{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:F3NK4QMFHOUUPRYHPNPVC55AL5","short_pith_number":"pith:F3NK4QMF","schema_version":"1.0","canonical_sha256":"2edaae41853ba947c7077b5f5177a05f48ba7ea3f44423a14cb704eab03354dd","source":{"kind":"arxiv","id":"1301.5953","version":1},"attestation_state":"computed","paper":{"title":"Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andrzej Proskurowski, Dani\\\"el Paulusma, Hajo Broersma, Ji\\v{r}\\'i Fiala, Petr A. Golovach, Tom\\'a\\v{s} Kaiser","submitted_at":"2013-01-25T02:24:26Z","abstract_excerpt":"Hung and Chang showed that for all k>=1 an interval graph has a path cover of size at most k if and only if its scattering number is at most k. They also showed that an interval graph has a Hamilton cycle if and only if its scattering number is at most 0. We complete this characterization by proving that for all k<=-1 an interval graph is -(k+1)-Hamilton-connected if and only if its scattering number is at most k. We also give an O(m+n) time algorithm for computing the scattering number of an interval graph with n vertices an m edges, which improves the O(n^4) time bound of Kratsch, Kloks and "},"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":"1301.5953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-01-25T02:24:26Z","cross_cats_sorted":[],"title_canon_sha256":"afe8a8046f475342ba0f2caca48474a8b36f46476f318fb3774a5ef574ba78f4","abstract_canon_sha256":"277d04879ab71890d7c4cf177ee0ac7bd983be6cb06c1771168d37e005502f90"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:27.508261Z","signature_b64":"d5lLeYkdLprdtH2o5QRx/18Gn7SPmLLd9De5a5UgkxPO3OV4xTk09TB6Bv+bWbijBL0WwBP7b9fH+L3g2huaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2edaae41853ba947c7077b5f5177a05f48ba7ea3f44423a14cb704eab03354dd","last_reissued_at":"2026-05-18T03:35:27.507609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:27.507609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andrzej Proskurowski, Dani\\\"el Paulusma, Hajo Broersma, Ji\\v{r}\\'i Fiala, Petr A. Golovach, Tom\\'a\\v{s} Kaiser","submitted_at":"2013-01-25T02:24:26Z","abstract_excerpt":"Hung and Chang showed that for all k>=1 an interval graph has a path cover of size at most k if and only if its scattering number is at most k. They also showed that an interval graph has a Hamilton cycle if and only if its scattering number is at most 0. We complete this characterization by proving that for all k<=-1 an interval graph is -(k+1)-Hamilton-connected if and only if its scattering number is at most k. We also give an O(m+n) time algorithm for computing the scattering number of an interval graph with n vertices an m edges, which improves the O(n^4) time bound of Kratsch, Kloks and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5953","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":"1301.5953","created_at":"2026-05-18T03:35:27.507712+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.5953v1","created_at":"2026-05-18T03:35:27.507712+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5953","created_at":"2026-05-18T03:35:27.507712+00:00"},{"alias_kind":"pith_short_12","alias_value":"F3NK4QMFHOUU","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"F3NK4QMFHOUUPRYH","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"F3NK4QMF","created_at":"2026-05-18T12:27:43.054852+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/F3NK4QMFHOUUPRYHPNPVC55AL5","json":"https://pith.science/pith/F3NK4QMFHOUUPRYHPNPVC55AL5.json","graph_json":"https://pith.science/api/pith-number/F3NK4QMFHOUUPRYHPNPVC55AL5/graph.json","events_json":"https://pith.science/api/pith-number/F3NK4QMFHOUUPRYHPNPVC55AL5/events.json","paper":"https://pith.science/paper/F3NK4QMF"},"agent_actions":{"view_html":"https://pith.science/pith/F3NK4QMFHOUUPRYHPNPVC55AL5","download_json":"https://pith.science/pith/F3NK4QMFHOUUPRYHPNPVC55AL5.json","view_paper":"https://pith.science/paper/F3NK4QMF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.5953&json=true","fetch_graph":"https://pith.science/api/pith-number/F3NK4QMFHOUUPRYHPNPVC55AL5/graph.json","fetch_events":"https://pith.science/api/pith-number/F3NK4QMFHOUUPRYHPNPVC55AL5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F3NK4QMFHOUUPRYHPNPVC55AL5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F3NK4QMFHOUUPRYHPNPVC55AL5/action/storage_attestation","attest_author":"https://pith.science/pith/F3NK4QMFHOUUPRYHPNPVC55AL5/action/author_attestation","sign_citation":"https://pith.science/pith/F3NK4QMFHOUUPRYHPNPVC55AL5/action/citation_signature","submit_replication":"https://pith.science/pith/F3NK4QMFHOUUPRYHPNPVC55AL5/action/replication_record"}},"created_at":"2026-05-18T03:35:27.507712+00:00","updated_at":"2026-05-18T03:35:27.507712+00:00"}