{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JEI7WCQ63V7APNOZ6Z6NOVMZX2","short_pith_number":"pith:JEI7WCQ6","schema_version":"1.0","canonical_sha256":"4911fb0a1edd7e07b5d9f67cd75599beb9217dbffba91e66596e68c50f221e7d","source":{"kind":"arxiv","id":"1607.07174","version":2},"attestation_state":"computed","paper":{"title":"The $k$-strong induced arboricity of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Daniel Goncalves, Jonathan Rollin, Maria Axenovich, Torsten Ueckerdt","submitted_at":"2016-07-25T08:04:52Z","abstract_excerpt":"The induced arboricity of a graph $G$ is the smallest number of induced forests covering the edges of $G$. This is a well-defined parameter bounded from above by the number of edges of $G$ when each forest in a cover consists of exactly one edge. Not all edges of a graph necessarily belong to induced forests with larger components. For $k\\geq 1$, we call an edge $k$-valid if it is contained in an induced tree on $k$ edges. The $k$-strong induced arboricity of $G$, denoted by $f_k(G)$, is the smallest number of induced forests with components of sizes at least $k$ that cover all $k$-valid edges"},"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":"1607.07174","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-25T08:04:52Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"8061842e2cfd365db7cca9d654e17f4ebf79aeb831cbb2a99a342abb5e76454e","abstract_canon_sha256":"321c55a97a288c035ef7cf642535c151b63f82f3f16a856e96968afdf242ac06"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:21.039588Z","signature_b64":"pOX0sd6hH5ySaCblZmFV4j2WC3PDsrxba+1ZSI50Ys/rActDveEJULD0m6e6nLXie21dBvbCxEULzZOCIo7kDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4911fb0a1edd7e07b5d9f67cd75599beb9217dbffba91e66596e68c50f221e7d","last_reissued_at":"2026-05-18T00:43:21.039081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:21.039081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $k$-strong induced arboricity of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Daniel Goncalves, Jonathan Rollin, Maria Axenovich, Torsten Ueckerdt","submitted_at":"2016-07-25T08:04:52Z","abstract_excerpt":"The induced arboricity of a graph $G$ is the smallest number of induced forests covering the edges of $G$. This is a well-defined parameter bounded from above by the number of edges of $G$ when each forest in a cover consists of exactly one edge. Not all edges of a graph necessarily belong to induced forests with larger components. For $k\\geq 1$, we call an edge $k$-valid if it is contained in an induced tree on $k$ edges. The $k$-strong induced arboricity of $G$, denoted by $f_k(G)$, is the smallest number of induced forests with components of sizes at least $k$ that cover all $k$-valid edges"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07174","kind":"arxiv","version":2},"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":"1607.07174","created_at":"2026-05-18T00:43:21.039163+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.07174v2","created_at":"2026-05-18T00:43:21.039163+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07174","created_at":"2026-05-18T00:43:21.039163+00:00"},{"alias_kind":"pith_short_12","alias_value":"JEI7WCQ63V7A","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JEI7WCQ63V7APNOZ","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JEI7WCQ6","created_at":"2026-05-18T12:30:25.849896+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/JEI7WCQ63V7APNOZ6Z6NOVMZX2","json":"https://pith.science/pith/JEI7WCQ63V7APNOZ6Z6NOVMZX2.json","graph_json":"https://pith.science/api/pith-number/JEI7WCQ63V7APNOZ6Z6NOVMZX2/graph.json","events_json":"https://pith.science/api/pith-number/JEI7WCQ63V7APNOZ6Z6NOVMZX2/events.json","paper":"https://pith.science/paper/JEI7WCQ6"},"agent_actions":{"view_html":"https://pith.science/pith/JEI7WCQ63V7APNOZ6Z6NOVMZX2","download_json":"https://pith.science/pith/JEI7WCQ63V7APNOZ6Z6NOVMZX2.json","view_paper":"https://pith.science/paper/JEI7WCQ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.07174&json=true","fetch_graph":"https://pith.science/api/pith-number/JEI7WCQ63V7APNOZ6Z6NOVMZX2/graph.json","fetch_events":"https://pith.science/api/pith-number/JEI7WCQ63V7APNOZ6Z6NOVMZX2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JEI7WCQ63V7APNOZ6Z6NOVMZX2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JEI7WCQ63V7APNOZ6Z6NOVMZX2/action/storage_attestation","attest_author":"https://pith.science/pith/JEI7WCQ63V7APNOZ6Z6NOVMZX2/action/author_attestation","sign_citation":"https://pith.science/pith/JEI7WCQ63V7APNOZ6Z6NOVMZX2/action/citation_signature","submit_replication":"https://pith.science/pith/JEI7WCQ63V7APNOZ6Z6NOVMZX2/action/replication_record"}},"created_at":"2026-05-18T00:43:21.039163+00:00","updated_at":"2026-05-18T00:43:21.039163+00:00"}