{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QXTZWNBPHZCLVJ4EO2RV5VGCM6","short_pith_number":"pith:QXTZWNBP","schema_version":"1.0","canonical_sha256":"85e79b342f3e44baa78476a35ed4c267963e6caba14a7288ca1e1442998e1c5d","source":{"kind":"arxiv","id":"1405.0087","version":1},"attestation_state":"computed","paper":{"title":"Domination games played on line graphs of complete multipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Hovhannes G. Tananyan","submitted_at":"2014-05-01T04:05:03Z","abstract_excerpt":"The domination game on a graph $G$ (introduced by B. Bre\\v{s}ar, S. Klav\\v{z}ar, D.F. Rall \\cite{BKR2010}) consists of two players, Dominator and Staller, who take turns choosing a vertex from $G$ such that whenever a vertex is chosen by either player, at least one additional vertex is dominated. Dominator wishes to dominate the graph in as few steps as possible, and Staller wishes to delay this process as much as possible. The game domination number $\\gamma _{{\\small g}}(G)$ is the number of vertices chosen when Dominator starts the game; when Staller starts, it is denoted by $\\gamma _{{\\smal"},"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":"1405.0087","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-05-01T04:05:03Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7cb7c7152b697406b517109840fe9cba9411e71557a8e80de9b89dc338a2a16c","abstract_canon_sha256":"c6086140bb9a2dfd676ab5682d3c8d046e52977a6d902794b221b2b16af067d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:49.033305Z","signature_b64":"IfOEmkt6qKwg2H7TH9jxh6LBpqKeHmEX+aF75msmlBgn+Tv+7GTAUZIglRRA9FLWb9fK1Hnc8AZelxEoTYpgAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85e79b342f3e44baa78476a35ed4c267963e6caba14a7288ca1e1442998e1c5d","last_reissued_at":"2026-05-18T02:52:49.032892Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:49.032892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Domination games played on line graphs of complete multipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Hovhannes G. Tananyan","submitted_at":"2014-05-01T04:05:03Z","abstract_excerpt":"The domination game on a graph $G$ (introduced by B. Bre\\v{s}ar, S. Klav\\v{z}ar, D.F. Rall \\cite{BKR2010}) consists of two players, Dominator and Staller, who take turns choosing a vertex from $G$ such that whenever a vertex is chosen by either player, at least one additional vertex is dominated. Dominator wishes to dominate the graph in as few steps as possible, and Staller wishes to delay this process as much as possible. The game domination number $\\gamma _{{\\small g}}(G)$ is the number of vertices chosen when Dominator starts the game; when Staller starts, it is denoted by $\\gamma _{{\\smal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0087","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":"1405.0087","created_at":"2026-05-18T02:52:49.032952+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.0087v1","created_at":"2026-05-18T02:52:49.032952+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0087","created_at":"2026-05-18T02:52:49.032952+00:00"},{"alias_kind":"pith_short_12","alias_value":"QXTZWNBPHZCL","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QXTZWNBPHZCLVJ4E","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QXTZWNBP","created_at":"2026-05-18T12:28:46.137349+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/QXTZWNBPHZCLVJ4EO2RV5VGCM6","json":"https://pith.science/pith/QXTZWNBPHZCLVJ4EO2RV5VGCM6.json","graph_json":"https://pith.science/api/pith-number/QXTZWNBPHZCLVJ4EO2RV5VGCM6/graph.json","events_json":"https://pith.science/api/pith-number/QXTZWNBPHZCLVJ4EO2RV5VGCM6/events.json","paper":"https://pith.science/paper/QXTZWNBP"},"agent_actions":{"view_html":"https://pith.science/pith/QXTZWNBPHZCLVJ4EO2RV5VGCM6","download_json":"https://pith.science/pith/QXTZWNBPHZCLVJ4EO2RV5VGCM6.json","view_paper":"https://pith.science/paper/QXTZWNBP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.0087&json=true","fetch_graph":"https://pith.science/api/pith-number/QXTZWNBPHZCLVJ4EO2RV5VGCM6/graph.json","fetch_events":"https://pith.science/api/pith-number/QXTZWNBPHZCLVJ4EO2RV5VGCM6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QXTZWNBPHZCLVJ4EO2RV5VGCM6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QXTZWNBPHZCLVJ4EO2RV5VGCM6/action/storage_attestation","attest_author":"https://pith.science/pith/QXTZWNBPHZCLVJ4EO2RV5VGCM6/action/author_attestation","sign_citation":"https://pith.science/pith/QXTZWNBPHZCLVJ4EO2RV5VGCM6/action/citation_signature","submit_replication":"https://pith.science/pith/QXTZWNBPHZCLVJ4EO2RV5VGCM6/action/replication_record"}},"created_at":"2026-05-18T02:52:49.032952+00:00","updated_at":"2026-05-18T02:52:49.032952+00:00"}