{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GWFVX3H25NQ4WFN6WNDWDYYMBI","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":"dd5fe5b2989c19d769b8988355236eb545604fc015a98ff400de21bdc17a7e4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-23T09:19:21Z","title_canon_sha256":"8a990ad1ade69126a2ec98b61c762a15fd4aa2048586d486224a7feab995ed0b"},"schema_version":"1.0","source":{"id":"1810.09736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09736","created_at":"2026-05-18T00:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09736v1","created_at":"2026-05-18T00:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09736","created_at":"2026-05-18T00:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"GWFVX3H25NQ4","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GWFVX3H25NQ4WFN6","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GWFVX3H2","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:9a281eb5534076eddc027600afaac95a8e960ad7f82cbdd0ff916f8874bdfcdf","target":"graph","created_at":"2026-05-18T00:02:29Z","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 edge-colored connected graph. An edge-cut $R$ of $G$ is called a rainbow cut if no two edges of it are colored the same. An edge-colored graph $G$ is rainbow disconnected if for every two vertices $u$ and $v$, there exists a $u-v$ rainbow cut. 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 first solve a conjecture that determines the maximum size of a connected graph $G$ of order $n$ with $rd(G) = k$ for given ","authors_text":"Renying Chang, Xueliang Li, Xuqing Bai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-23T09:19:21Z","title":"More on rainbow disconnection in graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09736","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:b4e1c9f64680b0ed9d7aeac7b62d8d6b71b0a93ce4c86b6552885aae687c93b6","target":"record","created_at":"2026-05-18T00:02:29Z","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":"dd5fe5b2989c19d769b8988355236eb545604fc015a98ff400de21bdc17a7e4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-23T09:19:21Z","title_canon_sha256":"8a990ad1ade69126a2ec98b61c762a15fd4aa2048586d486224a7feab995ed0b"},"schema_version":"1.0","source":{"id":"1810.09736","kind":"arxiv","version":1}},"canonical_sha256":"358b5becfaeb61cb15beb34761e30c0a1f12af16873a799ec36c0c63b9a30a94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"358b5becfaeb61cb15beb34761e30c0a1f12af16873a799ec36c0c63b9a30a94","first_computed_at":"2026-05-18T00:02:29.572018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:29.572018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fEZZOO7XdJdzZ1jR1MagMAYMRGqwH0R9zuNYEFDhXloVB55DO+JtYU+eiozmrPuAFq1xwWtVXzO5yEzhTXtOAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:29.572751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.09736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4e1c9f64680b0ed9d7aeac7b62d8d6b71b0a93ce4c86b6552885aae687c93b6","sha256:9a281eb5534076eddc027600afaac95a8e960ad7f82cbdd0ff916f8874bdfcdf"],"state_sha256":"a9c9b835897904c8242fb62a8ef5b1cc602435f85d5427a39d78c2bcf932ac8b"}