{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OBU66AXYZBG4Y2TQPZRNPR5NB3","short_pith_number":"pith:OBU66AXY","schema_version":"1.0","canonical_sha256":"7069ef02f8c84dcc6a707e62d7c7ad0ee5a161de23dbd62f44e913a704cfccb1","source":{"kind":"arxiv","id":"1507.02384","version":1},"attestation_state":"computed","paper":{"title":"Maximum matching width: new characterizations and a fast algorithm for dominating set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Jan Arne Telle, Jisu Jeong, Sigve Hortemo S{\\ae}ther","submitted_at":"2015-07-09T05:58:47Z","abstract_excerpt":"We give alternative definitions for maximum matching width, e.g. a graph $G$ has $\\operatorname{mmw}(G) \\leq k$ if and only if it is a subgraph of a chordal graph $H$ and for every maximal clique $X$ of $H$ there exists $A,B,C \\subseteq X$ with $A \\cup B \\cup C=X$ and $|A|,|B|,|C| \\leq k$ such that any subset of $X$ that is a minimal separator of $H$ is a subset of either $A, B$ or $C$. Treewidth and branchwidth have alternative definitions through intersections of subtrees, where treewidth focuses on nodes and branchwidth focuses on edges. We show that mm-width combines both aspects, focusing"},"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":"1507.02384","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-09T05:58:47Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"a6a18a0cfdf85b2b602faa64269059135ddfca76bc3b036c1dbdefd22b95c2fc","abstract_canon_sha256":"ac617e51ede4eca1d23d63ba817085977d677f44eefee46b90b40b4f273b7bf8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:06.842929Z","signature_b64":"nbJRZarDaVAmKz3yJFUrcrNzDY8SwzJBAgOgmVO2lXQQm6sHNHlhD1s+LuUiJOwHInM9W1hAxdYolJDjTxnSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7069ef02f8c84dcc6a707e62d7c7ad0ee5a161de23dbd62f44e913a704cfccb1","last_reissued_at":"2026-05-18T01:37:06.842337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:06.842337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximum matching width: new characterizations and a fast algorithm for dominating set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Jan Arne Telle, Jisu Jeong, Sigve Hortemo S{\\ae}ther","submitted_at":"2015-07-09T05:58:47Z","abstract_excerpt":"We give alternative definitions for maximum matching width, e.g. a graph $G$ has $\\operatorname{mmw}(G) \\leq k$ if and only if it is a subgraph of a chordal graph $H$ and for every maximal clique $X$ of $H$ there exists $A,B,C \\subseteq X$ with $A \\cup B \\cup C=X$ and $|A|,|B|,|C| \\leq k$ such that any subset of $X$ that is a minimal separator of $H$ is a subset of either $A, B$ or $C$. Treewidth and branchwidth have alternative definitions through intersections of subtrees, where treewidth focuses on nodes and branchwidth focuses on edges. We show that mm-width combines both aspects, focusing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02384","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":"1507.02384","created_at":"2026-05-18T01:37:06.842420+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.02384v1","created_at":"2026-05-18T01:37:06.842420+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02384","created_at":"2026-05-18T01:37:06.842420+00:00"},{"alias_kind":"pith_short_12","alias_value":"OBU66AXYZBG4","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OBU66AXYZBG4Y2TQ","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OBU66AXY","created_at":"2026-05-18T12:29:34.919912+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/OBU66AXYZBG4Y2TQPZRNPR5NB3","json":"https://pith.science/pith/OBU66AXYZBG4Y2TQPZRNPR5NB3.json","graph_json":"https://pith.science/api/pith-number/OBU66AXYZBG4Y2TQPZRNPR5NB3/graph.json","events_json":"https://pith.science/api/pith-number/OBU66AXYZBG4Y2TQPZRNPR5NB3/events.json","paper":"https://pith.science/paper/OBU66AXY"},"agent_actions":{"view_html":"https://pith.science/pith/OBU66AXYZBG4Y2TQPZRNPR5NB3","download_json":"https://pith.science/pith/OBU66AXYZBG4Y2TQPZRNPR5NB3.json","view_paper":"https://pith.science/paper/OBU66AXY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.02384&json=true","fetch_graph":"https://pith.science/api/pith-number/OBU66AXYZBG4Y2TQPZRNPR5NB3/graph.json","fetch_events":"https://pith.science/api/pith-number/OBU66AXYZBG4Y2TQPZRNPR5NB3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OBU66AXYZBG4Y2TQPZRNPR5NB3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OBU66AXYZBG4Y2TQPZRNPR5NB3/action/storage_attestation","attest_author":"https://pith.science/pith/OBU66AXYZBG4Y2TQPZRNPR5NB3/action/author_attestation","sign_citation":"https://pith.science/pith/OBU66AXYZBG4Y2TQPZRNPR5NB3/action/citation_signature","submit_replication":"https://pith.science/pith/OBU66AXYZBG4Y2TQPZRNPR5NB3/action/replication_record"}},"created_at":"2026-05-18T01:37:06.842420+00:00","updated_at":"2026-05-18T01:37:06.842420+00:00"}