{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:R35GXEPEODH3SWZ3SXWON4DUHS","short_pith_number":"pith:R35GXEPE","schema_version":"1.0","canonical_sha256":"8efa6b91e470cfb95b3b95ece6f0743cb71ad2c4d3efff4e11485562ba36e41d","source":{"kind":"arxiv","id":"2405.04617","version":2},"attestation_state":"computed","paper":{"title":"Excluding a clique or a biclique in graphs of bounded induced matching treewidth","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bartosz Walczak, Jadwiga Czy\\.zewska, Marcin Bria\\'nski, Martin Milani\\v{c}, Pawe{\\l} Rz\\k{a}\\.zewski, Rose McCarty, Tara Abrishami","submitted_at":"2024-05-07T19:01:16Z","abstract_excerpt":"For a tree decomposition $\\mathcal{T}$ of a graph $G$, let $\\mu(\\mathcal{T})$ denote the maximum size of an induced matching in $G$ with the property that some bag of $\\mathcal{T}$ contains at least one endpoint of every edge of the matching. The induced matching treewidth of a graph $G$ is the minimum value of $\\mu(\\mathcal{T})$ over all tree decompositions $\\mathcal{T}$ of $G$. Classes of graphs with bounded induced matching treewidth admit polynomial-time algorithms for a number of problems, including INDEPENDENT SET, $k$-COLORING, ODD CYCLE TRANSVERSAL, and FEEDBACK VERTEX SET. In this pap"},"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":"2405.04617","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-05-07T19:01:16Z","cross_cats_sorted":[],"title_canon_sha256":"8a7cdf6366f40dd521272095aa9af6178f8160bde1be03b52b6827e6e3b09c79","abstract_canon_sha256":"8677e95c8184119f3256146f16b96a7a7ad8d08ed7a5af2fe2794584b5901b55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:24:16.537624Z","signature_b64":"Z+cBHU1/6zc0Rhe1YbTAdivrwrevqMMoXG3czWSo+3fRe5ua+HF0vi0HJtKhDuzcJrRJ13n4n11k6BK+w2KRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8efa6b91e470cfb95b3b95ece6f0743cb71ad2c4d3efff4e11485562ba36e41d","last_reissued_at":"2026-07-05T09:24:16.537149Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:24:16.537149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Excluding a clique or a biclique in graphs of bounded induced matching treewidth","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bartosz Walczak, Jadwiga Czy\\.zewska, Marcin Bria\\'nski, Martin Milani\\v{c}, Pawe{\\l} Rz\\k{a}\\.zewski, Rose McCarty, Tara Abrishami","submitted_at":"2024-05-07T19:01:16Z","abstract_excerpt":"For a tree decomposition $\\mathcal{T}$ of a graph $G$, let $\\mu(\\mathcal{T})$ denote the maximum size of an induced matching in $G$ with the property that some bag of $\\mathcal{T}$ contains at least one endpoint of every edge of the matching. The induced matching treewidth of a graph $G$ is the minimum value of $\\mu(\\mathcal{T})$ over all tree decompositions $\\mathcal{T}$ of $G$. Classes of graphs with bounded induced matching treewidth admit polynomial-time algorithms for a number of problems, including INDEPENDENT SET, $k$-COLORING, ODD CYCLE TRANSVERSAL, and FEEDBACK VERTEX SET. In this pap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.04617","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.04617/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2405.04617","created_at":"2026-07-05T09:24:16.537213+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.04617v2","created_at":"2026-07-05T09:24:16.537213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.04617","created_at":"2026-07-05T09:24:16.537213+00:00"},{"alias_kind":"pith_short_12","alias_value":"R35GXEPEODH3","created_at":"2026-07-05T09:24:16.537213+00:00"},{"alias_kind":"pith_short_16","alias_value":"R35GXEPEODH3SWZ3","created_at":"2026-07-05T09:24:16.537213+00:00"},{"alias_kind":"pith_short_8","alias_value":"R35GXEPE","created_at":"2026-07-05T09:24:16.537213+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.15149","citing_title":"Induced subgraphs of graphs with large deficiency","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R35GXEPEODH3SWZ3SXWON4DUHS","json":"https://pith.science/pith/R35GXEPEODH3SWZ3SXWON4DUHS.json","graph_json":"https://pith.science/api/pith-number/R35GXEPEODH3SWZ3SXWON4DUHS/graph.json","events_json":"https://pith.science/api/pith-number/R35GXEPEODH3SWZ3SXWON4DUHS/events.json","paper":"https://pith.science/paper/R35GXEPE"},"agent_actions":{"view_html":"https://pith.science/pith/R35GXEPEODH3SWZ3SXWON4DUHS","download_json":"https://pith.science/pith/R35GXEPEODH3SWZ3SXWON4DUHS.json","view_paper":"https://pith.science/paper/R35GXEPE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.04617&json=true","fetch_graph":"https://pith.science/api/pith-number/R35GXEPEODH3SWZ3SXWON4DUHS/graph.json","fetch_events":"https://pith.science/api/pith-number/R35GXEPEODH3SWZ3SXWON4DUHS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R35GXEPEODH3SWZ3SXWON4DUHS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R35GXEPEODH3SWZ3SXWON4DUHS/action/storage_attestation","attest_author":"https://pith.science/pith/R35GXEPEODH3SWZ3SXWON4DUHS/action/author_attestation","sign_citation":"https://pith.science/pith/R35GXEPEODH3SWZ3SXWON4DUHS/action/citation_signature","submit_replication":"https://pith.science/pith/R35GXEPEODH3SWZ3SXWON4DUHS/action/replication_record"}},"created_at":"2026-07-05T09:24:16.537213+00:00","updated_at":"2026-07-05T09:24:16.537213+00:00"}