{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GB6MADSO56KRCVMQIX7ZZ7CML4","short_pith_number":"pith:GB6MADSO","schema_version":"1.0","canonical_sha256":"307cc00e4eef9511559045ff9cfc4c5f3ca66098adf2c38d94dd0e84b3032aff","source":{"kind":"arxiv","id":"1712.08362","version":3},"attestation_state":"computed","paper":{"title":"Connected Vertex Cover for $(sP_1+P_5)$-Free Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Daniel Paulusma, Giacomo Paesani, Matthew Johnson","submitted_at":"2017-12-22T09:18:52Z","abstract_excerpt":"The Connected Vertex Cover problem is to decide if a graph G has a vertex cover of size at most $k$ that induces a connected subgraph of $G$. This is a well-studied problem, known to be NP-complete for restricted graph classes, and, in particular, for $H$-free graphs if $H$ is not a linear forest (a graph is $H$-free if it does not contain $H$ as an induced subgraph). It is easy to see that Connected Vertex Cover is polynomial-time solvable for $P_4$-free graphs. We continue the search for tractable graph classes: we prove that it is also polynomial-time solvable for $(sP_1+P_5)$-free graphs f"},"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":"1712.08362","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-12-22T09:18:52Z","cross_cats_sorted":["cs.CC","cs.DM","math.CO"],"title_canon_sha256":"8d2b48aeb97cdfc13037c269c9886cc01a1bc1cf52193c50b7efca73d616454c","abstract_canon_sha256":"003abd69e013f9dbfbfb1f4b7e2ce8c5f6c5d05f71903b6a521bb527d01f68cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:28.112013Z","signature_b64":"HbC3Td4Cc23cxIYJJR9VG1Pd71fXgzARsgNa8PtEreaUwBtJ4G1El53qTqIp9InJ6eZ9i9jVG9cXOpZMjiUiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"307cc00e4eef9511559045ff9cfc4c5f3ca66098adf2c38d94dd0e84b3032aff","last_reissued_at":"2026-05-18T00:11:28.111638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:28.111638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connected Vertex Cover for $(sP_1+P_5)$-Free Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Daniel Paulusma, Giacomo Paesani, Matthew Johnson","submitted_at":"2017-12-22T09:18:52Z","abstract_excerpt":"The Connected Vertex Cover problem is to decide if a graph G has a vertex cover of size at most $k$ that induces a connected subgraph of $G$. This is a well-studied problem, known to be NP-complete for restricted graph classes, and, in particular, for $H$-free graphs if $H$ is not a linear forest (a graph is $H$-free if it does not contain $H$ as an induced subgraph). It is easy to see that Connected Vertex Cover is polynomial-time solvable for $P_4$-free graphs. We continue the search for tractable graph classes: we prove that it is also polynomial-time solvable for $(sP_1+P_5)$-free graphs f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08362","kind":"arxiv","version":3},"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":"1712.08362","created_at":"2026-05-18T00:11:28.111694+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.08362v3","created_at":"2026-05-18T00:11:28.111694+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08362","created_at":"2026-05-18T00:11:28.111694+00:00"},{"alias_kind":"pith_short_12","alias_value":"GB6MADSO56KR","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"GB6MADSO56KRCVMQ","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"GB6MADSO","created_at":"2026-05-18T12:31:15.632608+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/GB6MADSO56KRCVMQIX7ZZ7CML4","json":"https://pith.science/pith/GB6MADSO56KRCVMQIX7ZZ7CML4.json","graph_json":"https://pith.science/api/pith-number/GB6MADSO56KRCVMQIX7ZZ7CML4/graph.json","events_json":"https://pith.science/api/pith-number/GB6MADSO56KRCVMQIX7ZZ7CML4/events.json","paper":"https://pith.science/paper/GB6MADSO"},"agent_actions":{"view_html":"https://pith.science/pith/GB6MADSO56KRCVMQIX7ZZ7CML4","download_json":"https://pith.science/pith/GB6MADSO56KRCVMQIX7ZZ7CML4.json","view_paper":"https://pith.science/paper/GB6MADSO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.08362&json=true","fetch_graph":"https://pith.science/api/pith-number/GB6MADSO56KRCVMQIX7ZZ7CML4/graph.json","fetch_events":"https://pith.science/api/pith-number/GB6MADSO56KRCVMQIX7ZZ7CML4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GB6MADSO56KRCVMQIX7ZZ7CML4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GB6MADSO56KRCVMQIX7ZZ7CML4/action/storage_attestation","attest_author":"https://pith.science/pith/GB6MADSO56KRCVMQIX7ZZ7CML4/action/author_attestation","sign_citation":"https://pith.science/pith/GB6MADSO56KRCVMQIX7ZZ7CML4/action/citation_signature","submit_replication":"https://pith.science/pith/GB6MADSO56KRCVMQIX7ZZ7CML4/action/replication_record"}},"created_at":"2026-05-18T00:11:28.111694+00:00","updated_at":"2026-05-18T00:11:28.111694+00:00"}