{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:MXUOK4QXJL2RHRTCKWSJDQQ57S","short_pith_number":"pith:MXUOK4QX","schema_version":"1.0","canonical_sha256":"65e8e572174af513c66255a491c21dfc905fb6dc36b2d40f0d49fda6a2b125bf","source":{"kind":"arxiv","id":"1907.09817","version":1},"attestation_state":"computed","paper":{"title":"Non-separating Planar Graphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Graham Farr, Hooman R. Dehkordi","submitted_at":"2019-07-23T11:15:45Z","abstract_excerpt":"A graph $G$ is a non-separating planar graph if there is a drawing $D$ of $G$ on the plane such that (1) no two edges cross each other in $D$ and (2) for any cycle $C$ in $D$, any two vertices not in $C$ are on the same side of $C$ in $D$.\n  Non-separating planar graphs are closed under taking minors and are a subclass of planar graphs and a superclass of outerplanar graphs.\n  In this paper, we show that a graph is a non-separating planar graph if and only if it does not contain $K_1 \\cup K_4$ or $K_1 \\cup K_{2,3}$ or $K_{1,1,3}$ as a minor.\n  Furthermore, we provide a structural characterisat"},"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":"1907.09817","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2019-07-23T11:15:45Z","cross_cats_sorted":[],"title_canon_sha256":"3ab5c3e25ad322b327187607ddb7ef11ead295bcba57d648f95023c188424ab4","abstract_canon_sha256":"dc002c611f93dc9424f6bdd78861c900f19de08b93fa83d9394a3a025ebb45f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:49.966695Z","signature_b64":"8JbtHlcu2ktjPlLdMyfdvSRAr/cGdnXJ9REzKn64Mk5DZzi8aTGDL+dSKjVqY83p6YVlI8w63K4zQk1d1D9zBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65e8e572174af513c66255a491c21dfc905fb6dc36b2d40f0d49fda6a2b125bf","last_reissued_at":"2026-05-17T23:39:49.966009Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:49.966009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-separating Planar Graphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Graham Farr, Hooman R. Dehkordi","submitted_at":"2019-07-23T11:15:45Z","abstract_excerpt":"A graph $G$ is a non-separating planar graph if there is a drawing $D$ of $G$ on the plane such that (1) no two edges cross each other in $D$ and (2) for any cycle $C$ in $D$, any two vertices not in $C$ are on the same side of $C$ in $D$.\n  Non-separating planar graphs are closed under taking minors and are a subclass of planar graphs and a superclass of outerplanar graphs.\n  In this paper, we show that a graph is a non-separating planar graph if and only if it does not contain $K_1 \\cup K_4$ or $K_1 \\cup K_{2,3}$ or $K_{1,1,3}$ as a minor.\n  Furthermore, we provide a structural characterisat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09817","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":"1907.09817","created_at":"2026-05-17T23:39:49.966102+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.09817v1","created_at":"2026-05-17T23:39:49.966102+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09817","created_at":"2026-05-17T23:39:49.966102+00:00"},{"alias_kind":"pith_short_12","alias_value":"MXUOK4QXJL2R","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"MXUOK4QXJL2RHRTC","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"MXUOK4QX","created_at":"2026-05-18T12:33:24.271573+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/MXUOK4QXJL2RHRTCKWSJDQQ57S","json":"https://pith.science/pith/MXUOK4QXJL2RHRTCKWSJDQQ57S.json","graph_json":"https://pith.science/api/pith-number/MXUOK4QXJL2RHRTCKWSJDQQ57S/graph.json","events_json":"https://pith.science/api/pith-number/MXUOK4QXJL2RHRTCKWSJDQQ57S/events.json","paper":"https://pith.science/paper/MXUOK4QX"},"agent_actions":{"view_html":"https://pith.science/pith/MXUOK4QXJL2RHRTCKWSJDQQ57S","download_json":"https://pith.science/pith/MXUOK4QXJL2RHRTCKWSJDQQ57S.json","view_paper":"https://pith.science/paper/MXUOK4QX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.09817&json=true","fetch_graph":"https://pith.science/api/pith-number/MXUOK4QXJL2RHRTCKWSJDQQ57S/graph.json","fetch_events":"https://pith.science/api/pith-number/MXUOK4QXJL2RHRTCKWSJDQQ57S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MXUOK4QXJL2RHRTCKWSJDQQ57S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MXUOK4QXJL2RHRTCKWSJDQQ57S/action/storage_attestation","attest_author":"https://pith.science/pith/MXUOK4QXJL2RHRTCKWSJDQQ57S/action/author_attestation","sign_citation":"https://pith.science/pith/MXUOK4QXJL2RHRTCKWSJDQQ57S/action/citation_signature","submit_replication":"https://pith.science/pith/MXUOK4QXJL2RHRTCKWSJDQQ57S/action/replication_record"}},"created_at":"2026-05-17T23:39:49.966102+00:00","updated_at":"2026-05-17T23:39:49.966102+00:00"}