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This is then used to determine $\\min(\\max(|V(H_1)|, |V(H_2)|))$ where (i) $H_1$ and $H_2$ are induced subgraphs of $Q_k$, and (ii) together they cover all the edges of $Q_k$, that is $E(H_1)\\cup E(H_2) = E(Q_k)$."},"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":"1112.3015","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-13T20:14:34Z","cross_cats_sorted":[],"title_canon_sha256":"18e1efb57e38e6c091fc9c73c29a1bc60a3aa28a90fa102ab78201d352dedd08","abstract_canon_sha256":"377c5a02d48ac83a48dc0436aff58f190f9ae9558ffaba312b7c9fe9f4fdd4b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:31.747509Z","signature_b64":"CqblgnS0Jl2WQ4hx/3QfLCpV5+e1nxLPFgSGmeGd8G2ic8oxrc1HSlswGi1+FTy6umVN3gjllzu92W90BGPPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e07de603fd8146677461614a0a311f45d2ebc13a2687d8cc3f58049fafdb0434","last_reissued_at":"2026-05-18T04:06:31.746759Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:31.746759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Induced subgraphs of hypercubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geir Agnarsson","submitted_at":"2011-12-13T20:14:34Z","abstract_excerpt":"Let $Q_k$ denote the $k$-dimensional hypercube on $2^k$ vertices. 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