{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:BV6J2IQNQ3ECFH5THG2IC3INIT","short_pith_number":"pith:BV6J2IQN","schema_version":"1.0","canonical_sha256":"0d7c9d220d86c8229fb339b4816d0d44eff92cfde8d66425a4a6208c037fec43","source":{"kind":"arxiv","id":"1310.2355","version":1},"attestation_state":"computed","paper":{"title":"Some upper bounds for 3-rainbow index of graphs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tingting Liu, Yumei Hu","submitted_at":"2013-10-09T05:32:54Z","abstract_excerpt":"A tree $T$, in an edge-colored graph $G$, is called {\\em a rainbow tree} if no two edges of $T$ are assigned the same color. A {\\em $k$-rainbow coloring}of $G$ is an edge coloring of $G$ having the property that for every set $S$ of $k$ vertices of $G$, there exists a rainbow tree $T$ in $G$ such that $S\\subseteq V(T)$. The minimum number of colors needed in a $k$-rainbow coloring of $G$ is the {\\em $k$-rainbow index of $G$}, denoted by $rx_k(G)$. In this paper, we consider 3-rainbow index $rx_3(G)$ of $G$. We first show that for connected graph $G$ with minimum degree $\\delta(G)\\geq 3$, the t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.2355","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-10-09T05:32:54Z","cross_cats_sorted":[],"title_canon_sha256":"3bc0abdbe983e28be5306754d0b25f7e5ba055614f1a6ce8e9f697ff2e5daf80","abstract_canon_sha256":"67dc85526e9a81e749811729568950c1c680eb8d5a989603a4ff1cd354b08822"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:57.151650Z","signature_b64":"9IT08CVF945EofSkc0pW67T0CO964Eeqg4792jBSVx3qYUHtUnvCoPsJsfhNZ+UapQDC0kQ5fHynju3Pud5XAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d7c9d220d86c8229fb339b4816d0d44eff92cfde8d66425a4a6208c037fec43","last_reissued_at":"2026-05-18T03:10:57.150900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:57.150900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some upper bounds for 3-rainbow index of graphs","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Tingting Liu, Yumei Hu","submitted_at":"2013-10-09T05:32:54Z","abstract_excerpt":"A tree $T$, in an edge-colored graph $G$, is called {\\em a rainbow tree} if no two edges of $T$ are assigned the same color. A {\\em $k$-rainbow coloring}of $G$ is an edge coloring of $G$ having the property that for every set $S$ of $k$ vertices of $G$, there exists a rainbow tree $T$ in $G$ such that $S\\subseteq V(T)$. The minimum number of colors needed in a $k$-rainbow coloring of $G$ is the {\\em $k$-rainbow index of $G$}, denoted by $rx_k(G)$. In this paper, we consider 3-rainbow index $rx_3(G)$ of $G$. We first show that for connected graph $G$ with minimum degree $\\delta(G)\\geq 3$, the t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2355","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.2355","created_at":"2026-05-18T03:10:57.151025+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.2355v1","created_at":"2026-05-18T03:10:57.151025+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2355","created_at":"2026-05-18T03:10:57.151025+00:00"},{"alias_kind":"pith_short_12","alias_value":"BV6J2IQNQ3EC","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"BV6J2IQNQ3ECFH5T","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"BV6J2IQN","created_at":"2026-05-18T12:27:40.988391+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BV6J2IQNQ3ECFH5THG2IC3INIT","json":"https://pith.science/pith/BV6J2IQNQ3ECFH5THG2IC3INIT.json","graph_json":"https://pith.science/api/pith-number/BV6J2IQNQ3ECFH5THG2IC3INIT/graph.json","events_json":"https://pith.science/api/pith-number/BV6J2IQNQ3ECFH5THG2IC3INIT/events.json","paper":"https://pith.science/paper/BV6J2IQN"},"agent_actions":{"view_html":"https://pith.science/pith/BV6J2IQNQ3ECFH5THG2IC3INIT","download_json":"https://pith.science/pith/BV6J2IQNQ3ECFH5THG2IC3INIT.json","view_paper":"https://pith.science/paper/BV6J2IQN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.2355&json=true","fetch_graph":"https://pith.science/api/pith-number/BV6J2IQNQ3ECFH5THG2IC3INIT/graph.json","fetch_events":"https://pith.science/api/pith-number/BV6J2IQNQ3ECFH5THG2IC3INIT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BV6J2IQNQ3ECFH5THG2IC3INIT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BV6J2IQNQ3ECFH5THG2IC3INIT/action/storage_attestation","attest_author":"https://pith.science/pith/BV6J2IQNQ3ECFH5THG2IC3INIT/action/author_attestation","sign_citation":"https://pith.science/pith/BV6J2IQNQ3ECFH5THG2IC3INIT/action/citation_signature","submit_replication":"https://pith.science/pith/BV6J2IQNQ3ECFH5THG2IC3INIT/action/replication_record"}},"created_at":"2026-05-18T03:10:57.151025+00:00","updated_at":"2026-05-18T03:10:57.151025+00:00"}