{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6FFB45JQNWD475KQHXNX7UIODL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4975b421e4d3b4bcc7dff4158cbad897ae109b7e12a23ed12b5bb736079512aa","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-09T21:49:50Z","title_canon_sha256":"4fd31995f07d5a0a0172cffd2674c936b19bb4af164e6284bde48f0ebd7de7f0"},"schema_version":"1.0","source":{"id":"1803.03704","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03704","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03704v1","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03704","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"pith_short_12","alias_value":"6FFB45JQNWD4","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6FFB45JQNWD475KQ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6FFB45JQ","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:c5030881e5df84c62e6e80eba63b8e6458733711bb46f39fe63e5284f32c8e98","target":"graph","created_at":"2026-05-18T00:21:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The Barat-Thomassen conjecture, recently proved in [Bensmail et al.: A proof of the Barat-Thomassen conjecture. J. Combin. Theory Ser. B, 124:39-55, 2017.], asserts that for every tree T, there is a constant $c_T$ such that every $c_T$-edge connected graph G with number of edges (size) divisible by the size of T admits an edge partition into copies of T (a T-decomposition). In this paper, we investigate in which case the connectivity requirement can be dropped to a minimum degree condition. For instance, it was shown in [Bensmail et al.: Edge-partitioning a graph into paths: beyond the Barat-T","authors_text":"St\\'ephan Thomass\\'e, Tereza Klimo\\v{s}ov\\'a","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-09T21:49:50Z","title":"Edge-decomposing graphs into coprime forests"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03704","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2074afc712e6028a187070969aa98fb2e27e4342c5ba7223aae15c24e8e10adf","target":"record","created_at":"2026-05-18T00:21:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4975b421e4d3b4bcc7dff4158cbad897ae109b7e12a23ed12b5bb736079512aa","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-09T21:49:50Z","title_canon_sha256":"4fd31995f07d5a0a0172cffd2674c936b19bb4af164e6284bde48f0ebd7de7f0"},"schema_version":"1.0","source":{"id":"1803.03704","kind":"arxiv","version":1}},"canonical_sha256":"f14a1e75306d87cff5503ddb7fd10e1ad21617ce2431843e583e96e4c1822b30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f14a1e75306d87cff5503ddb7fd10e1ad21617ce2431843e583e96e4c1822b30","first_computed_at":"2026-05-18T00:21:38.415630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:38.415630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lo+52DdCqodO4UHAppKf5DD/c6Rm+d7xE/eXjEDmLdHBBZWoRtyVhgNU2xxovHfuzPR1OHnSeMSyetg8LFD7Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:38.416181Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03704","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2074afc712e6028a187070969aa98fb2e27e4342c5ba7223aae15c24e8e10adf","sha256:c5030881e5df84c62e6e80eba63b8e6458733711bb46f39fe63e5284f32c8e98"],"state_sha256":"dfc90706ee217bfc7ed9ce08a85f9ee1d337eda3d5188ed8f992e9b3ad26b86c"}