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Suen and Tarr, improving a result of Clark and Suen, showed $\\gamma(G \\square H) \\ge \\frac{1}{2}\\gamma(G)\\gamma(H) + \\frac{1}{2}\\min(\\gamma(G),\\gamma(H))$. We further improve their result by showing $\\gamma(G \\square H) \\ge \\frac{1}{2}\\gamma(G)\\gamma(H) + \\frac{1}{2}\\max(\\gamma(G),\\gamma(H)).$"},"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":"1706.03682","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-12T15:21:30Z","cross_cats_sorted":[],"title_canon_sha256":"24fb27402e335aeb2d10c7370e4f081f0741aec58618c99c1647aa543d2a3021","abstract_canon_sha256":"63a4d843733f0048fcb0d0def5ba729381858cb99e9e51a5b913a0f955ab3b3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:59.583044Z","signature_b64":"CENSt+HfBh77sfiWhRA/QBaW7r9eDGEKncMydSpxlE5yr0zWf5MK1QUqiHgrIwVZy1UcB0u2fUQlegeyzIXyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f39b4f80a14bfce8cfff87ed40b7a5d5c6620433cefb2edbffffea1b33b2985f","last_reissued_at":"2026-05-18T00:31:59.582696Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:59.582696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An improved bound in Vizing's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shira Zerbib","submitted_at":"2017-06-12T15:21:30Z","abstract_excerpt":"A well-known conjecture of Vizing is that $\\gamma(G \\square H) \\ge \\gamma(G)\\gamma(H)$ for any pair of graphs $G, H$, where $\\gamma$ is the domination number and $G \\square H$ is the Cartesian product of $G$ and $H$. Suen and Tarr, improving a result of Clark and Suen, showed $\\gamma(G \\square H) \\ge \\frac{1}{2}\\gamma(G)\\gamma(H) + \\frac{1}{2}\\min(\\gamma(G),\\gamma(H))$. We further improve their result by showing $\\gamma(G \\square H) \\ge \\frac{1}{2}\\gamma(G)\\gamma(H) + \\frac{1}{2}\\max(\\gamma(G),\\gamma(H)).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03682","kind":"arxiv","version":3},"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":"1706.03682","created_at":"2026-05-18T00:31:59.582747+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.03682v3","created_at":"2026-05-18T00:31:59.582747+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03682","created_at":"2026-05-18T00:31:59.582747+00:00"},{"alias_kind":"pith_short_12","alias_value":"6ONU7AFBJP6O","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6ONU7AFBJP6ORT77","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6ONU7AFB","created_at":"2026-05-18T12:31:03.183658+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/6ONU7AFBJP6ORT77Q7WUBN5F2X","json":"https://pith.science/pith/6ONU7AFBJP6ORT77Q7WUBN5F2X.json","graph_json":"https://pith.science/api/pith-number/6ONU7AFBJP6ORT77Q7WUBN5F2X/graph.json","events_json":"https://pith.science/api/pith-number/6ONU7AFBJP6ORT77Q7WUBN5F2X/events.json","paper":"https://pith.science/paper/6ONU7AFB"},"agent_actions":{"view_html":"https://pith.science/pith/6ONU7AFBJP6ORT77Q7WUBN5F2X","download_json":"https://pith.science/pith/6ONU7AFBJP6ORT77Q7WUBN5F2X.json","view_paper":"https://pith.science/paper/6ONU7AFB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.03682&json=true","fetch_graph":"https://pith.science/api/pith-number/6ONU7AFBJP6ORT77Q7WUBN5F2X/graph.json","fetch_events":"https://pith.science/api/pith-number/6ONU7AFBJP6ORT77Q7WUBN5F2X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6ONU7AFBJP6ORT77Q7WUBN5F2X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6ONU7AFBJP6ORT77Q7WUBN5F2X/action/storage_attestation","attest_author":"https://pith.science/pith/6ONU7AFBJP6ORT77Q7WUBN5F2X/action/author_attestation","sign_citation":"https://pith.science/pith/6ONU7AFBJP6ORT77Q7WUBN5F2X/action/citation_signature","submit_replication":"https://pith.science/pith/6ONU7AFBJP6ORT77Q7WUBN5F2X/action/replication_record"}},"created_at":"2026-05-18T00:31:59.582747+00:00","updated_at":"2026-05-18T00:31:59.582747+00:00"}