{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VDVN3GEW3JCTSOHM7R62PBTVEY","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":"1e6e624503cc3d756b97629e9abe5e3bf432577da4853205d70ab99e57eb1dd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-13T13:03:16Z","title_canon_sha256":"a7dda8e13040be220d9062aab9c819be0b0491cf704c1e4d0c8f89b2d3d6d586"},"schema_version":"1.0","source":{"id":"1109.2769","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2769","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2769v2","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2769","created_at":"2026-05-18T04:11:07Z"},{"alias_kind":"pith_short_12","alias_value":"VDVN3GEW3JCT","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"VDVN3GEW3JCTSOHM","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"VDVN3GEW","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:930a42d950caa1c6c286cb85fcfd3aae99caedbff4d0661c2c4078e2058c7224","target":"graph","created_at":"2026-05-18T04:11:07Z","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 path in an edge-colored graph $G$, where adjacent edges may have the same color, is called rainbow if no two edges of the path are colored the same. The rainbow connection number $rc(G)$ of $G$ is the smallest integer $k$ for which there exists a $k$-edge-coloring of $G$ such that every pair of distinct vertices of $G$ is connected by a rainbow path. It is known that for every integer $k\\geq 2$ deciding if a graph $G$ has $rc(G)\\leq k$ is NP-Hard, and a graph $G$ with $rc(G)\\leq k$ has diameter $diam(G)\\leq k$. In foregoing papers, we showed that a bridgeless graph with diameter 2 has rainbo","authors_text":"Hengzhe Li, Xueliang Li, Yuefang Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-13T13:03:16Z","title":"Upper bound for the rainbow connection number of bridgeless graphs with diameter 3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2769","kind":"arxiv","version":2},"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":"sha256:3897c609c440d753397fdfe266ee37c76db74e382639b8904305c7fffa2eccb6","target":"record","created_at":"2026-05-18T04:11:07Z","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":"1e6e624503cc3d756b97629e9abe5e3bf432577da4853205d70ab99e57eb1dd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-13T13:03:16Z","title_canon_sha256":"a7dda8e13040be220d9062aab9c819be0b0491cf704c1e4d0c8f89b2d3d6d586"},"schema_version":"1.0","source":{"id":"1109.2769","kind":"arxiv","version":2}},"canonical_sha256":"a8eadd9896da453938ecfc7da78675263940b4ef9aa25aa3ecc02d1eabfbb22b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8eadd9896da453938ecfc7da78675263940b4ef9aa25aa3ecc02d1eabfbb22b","first_computed_at":"2026-05-18T04:11:07.100759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:07.100759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"If4csnMmWsxTX/Wbl/sohYp4Ivd5XEPlvdkjTWyFoHTFZXiqW31OJoXnHkMfZB2xWSmLATXCL/5pX0rOU2gGBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:07.101309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2769","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3897c609c440d753397fdfe266ee37c76db74e382639b8904305c7fffa2eccb6","sha256:930a42d950caa1c6c286cb85fcfd3aae99caedbff4d0661c2c4078e2058c7224"],"state_sha256":"967bdf5878b11fc435ef00c4b1bd8da5351c74f1059d2159724034d0a3792fb3"}