{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZEOKRGZXIING3DZLLSIQPXLXTP","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":"9516a88b81c420680df867fbdbc48e6e654d479b8dc4a06356467abb0faefe83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-22T12:46:36Z","title_canon_sha256":"d7ad5b288c3ab59170f3894dc6a7cd0c1561798ab23022958c5298fdc2ab1e0d"},"schema_version":"1.0","source":{"id":"1706.07292","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07292","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07292v1","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07292","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZEOKRGZXIING","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZEOKRGZXIING3DZL","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZEOKRGZX","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:68ee8e93d81f30d163ed3503859882f958cb52b670f5b15fdcbc23214f03d8b2","target":"graph","created_at":"2026-05-18T00:41:52Z","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":"A celebrated theorem of Stiebitz asserts that any graph with minimum degree at least $s+t+1$ can be partitioned into two parts which induce two subgraphs with minimum degree at least $s$ and $t$, respectively. This resolved a conjecture of Thomassen. In this paper, we prove that for $s,t\\geq 2$, if a graph $G$ contains no cycle of length four and has minimum degree at least $s+t-1$, then $G$ can be partitioned into two parts which induce two subgraphs with minimum degree at least $s$ and $t$, respectively. This improves the result of Diwan, who proved the same statement for graphs of girth at ","authors_text":"Jie Ma, Tianchi Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-22T12:46:36Z","title":"Decomposing $C_4$-free graphs under degree constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07292","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:dffedd51a5d3e5668b24fa094adcbe02d2e0340cc6a6f103048a27675e1d3d76","target":"record","created_at":"2026-05-18T00:41:52Z","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":"9516a88b81c420680df867fbdbc48e6e654d479b8dc4a06356467abb0faefe83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-22T12:46:36Z","title_canon_sha256":"d7ad5b288c3ab59170f3894dc6a7cd0c1561798ab23022958c5298fdc2ab1e0d"},"schema_version":"1.0","source":{"id":"1706.07292","kind":"arxiv","version":1}},"canonical_sha256":"c91ca89b37421a6d8f2b5c9107dd779bc7f3fe59f7a92c72decb902ac2cb7319","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c91ca89b37421a6d8f2b5c9107dd779bc7f3fe59f7a92c72decb902ac2cb7319","first_computed_at":"2026-05-18T00:41:52.041710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:52.041710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tpiA+l8heJMmKQG60Lrwoiw5rr2xCKF06tkoPWp0gh10amVfNAlg2R7pCei8dPiK3sE1IDlDT0TxYmnAncSjCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:52.042353Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07292","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dffedd51a5d3e5668b24fa094adcbe02d2e0340cc6a6f103048a27675e1d3d76","sha256:68ee8e93d81f30d163ed3503859882f958cb52b670f5b15fdcbc23214f03d8b2"],"state_sha256":"915600e0ada731b88dfb85163083199bff41e8609ae582a933c1ba7b2033a16a"}