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The case when $G$ is the complete graph $K_n$ implies an approximate version of the tree packing conjecture of Gy\\'arf\\'as and Lehel for bounded degree trees, and of the Oberwolfa"},"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":"1604.07282","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-04-25T14:36:32Z","cross_cats_sorted":[],"title_canon_sha256":"fa6c9f56edfc68b0f4e171a944d2b817e2531b77df996d865e18861e04984ba0","abstract_canon_sha256":"8eff5cfcf0268d4b541bf70a19d7cf77e7bf8c92def1e1c93a3076a3b5d09cee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:15.918624Z","signature_b64":"sG4lmnH4tJyyAFg3jFBCGrcO8VachbMWWlA3WpFa4Kpv07YlKtK9Qsl09BJ1tCPwkopY4cXUe3zTlCKm70aXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"937152352d9f1133f289c75d615e897d35103ea29c7430791c91d3a872c65499","last_reissued_at":"2026-05-18T00:34:15.918101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:15.918101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A blow-up lemma for approximate decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniela K\\\"uhn, Deryk Osthus, Jaehoon Kim, Mykhaylo Tyomkyn","submitted_at":"2016-04-25T14:36:32Z","abstract_excerpt":"We develop a new method for constructing approximate decompositions of dense graphs into sparse graphs and apply it to longstanding decomposition problems. 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