{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YIYDXBL4DVG66SDLND4EFLRTX6","short_pith_number":"pith:YIYDXBL4","schema_version":"1.0","canonical_sha256":"c2303b857c1d4def486b68f842ae33bfa28edf013bbac680f98b83f8d8109c4f","source":{"kind":"arxiv","id":"1507.04901","version":1},"attestation_state":"computed","paper":{"title":"Relating $2$-rainbow domination to weak Roman domination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dieter Rautenbach, Jose D. Alvarado, Simone Dantas","submitted_at":"2015-07-17T10:05:24Z","abstract_excerpt":"Addressing a problem posed by Chellali, Haynes, and Hedetniemi (Discrete Appl. Math. 178 (2014) 27-32) we prove $\\gamma_{r2}(G)\\leq 2\\gamma_r(G)$ for every graph $G$, where $\\gamma_{r2}(G)$ and $\\gamma_r(G)$ denote the $2$-rainbow domination number and the weak Roman domination number of $G$, respectively. We characterize the extremal graphs for this inequality that are $\\{ K_4,K_4-e\\}$-free, and show that the recognition of the $K_5$-free extremal graphs is NP-hard."},"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":"1507.04901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-17T10:05:24Z","cross_cats_sorted":[],"title_canon_sha256":"4cd819ab4b9f634c2a8b400a460c7bf588bfa2622f0e499d84df559ad95bb52a","abstract_canon_sha256":"949dfd9c8cd2b716f955a2d78aa5cf6e3024d464f3891a4be107c83ca89c5f14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:42.470173Z","signature_b64":"pq8u7g7NTabzSnepVdLYGdGMy7yFqAs4SDKUZ4tmuc501DILTbhKYR2pMrXlgjExDYG86IWcRpCYCdAL/CfBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2303b857c1d4def486b68f842ae33bfa28edf013bbac680f98b83f8d8109c4f","last_reissued_at":"2026-05-18T01:36:42.469591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:42.469591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relating $2$-rainbow domination to weak Roman domination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dieter Rautenbach, Jose D. Alvarado, Simone Dantas","submitted_at":"2015-07-17T10:05:24Z","abstract_excerpt":"Addressing a problem posed by Chellali, Haynes, and Hedetniemi (Discrete Appl. Math. 178 (2014) 27-32) we prove $\\gamma_{r2}(G)\\leq 2\\gamma_r(G)$ for every graph $G$, where $\\gamma_{r2}(G)$ and $\\gamma_r(G)$ denote the $2$-rainbow domination number and the weak Roman domination number of $G$, respectively. We characterize the extremal graphs for this inequality that are $\\{ K_4,K_4-e\\}$-free, and show that the recognition of the $K_5$-free extremal graphs is NP-hard."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04901","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":"1507.04901","created_at":"2026-05-18T01:36:42.469694+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.04901v1","created_at":"2026-05-18T01:36:42.469694+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04901","created_at":"2026-05-18T01:36:42.469694+00:00"},{"alias_kind":"pith_short_12","alias_value":"YIYDXBL4DVG6","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"YIYDXBL4DVG66SDL","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"YIYDXBL4","created_at":"2026-05-18T12:29:50.041715+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/YIYDXBL4DVG66SDLND4EFLRTX6","json":"https://pith.science/pith/YIYDXBL4DVG66SDLND4EFLRTX6.json","graph_json":"https://pith.science/api/pith-number/YIYDXBL4DVG66SDLND4EFLRTX6/graph.json","events_json":"https://pith.science/api/pith-number/YIYDXBL4DVG66SDLND4EFLRTX6/events.json","paper":"https://pith.science/paper/YIYDXBL4"},"agent_actions":{"view_html":"https://pith.science/pith/YIYDXBL4DVG66SDLND4EFLRTX6","download_json":"https://pith.science/pith/YIYDXBL4DVG66SDLND4EFLRTX6.json","view_paper":"https://pith.science/paper/YIYDXBL4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.04901&json=true","fetch_graph":"https://pith.science/api/pith-number/YIYDXBL4DVG66SDLND4EFLRTX6/graph.json","fetch_events":"https://pith.science/api/pith-number/YIYDXBL4DVG66SDLND4EFLRTX6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YIYDXBL4DVG66SDLND4EFLRTX6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YIYDXBL4DVG66SDLND4EFLRTX6/action/storage_attestation","attest_author":"https://pith.science/pith/YIYDXBL4DVG66SDLND4EFLRTX6/action/author_attestation","sign_citation":"https://pith.science/pith/YIYDXBL4DVG66SDLND4EFLRTX6/action/citation_signature","submit_replication":"https://pith.science/pith/YIYDXBL4DVG66SDLND4EFLRTX6/action/replication_record"}},"created_at":"2026-05-18T01:36:42.469694+00:00","updated_at":"2026-05-18T01:36:42.469694+00:00"}