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Carraher, Hartke, and Horn showed that for $n$ and $C$ large enough, if $G$ is an edge-colored copy of $K_n$ in which each color class has size at most $n/2$, then $G$ has at least $\\lfloor n/(C\\log n)\\rfloor$ edge-disjoint rainbow spanning trees. Here we strengthen this result by showing that if $G$ is any edge-colored graph with $n$ vertices in which each color appears on at most $\\delta\\cdot\\lambda_1/2$ edges, where $\\delta\\geq C\\log n$ for $n$ and $C$ sufficiently large and $\\lambda"},"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":"1704.00048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-31T20:26:17Z","cross_cats_sorted":[],"title_canon_sha256":"81664cdacf5f5e8cddde327a3eeafaf4fb2160361d993e479da007569e02448d","abstract_canon_sha256":"3c3269c09e46ec489afbcc474db1199c063f216fae2bd51d581cd86a7fc0d6f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:25.578756Z","signature_b64":"kenhhLPipF7c81d68q9trwhRy5kScDJBXOWdforcaRtyOBY2kweKSS8n9R5kMokcVbAdPrfoY6fTwM5eTLFYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"973bef9abddf39857731edd5ea14d7e585839f9c6eca514edd897e4360efc81e","last_reissued_at":"2026-05-18T00:47:25.578066Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:25.578066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Many edge-disjoint rainbow spanning trees in general graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lauren M. Nelsen, Paul Horn","submitted_at":"2017-03-31T20:26:17Z","abstract_excerpt":"A rainbow spanning tree in an edge-colored graph is a spanning tree in which each edge is a different color. Carraher, Hartke, and Horn showed that for $n$ and $C$ large enough, if $G$ is an edge-colored copy of $K_n$ in which each color class has size at most $n/2$, then $G$ has at least $\\lfloor n/(C\\log n)\\rfloor$ edge-disjoint rainbow spanning trees. Here we strengthen this result by showing that if $G$ is any edge-colored graph with $n$ vertices in which each color appears on at most $\\delta\\cdot\\lambda_1/2$ edges, where $\\delta\\geq C\\log n$ for $n$ and $C$ sufficiently large and $\\lambda"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00048","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":"1704.00048","created_at":"2026-05-18T00:47:25.578173+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.00048v1","created_at":"2026-05-18T00:47:25.578173+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00048","created_at":"2026-05-18T00:47:25.578173+00:00"},{"alias_kind":"pith_short_12","alias_value":"S4567GV5344Y","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"S4567GV5344YK5ZR","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"S4567GV5","created_at":"2026-05-18T12:31:43.269735+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/S4567GV5344YK5ZR5XK6UFGX4W","json":"https://pith.science/pith/S4567GV5344YK5ZR5XK6UFGX4W.json","graph_json":"https://pith.science/api/pith-number/S4567GV5344YK5ZR5XK6UFGX4W/graph.json","events_json":"https://pith.science/api/pith-number/S4567GV5344YK5ZR5XK6UFGX4W/events.json","paper":"https://pith.science/paper/S4567GV5"},"agent_actions":{"view_html":"https://pith.science/pith/S4567GV5344YK5ZR5XK6UFGX4W","download_json":"https://pith.science/pith/S4567GV5344YK5ZR5XK6UFGX4W.json","view_paper":"https://pith.science/paper/S4567GV5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.00048&json=true","fetch_graph":"https://pith.science/api/pith-number/S4567GV5344YK5ZR5XK6UFGX4W/graph.json","fetch_events":"https://pith.science/api/pith-number/S4567GV5344YK5ZR5XK6UFGX4W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S4567GV5344YK5ZR5XK6UFGX4W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S4567GV5344YK5ZR5XK6UFGX4W/action/storage_attestation","attest_author":"https://pith.science/pith/S4567GV5344YK5ZR5XK6UFGX4W/action/author_attestation","sign_citation":"https://pith.science/pith/S4567GV5344YK5ZR5XK6UFGX4W/action/citation_signature","submit_replication":"https://pith.science/pith/S4567GV5344YK5ZR5XK6UFGX4W/action/replication_record"}},"created_at":"2026-05-18T00:47:25.578173+00:00","updated_at":"2026-05-18T00:47:25.578173+00:00"}