5U7HFG3J5ODOGMKH326UZEJ7J/events.json","paper":"https://pith.science/paper/V5U7HFG3"},"agent_actions":{"view_html":"https://pith.science/pith/V5U7HFG3J5ODOGMKH326UZEJ7J","download_json":"https://pith.science/pith/V5U7HFG3J5ODOGMKH326UZEJ7J.json","view_paper":"https://pith.science/paper/V5U7HFG3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.3254&json=true","fetch_graph":"https://pith.science/api/pith-number/V5U7HFG3J5ODOGMKH326UZEJ7J/graph.json","fetch_events":"https://pith.science/api/pith-number/V5U7HFG3J5ODOGMKH326UZEJ7J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V5U7HFG3J5ODOGMKH326UZEJ7J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V5U7HFG3J5ODOGMKH326UZEJ7J/action/storage_attestation","attest_author":"https://pith.science/pith/V5U7HFG3J5ODOGMKH326UZEJ7J/action/author_attestation","sign_citation":"https://pith.science/pith/V5U7HFG3J5ODOGMKH326UZEJ7J/action/citation_signature","submit_replication":"https://pith.science/pith/V5U7HFG3J5ODOGMKH326UZEJ7J/action/replication_record"}},"created_at":"2026-05-18T04:06:19.672091+00:00","updated_at":"2026-05-18T04:06:19.672091+00:00"}