{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:ZDI5QLBQYM65CF4LCDYS34TSKL","short_pith_number":"pith:ZDI5QLBQ","schema_version":"1.0","canonical_sha256":"c8d1d82c30c33dd1178b10f12df27252dbcb79b44d62e1e59a9b4b11083dd2b4","source":{"kind":"arxiv","id":"2011.04255","version":1},"attestation_state":"computed","paper":{"title":"Total domination in plane triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"A. Garc\\'ia, C. Hernando, G. Hern\\'andez, J. Tejel, M. Claverol, M. Maureso, M. Mora","submitted_at":"2020-11-09T09:03:40Z","abstract_excerpt":"A total dominating set of a graph $G=(V,E)$ is a subset $D$ of $V$ such that every vertex in $V$ is adjacent to at least one vertex in $D$. The total domination number of $G$, denoted by $\\gamma _t (G)$, is the minimum cardinality of a total dominating set of $G$. A near-triangulation is a biconnected planar graph that admits a plane embedding such that all of its faces are triangles except possibly the outer face. We show in this paper that $\\gamma _t (G) \\le \\lfloor \\frac{2n}{5}\\rfloor$ for any near-triangulation $G$ of order $n\\ge 5$, with two exceptions."},"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":"2011.04255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-11-09T09:03:40Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"2a4d27e5f760eaa5135b5784b0c027eb22ff95cff62ae4ea217d721ff1bd25e1","abstract_canon_sha256":"70e97776200d1f569c7eb3a20bf7b566016d381dab1b4abfe593b08ee3b1531c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:17:03.214355Z","signature_b64":"w4Ogp/q3xFSbCBL6GTrfU5BdtiNkl8sst8WRGkoWHunwyojPlK8pr8b3B8j+fwLyfEwAEBc9TIhkbIUBazgpDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8d1d82c30c33dd1178b10f12df27252dbcb79b44d62e1e59a9b4b11083dd2b4","last_reissued_at":"2026-07-05T08:17:03.213910Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:17:03.213910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Total domination in plane triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"A. Garc\\'ia, C. Hernando, G. Hern\\'andez, J. Tejel, M. Claverol, M. Maureso, M. Mora","submitted_at":"2020-11-09T09:03:40Z","abstract_excerpt":"A total dominating set of a graph $G=(V,E)$ is a subset $D$ of $V$ such that every vertex in $V$ is adjacent to at least one vertex in $D$. The total domination number of $G$, denoted by $\\gamma _t (G)$, is the minimum cardinality of a total dominating set of $G$. A near-triangulation is a biconnected planar graph that admits a plane embedding such that all of its faces are triangles except possibly the outer face. We show in this paper that $\\gamma _t (G) \\le \\lfloor \\frac{2n}{5}\\rfloor$ for any near-triangulation $G$ of order $n\\ge 5$, with two exceptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.04255","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.04255/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":"2011.04255","created_at":"2026-07-05T08:17:03.213973+00:00"},{"alias_kind":"arxiv_version","alias_value":"2011.04255v1","created_at":"2026-07-05T08:17:03.213973+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.04255","created_at":"2026-07-05T08:17:03.213973+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZDI5QLBQYM65","created_at":"2026-07-05T08:17:03.213973+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZDI5QLBQYM65CF4L","created_at":"2026-07-05T08:17:03.213973+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZDI5QLBQ","created_at":"2026-07-05T08:17:03.213973+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/ZDI5QLBQYM65CF4LCDYS34TSKL","json":"https://pith.science/pith/ZDI5QLBQYM65CF4LCDYS34TSKL.json","graph_json":"https://pith.science/api/pith-number/ZDI5QLBQYM65CF4LCDYS34TSKL/graph.json","events_json":"https://pith.science/api/pith-number/ZDI5QLBQYM65CF4LCDYS34TSKL/events.json","paper":"https://pith.science/paper/ZDI5QLBQ"},"agent_actions":{"view_html":"https://pith.science/pith/ZDI5QLBQYM65CF4LCDYS34TSKL","download_json":"https://pith.science/pith/ZDI5QLBQYM65CF4LCDYS34TSKL.json","view_paper":"https://pith.science/paper/ZDI5QLBQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2011.04255&json=true","fetch_graph":"https://pith.science/api/pith-number/ZDI5QLBQYM65CF4LCDYS34TSKL/graph.json","fetch_events":"https://pith.science/api/pith-number/ZDI5QLBQYM65CF4LCDYS34TSKL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZDI5QLBQYM65CF4LCDYS34TSKL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZDI5QLBQYM65CF4LCDYS34TSKL/action/storage_attestation","attest_author":"https://pith.science/pith/ZDI5QLBQYM65CF4LCDYS34TSKL/action/author_attestation","sign_citation":"https://pith.science/pith/ZDI5QLBQYM65CF4LCDYS34TSKL/action/citation_signature","submit_replication":"https://pith.science/pith/ZDI5QLBQYM65CF4LCDYS34TSKL/action/replication_record"}},"created_at":"2026-07-05T08:17:03.213973+00:00","updated_at":"2026-07-05T08:17:03.213973+00:00"}