{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:DXK5GOTXDPAI2ZEUNVHBYPPNV4","short_pith_number":"pith:DXK5GOTX","schema_version":"1.0","canonical_sha256":"1dd5d33a771bc08d64946d4e1c3dedaf05fb8acc01a512d8eaf5bf594cc94f41","source":{"kind":"arxiv","id":"1112.3244","version":2},"attestation_state":"computed","paper":{"title":"k-Gap Interval Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"cs.DS","authors_text":"Erik Jan van Leeuwen, Fedor V. Fomin, Karol Suchan, Martin Vatshelle, Petr Golovach, Serge Gaspers, Stefan Szeider, Yngve Villanger","submitted_at":"2011-12-14T15:06:52Z","abstract_excerpt":"We initiate the study of a new parameterization of graph problems. In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an interval associated to one vertex has a nonempty intersection with an interval associated to the other vertex. A graph on n vertices is a k-gap interval graph if it has a multiple interval representation with at most n+k intervals in total. In order to scale up the nice algorithmic properties of interval graphs (where k=0), we parameterize graph problems by k,"},"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":"1112.3244","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-12-14T15:06:52Z","cross_cats_sorted":["cs.CC","cs.DM"],"title_canon_sha256":"98aa401341ccc107f997e57247afd8b2a60e1b7ca267e062d29cccc9632b0eb7","abstract_canon_sha256":"a13eca1ab6332126efd11b70f28e6d9ff1bb99f8032b5db26928d54e76c1255e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:09.218624Z","signature_b64":"g70DUs7Yq2H+ZfjcyG85SldPDfzI3+l1WPEvgaMLPp+fLA2M1u9osUnRf7QxKTAZMfmQogbAhxu1xLlR73lmDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dd5d33a771bc08d64946d4e1c3dedaf05fb8acc01a512d8eaf5bf594cc94f41","last_reissued_at":"2026-05-18T04:06:09.218109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:09.218109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"k-Gap Interval Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"cs.DS","authors_text":"Erik Jan van Leeuwen, Fedor V. Fomin, Karol Suchan, Martin Vatshelle, Petr Golovach, Serge Gaspers, Stefan Szeider, Yngve Villanger","submitted_at":"2011-12-14T15:06:52Z","abstract_excerpt":"We initiate the study of a new parameterization of graph problems. In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an interval associated to one vertex has a nonempty intersection with an interval associated to the other vertex. A graph on n vertices is a k-gap interval graph if it has a multiple interval representation with at most n+k intervals in total. In order to scale up the nice algorithmic properties of interval graphs (where k=0), we parameterize graph problems by k,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3244","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":"1112.3244","created_at":"2026-05-18T04:06:09.218183+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.3244v2","created_at":"2026-05-18T04:06:09.218183+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3244","created_at":"2026-05-18T04:06:09.218183+00:00"},{"alias_kind":"pith_short_12","alias_value":"DXK5GOTXDPAI","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"DXK5GOTXDPAI2ZEU","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"DXK5GOTX","created_at":"2026-05-18T12:26:26.731475+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/DXK5GOTXDPAI2ZEUNVHBYPPNV4","json":"https://pith.science/pith/DXK5GOTXDPAI2ZEUNVHBYPPNV4.json","graph_json":"https://pith.science/api/pith-number/DXK5GOTXDPAI2ZEUNVHBYPPNV4/graph.json","events_json":"https://pith.science/api/pith-number/DXK5GOTXDPAI2ZEUNVHBYPPNV4/events.json","paper":"https://pith.science/paper/DXK5GOTX"},"agent_actions":{"view_html":"https://pith.science/pith/DXK5GOTXDPAI2ZEUNVHBYPPNV4","download_json":"https://pith.science/pith/DXK5GOTXDPAI2ZEUNVHBYPPNV4.json","view_paper":"https://pith.science/paper/DXK5GOTX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.3244&json=true","fetch_graph":"https://pith.science/api/pith-number/DXK5GOTXDPAI2ZEUNVHBYPPNV4/graph.json","fetch_events":"https://pith.science/api/pith-number/DXK5GOTXDPAI2ZEUNVHBYPPNV4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DXK5GOTXDPAI2ZEUNVHBYPPNV4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DXK5GOTXDPAI2ZEUNVHBYPPNV4/action/storage_attestation","attest_author":"https://pith.science/pith/DXK5GOTXDPAI2ZEUNVHBYPPNV4/action/author_attestation","sign_citation":"https://pith.science/pith/DXK5GOTXDPAI2ZEUNVHBYPPNV4/action/citation_signature","submit_replication":"https://pith.science/pith/DXK5GOTXDPAI2ZEUNVHBYPPNV4/action/replication_record"}},"created_at":"2026-05-18T04:06:09.218183+00:00","updated_at":"2026-05-18T04:06:09.218183+00:00"}