{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:BZVDCIOL2CCWZTTWSUGKZLW6ME","short_pith_number":"pith:BZVDCIOL","schema_version":"1.0","canonical_sha256":"0e6a3121cbd0856cce76950cacaede6117fe4291cca0a2f10330614b1b7238db","source":{"kind":"arxiv","id":"1301.4008","version":1},"attestation_state":"computed","paper":{"title":"Simultaneous Domination in Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael A. Henning, Yair Caro","submitted_at":"2013-01-17T08:41:18Z","abstract_excerpt":"Let $F_1, F_2, ..., F_k$ be graphs with the same vertex set $V$. A subset $S \\subseteq V$ is a simultaneous dominating set if for every $i$, $1 \\le i \\le k$, every vertex of $F_i$ not in $S$ is adjacent to a vertex in $S$ in $F_i$; that is, the set $S$ is simultaneously a dominating set in each graph $F_i$. The cardinality of a smallest such set is the simultaneous domination number. We present general upper bounds on the simultaneous domination number. We investigate bounds in special cases, including the cases when the factors, $F_i$, are $r$-regular or the disjoint union of copies of $K_r$."},"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":"1301.4008","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-17T08:41:18Z","cross_cats_sorted":[],"title_canon_sha256":"1c5a2db6de71d9d3d4a09c2e7440171f8e4251efb37fb98285af2af81e4e2576","abstract_canon_sha256":"57f148c5005f782fac28a5e2c93973160d87e06556f81ebb8839357a35f91fcb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:14.636314Z","signature_b64":"eRBmbZppgstdxdL4NVnsMDtG13kNjWn30w6w0GV5i43l60Tyet4i2dIbgyOcsEvXpOG64a27t8mCNGWfJhc6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e6a3121cbd0856cce76950cacaede6117fe4291cca0a2f10330614b1b7238db","last_reissued_at":"2026-05-18T03:36:14.635633Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:14.635633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simultaneous Domination in Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael A. Henning, Yair Caro","submitted_at":"2013-01-17T08:41:18Z","abstract_excerpt":"Let $F_1, F_2, ..., F_k$ be graphs with the same vertex set $V$. A subset $S \\subseteq V$ is a simultaneous dominating set if for every $i$, $1 \\le i \\le k$, every vertex of $F_i$ not in $S$ is adjacent to a vertex in $S$ in $F_i$; that is, the set $S$ is simultaneously a dominating set in each graph $F_i$. The cardinality of a smallest such set is the simultaneous domination number. We present general upper bounds on the simultaneous domination number. We investigate bounds in special cases, including the cases when the factors, $F_i$, are $r$-regular or the disjoint union of copies of $K_r$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4008","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":"1301.4008","created_at":"2026-05-18T03:36:14.635752+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.4008v1","created_at":"2026-05-18T03:36:14.635752+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4008","created_at":"2026-05-18T03:36:14.635752+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZVDCIOL2CCW","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZVDCIOL2CCWZTTW","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZVDCIOL","created_at":"2026-05-18T12:27:40.988391+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/BZVDCIOL2CCWZTTWSUGKZLW6ME","json":"https://pith.science/pith/BZVDCIOL2CCWZTTWSUGKZLW6ME.json","graph_json":"https://pith.science/api/pith-number/BZVDCIOL2CCWZTTWSUGKZLW6ME/graph.json","events_json":"https://pith.science/api/pith-number/BZVDCIOL2CCWZTTWSUGKZLW6ME/events.json","paper":"https://pith.science/paper/BZVDCIOL"},"agent_actions":{"view_html":"https://pith.science/pith/BZVDCIOL2CCWZTTWSUGKZLW6ME","download_json":"https://pith.science/pith/BZVDCIOL2CCWZTTWSUGKZLW6ME.json","view_paper":"https://pith.science/paper/BZVDCIOL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.4008&json=true","fetch_graph":"https://pith.science/api/pith-number/BZVDCIOL2CCWZTTWSUGKZLW6ME/graph.json","fetch_events":"https://pith.science/api/pith-number/BZVDCIOL2CCWZTTWSUGKZLW6ME/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZVDCIOL2CCWZTTWSUGKZLW6ME/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZVDCIOL2CCWZTTWSUGKZLW6ME/action/storage_attestation","attest_author":"https://pith.science/pith/BZVDCIOL2CCWZTTWSUGKZLW6ME/action/author_attestation","sign_citation":"https://pith.science/pith/BZVDCIOL2CCWZTTWSUGKZLW6ME/action/citation_signature","submit_replication":"https://pith.science/pith/BZVDCIOL2CCWZTTWSUGKZLW6ME/action/replication_record"}},"created_at":"2026-05-18T03:36:14.635752+00:00","updated_at":"2026-05-18T03:36:14.635752+00:00"}