{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:75Z4TGHEQFZGNNZXWFYSCHQNUI","short_pith_number":"pith:75Z4TGHE","schema_version":"1.0","canonical_sha256":"ff73c998e4817266b737b171211e0da22e55b8df54d745a1051ac3a00e43a57b","source":{"kind":"arxiv","id":"1810.04397","version":2},"attestation_state":"computed","paper":{"title":"Maker-Breaker domination number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sandi Klav\\v{z}ar, Valentin Gledel, Vesna Ir\\v{s}i\\v{c}","submitted_at":"2018-10-10T07:30:34Z","abstract_excerpt":"The Maker-Breaker domination game is played on a graph $G$ by Dominator and Staller. The players alternatively select a vertex of $G$ that was not yet chosen in the course of the game. Dominator wins if at some point the vertices he has chosen form a dominating set. Staller wins if Dominator cannot form a dominating set. In this paper we introduce the Maker-Breaker domination number $\\gamma_{{\\rm MB}}(G)$ of $G$ as the minimum number of moves of Dominator to win the game provided that he has a winning strategy and is the first to play. If Staller plays first, then the corresponding invariant i"},"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":"1810.04397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-10T07:30:34Z","cross_cats_sorted":[],"title_canon_sha256":"ce4cb93bbd338c5eaaf9b925df3e98f37405d4d690db9aa95a81080b1609379a","abstract_canon_sha256":"dc1bf701a39ae75b8612d3181194bbbf19e6b7ed0c00743ffbc5a6cb0096fb17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:21.285412Z","signature_b64":"iWdvytXq0jHPfE0OJPBKjNxX99ZpXgR5Ydfhn50udBw47bNjejTbw6+MyeNKsXWnkApe88BMsPBe8Rag0sReBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff73c998e4817266b737b171211e0da22e55b8df54d745a1051ac3a00e43a57b","last_reissued_at":"2026-05-17T23:51:21.284934Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:21.284934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maker-Breaker domination number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sandi Klav\\v{z}ar, Valentin Gledel, Vesna Ir\\v{s}i\\v{c}","submitted_at":"2018-10-10T07:30:34Z","abstract_excerpt":"The Maker-Breaker domination game is played on a graph $G$ by Dominator and Staller. The players alternatively select a vertex of $G$ that was not yet chosen in the course of the game. Dominator wins if at some point the vertices he has chosen form a dominating set. Staller wins if Dominator cannot form a dominating set. In this paper we introduce the Maker-Breaker domination number $\\gamma_{{\\rm MB}}(G)$ of $G$ as the minimum number of moves of Dominator to win the game provided that he has a winning strategy and is the first to play. If Staller plays first, then the corresponding invariant i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04397","kind":"arxiv","version":2},"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":"1810.04397","created_at":"2026-05-17T23:51:21.284997+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.04397v2","created_at":"2026-05-17T23:51:21.284997+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04397","created_at":"2026-05-17T23:51:21.284997+00:00"},{"alias_kind":"pith_short_12","alias_value":"75Z4TGHEQFZG","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"75Z4TGHEQFZGNNZX","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"75Z4TGHE","created_at":"2026-05-18T12:32:11.075285+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/75Z4TGHEQFZGNNZXWFYSCHQNUI","json":"https://pith.science/pith/75Z4TGHEQFZGNNZXWFYSCHQNUI.json","graph_json":"https://pith.science/api/pith-number/75Z4TGHEQFZGNNZXWFYSCHQNUI/graph.json","events_json":"https://pith.science/api/pith-number/75Z4TGHEQFZGNNZXWFYSCHQNUI/events.json","paper":"https://pith.science/paper/75Z4TGHE"},"agent_actions":{"view_html":"https://pith.science/pith/75Z4TGHEQFZGNNZXWFYSCHQNUI","download_json":"https://pith.science/pith/75Z4TGHEQFZGNNZXWFYSCHQNUI.json","view_paper":"https://pith.science/paper/75Z4TGHE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.04397&json=true","fetch_graph":"https://pith.science/api/pith-number/75Z4TGHEQFZGNNZXWFYSCHQNUI/graph.json","fetch_events":"https://pith.science/api/pith-number/75Z4TGHEQFZGNNZXWFYSCHQNUI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/75Z4TGHEQFZGNNZXWFYSCHQNUI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/75Z4TGHEQFZGNNZXWFYSCHQNUI/action/storage_attestation","attest_author":"https://pith.science/pith/75Z4TGHEQFZGNNZXWFYSCHQNUI/action/author_attestation","sign_citation":"https://pith.science/pith/75Z4TGHEQFZGNNZXWFYSCHQNUI/action/citation_signature","submit_replication":"https://pith.science/pith/75Z4TGHEQFZGNNZXWFYSCHQNUI/action/replication_record"}},"created_at":"2026-05-17T23:51:21.284997+00:00","updated_at":"2026-05-17T23:51:21.284997+00:00"}