{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5WWEW4QLGZB7NDNEBJ766UHS3N","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":"38fbad2864c005b61520b69e6512e20283de67e3defcdcd9ae210430714f0cc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-09T06:34:25Z","title_canon_sha256":"078ddab06f2d1389ec311175148dda81599bbbe7d526a3a2c1aa2cc317a031a7"},"schema_version":"1.0","source":{"id":"1404.2377","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2377","created_at":"2026-05-18T02:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2377v2","created_at":"2026-05-18T02:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2377","created_at":"2026-05-18T02:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"5WWEW4QLGZB7","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5WWEW4QLGZB7NDNE","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5WWEW4QL","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:a470016af878e575e83a14d6aadc3b83190b0259f5ad9e18a79c19e9a7535e47","target":"graph","created_at":"2026-05-18T02:54:20Z","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 tree in an edge-colored graph is said to be rainbow if no two edges on the tree share the same color. An edge-coloring of $G$ is called 3-rainbow if for any three vertices in $G$, there exists a rainbow tree connecting them. The 3-rainbow index $rx_3(G)$ of $G$ is defined as the minimum number of colors that are needed in a 3-rainbow coloring of $G$. This concept, introduced by Chartrand et al., can be viewed as a generalization of the rainbow connection. In this paper, we study the 3-rainbow index by using connected three-way dominating sets and 3-dominating sets. We shown that for every co","authors_text":"Qingqiong Cai, Xueliang Li, Yan Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-09T06:34:25Z","title":"The 3-rainbow index and connected dominating sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2377","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":"sha256:3d7be0fc0a501e64c381f2df798ebfdcf919646b986400a02bcc9cded65683fa","target":"record","created_at":"2026-05-18T02:54:20Z","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":"38fbad2864c005b61520b69e6512e20283de67e3defcdcd9ae210430714f0cc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-09T06:34:25Z","title_canon_sha256":"078ddab06f2d1389ec311175148dda81599bbbe7d526a3a2c1aa2cc317a031a7"},"schema_version":"1.0","source":{"id":"1404.2377","kind":"arxiv","version":2}},"canonical_sha256":"edac4b720b3643f68da40a7fef50f2db594d619e73e8f37509573e57f30a9853","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edac4b720b3643f68da40a7fef50f2db594d619e73e8f37509573e57f30a9853","first_computed_at":"2026-05-18T02:54:20.709409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:20.709409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NwKmpon1NsCss4VDevBDvbwjcBgxJrMWAkcO4qnjbx3sE/dLINuQocM01drZx12UCMcXSMPnsFSm0gCHdRa7Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:20.709888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2377","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d7be0fc0a501e64c381f2df798ebfdcf919646b986400a02bcc9cded65683fa","sha256:a470016af878e575e83a14d6aadc3b83190b0259f5ad9e18a79c19e9a7535e47"],"state_sha256":"2473e9bfc40be06db63fdc0770f65299c3feec5d7e6d94449d01f12a2eea209c"}