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The independence domination number $ i\\gamma(G)$ of $G$ is the minimum integer $k$ such that every independent set of $G$ can be dominated by $k$ vertices. In this note, we prove that $NC(G)$ is $(|V|- i\\gamma(G)-1)$-collapsible."},"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":"1904.04519","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-09T08:24:51Z","cross_cats_sorted":[],"title_canon_sha256":"99a1f955e58fdc709f019b622f487e3e37e70f89f60ec04efabb77871cff80f4","abstract_canon_sha256":"4d3ab6e7d5c45025e96071ba5c3f715b816a8e7591642eef69b24e3821d9c253"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:58.864100Z","signature_b64":"ZyGVQnfcariAEZyKyLyQC3Bb1J/3C7cS1ZT8mXcAtxrSRx9Zn0ou2IudZgKkCS4OGTP2WsRzxSGa9k4xrOLGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"662af21d5be847a6c1f377e3087dfbb95ee10545ed4a83ec8a3c9455f8b2e225","last_reissued_at":"2026-05-17T23:48:58.863728Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:58.863728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Collapsibility of noncover complexes of chordal graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jinha Kim","submitted_at":"2019-04-09T08:24:51Z","abstract_excerpt":"Let $G$ be a graph on $V$. A vertex subset $S \\subset V$ is called a cover of $G$ if its complement is an independent set, and $S$ is called a noncover if it is not a cover of $G$. A noncover complex $NC(G)$ of $G$ is the simplicial complex on $V$ whose faces are noncovers of $G$. The independence domination number $ i\\gamma(G)$ of $G$ is the minimum integer $k$ such that every independent set of $G$ can be dominated by $k$ vertices. In this note, we prove that $NC(G)$ is $(|V|- i\\gamma(G)-1)$-collapsible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04519","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":"1904.04519","created_at":"2026-05-17T23:48:58.863795+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.04519v1","created_at":"2026-05-17T23:48:58.863795+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04519","created_at":"2026-05-17T23:48:58.863795+00:00"},{"alias_kind":"pith_short_12","alias_value":"MYVPEHK35BD2","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"MYVPEHK35BD2NQPT","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"MYVPEHK3","created_at":"2026-05-18T12:33:24.271573+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/MYVPEHK35BD2NQPTO7RQQ7P3XF","json":"https://pith.science/pith/MYVPEHK35BD2NQPTO7RQQ7P3XF.json","graph_json":"https://pith.science/api/pith-number/MYVPEHK35BD2NQPTO7RQQ7P3XF/graph.json","events_json":"https://pith.science/api/pith-number/MYVPEHK35BD2NQPTO7RQQ7P3XF/events.json","paper":"https://pith.science/paper/MYVPEHK3"},"agent_actions":{"view_html":"https://pith.science/pith/MYVPEHK35BD2NQPTO7RQQ7P3XF","download_json":"https://pith.science/pith/MYVPEHK35BD2NQPTO7RQQ7P3XF.json","view_paper":"https://pith.science/paper/MYVPEHK3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.04519&json=true","fetch_graph":"https://pith.science/api/pith-number/MYVPEHK35BD2NQPTO7RQQ7P3XF/graph.json","fetch_events":"https://pith.science/api/pith-number/MYVPEHK35BD2NQPTO7RQQ7P3XF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MYVPEHK35BD2NQPTO7RQQ7P3XF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MYVPEHK35BD2NQPTO7RQQ7P3XF/action/storage_attestation","attest_author":"https://pith.science/pith/MYVPEHK35BD2NQPTO7RQQ7P3XF/action/author_attestation","sign_citation":"https://pith.science/pith/MYVPEHK35BD2NQPTO7RQQ7P3XF/action/citation_signature","submit_replication":"https://pith.science/pith/MYVPEHK35BD2NQPTO7RQQ7P3XF/action/replication_record"}},"created_at":"2026-05-17T23:48:58.863795+00:00","updated_at":"2026-05-17T23:48:58.863795+00:00"}