{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TQCEIQTFQECV4D5MJ6TRQ3Z2XL","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":"64112cb5771a9db8b5ba280a838a7e2553bd9fde22470f187c87055daf701e97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-08T05:12:45Z","title_canon_sha256":"448a98610f6e3d4848c2da0df235dfdf848b08fb054ebea8d1e050c753a8fed9"},"schema_version":"1.0","source":{"id":"1901.02740","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.02740","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"arxiv_version","alias_value":"1901.02740v1","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02740","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"pith_short_12","alias_value":"TQCEIQTFQECV","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TQCEIQTFQECV4D5M","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TQCEIQTF","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:eb0ec65a2eda689a2220f036ddb070da7b73b46d37ecf970d662397259e46617","target":"graph","created_at":"2026-05-17T23:56:39Z","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":"Let $G$ be a nontrivial connected and edge-colored graph. An edge-cut $R$ of $G$ is called a rainbow cut if no two edges of it are colored with a same color. An edge-colored graph $G$ is called rainbow disconnected if for every two distinct vertices $u$ and $v$ of $G$, there exists a $u-v$ rainbow cut separating them. For a connected graph $G$, the rainbow disconnection number of $G$, denoted by $rd(G)$, is defined as the smallest number of colors that are needed in order to make $G$ rainbow disconnected. In this paper, we will study the Erd\\H{o}s-Gallai-type results for $rd(G)$, and completel","authors_text":"Xueliang Li, Xuqing Bai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-08T05:12:45Z","title":"Erd\\H{o}s-Gallai-type results for the rainbow disconnection number of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02740","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":"sha256:74747d0972ff6988dbece50ff260d4cc456727fdf36cbe6e63877d0711f7f4ae","target":"record","created_at":"2026-05-17T23:56:39Z","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":"64112cb5771a9db8b5ba280a838a7e2553bd9fde22470f187c87055daf701e97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-08T05:12:45Z","title_canon_sha256":"448a98610f6e3d4848c2da0df235dfdf848b08fb054ebea8d1e050c753a8fed9"},"schema_version":"1.0","source":{"id":"1901.02740","kind":"arxiv","version":1}},"canonical_sha256":"9c0444426581055e0fac4fa7186f3abacc6f9140b4dc98535499361d92a2d064","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c0444426581055e0fac4fa7186f3abacc6f9140b4dc98535499361d92a2d064","first_computed_at":"2026-05-17T23:56:39.578804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:39.578804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1RuAAsZgsfY3I/JqB+8aSQmY3612tJTC8r8uCtuKke0gXy4oYfjU9JPjaw6Ij7wqAAU8mMm45bsxItRK6YcCAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:39.579542Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.02740","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74747d0972ff6988dbece50ff260d4cc456727fdf36cbe6e63877d0711f7f4ae","sha256:eb0ec65a2eda689a2220f036ddb070da7b73b46d37ecf970d662397259e46617"],"state_sha256":"28ded45598221e157bb151411531a1a4e827d38ddeea0d40cfd0ef7fc899106b"}