{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GOFUCQ7RHKBHQCOJ3MWKA37RE4","short_pith_number":"pith:GOFUCQ7R","schema_version":"1.0","canonical_sha256":"338b4143f13a827809c9db2ca06ff1271b565ff427ff3545298c07a473e47300","source":{"kind":"arxiv","id":"1903.12641","version":2},"attestation_state":"computed","paper":{"title":"Connected max cut is polynomial for graphs without $K_5\\backslash e$ as a minor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Brahim Chaourar","submitted_at":"2019-03-29T17:42:37Z","abstract_excerpt":"Given a graph $G=(V, E)$, a connected cut $\\delta (U)$ is the set of edges of E linking all vertices of U to all vertices of $V\\backslash U$ such that the induced subgraphs $G[U]$ and $G[V\\backslash U]$ are connected. Given a positive weight function $w$ defined on $E$, the connected maximum cut problem (CMAX CUT) is to find a connected cut $\\Omega$ such that $w(\\Omega)$ is maximum among all connected cuts. CMAX CUT is NP-hard even for planar graphs. In this paper, we prove that CMAX CUT is polynomial for graphs without $K_5\\backslash e$ as a minor. We deduce a quadratic time algorithm for the"},"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":"1903.12641","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-29T17:42:37Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"09e327754d33a713b0d090be7ac2a583012c26dcb895c1afdd97c504d5709d9b","abstract_canon_sha256":"f09a9eb216b80f36d92907da15dd57e4ca3b094825eec3a99677e2ee5f876168"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:53.683200Z","signature_b64":"23ta0otxh2P4Lx9yulcU7X3GAWd7YX1khr4FurBscV29bH7SftHjB2mtoizirzI5mrilItrzxOjYCiU0HxZoCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"338b4143f13a827809c9db2ca06ff1271b565ff427ff3545298c07a473e47300","last_reissued_at":"2026-05-17T23:47:53.682757Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:53.682757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connected max cut is polynomial for graphs without $K_5\\backslash e$ as a minor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Brahim Chaourar","submitted_at":"2019-03-29T17:42:37Z","abstract_excerpt":"Given a graph $G=(V, E)$, a connected cut $\\delta (U)$ is the set of edges of E linking all vertices of U to all vertices of $V\\backslash U$ such that the induced subgraphs $G[U]$ and $G[V\\backslash U]$ are connected. Given a positive weight function $w$ defined on $E$, the connected maximum cut problem (CMAX CUT) is to find a connected cut $\\Omega$ such that $w(\\Omega)$ is maximum among all connected cuts. CMAX CUT is NP-hard even for planar graphs. In this paper, we prove that CMAX CUT is polynomial for graphs without $K_5\\backslash e$ as a minor. We deduce a quadratic time algorithm for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12641","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":"1903.12641","created_at":"2026-05-17T23:47:53.682826+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.12641v2","created_at":"2026-05-17T23:47:53.682826+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.12641","created_at":"2026-05-17T23:47:53.682826+00:00"},{"alias_kind":"pith_short_12","alias_value":"GOFUCQ7RHKBH","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"GOFUCQ7RHKBHQCOJ","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"GOFUCQ7R","created_at":"2026-05-18T12:33:18.533446+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.03389","citing_title":"Parameterized Algorithms for Maximum Cut with Connectivity Constraints","ref_index":13,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GOFUCQ7RHKBHQCOJ3MWKA37RE4","json":"https://pith.science/pith/GOFUCQ7RHKBHQCOJ3MWKA37RE4.json","graph_json":"https://pith.science/api/pith-number/GOFUCQ7RHKBHQCOJ3MWKA37RE4/graph.json","events_json":"https://pith.science/api/pith-number/GOFUCQ7RHKBHQCOJ3MWKA37RE4/events.json","paper":"https://pith.science/paper/GOFUCQ7R"},"agent_actions":{"view_html":"https://pith.science/pith/GOFUCQ7RHKBHQCOJ3MWKA37RE4","download_json":"https://pith.science/pith/GOFUCQ7RHKBHQCOJ3MWKA37RE4.json","view_paper":"https://pith.science/paper/GOFUCQ7R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.12641&json=true","fetch_graph":"https://pith.science/api/pith-number/GOFUCQ7RHKBHQCOJ3MWKA37RE4/graph.json","fetch_events":"https://pith.science/api/pith-number/GOFUCQ7RHKBHQCOJ3MWKA37RE4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GOFUCQ7RHKBHQCOJ3MWKA37RE4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GOFUCQ7RHKBHQCOJ3MWKA37RE4/action/storage_attestation","attest_author":"https://pith.science/pith/GOFUCQ7RHKBHQCOJ3MWKA37RE4/action/author_attestation","sign_citation":"https://pith.science/pith/GOFUCQ7RHKBHQCOJ3MWKA37RE4/action/citation_signature","submit_replication":"https://pith.science/pith/GOFUCQ7RHKBHQCOJ3MWKA37RE4/action/replication_record"}},"created_at":"2026-05-17T23:47:53.682826+00:00","updated_at":"2026-05-17T23:47:53.682826+00:00"}