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In this paper we determine, for large enough $n$, $AR(n,L\\cup tP_2)$ and $AR(n,L\\cup kP_3)$ for any large enough $t$ and $k$, and a graph $L$ satisfying some conditions. Consequently, we determine $AR(n,G)$, for large enough $n$, where $G$ is $P_3\\cup tP_2$ for any $t\\geq 3$, $P_4\\cup tP_2$ and $C_3\\cup tP"},"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":"1310.4331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-16T11:10:46Z","cross_cats_sorted":[],"title_canon_sha256":"af97b1d3dec01f9ce6ab9963a00512612dd69f5290fceb08510ae71fb06cb5b0","abstract_canon_sha256":"2f48a63e21a0c03bc760ebc9edad0e321cfde9d04ee1928464dec1b008be2b0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:39.176156Z","signature_b64":"LMoeA0zdMNzMtqiVC0jUJI7R/5YtdZrtym7TaybfwEX1UYVYdSyorJGjsk5/AsdEOwIHghlvTULnM47tfK76AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"293fa9c11bd25b068dd9505a0a34534da4aa4f988533ad43579b9229649535fd","last_reissued_at":"2026-05-18T00:44:39.175745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:39.175745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anti-Ramsey numbers of graphs with small connected components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shoni Gilboa, Yehuda Roditty","submitted_at":"2013-10-16T11:10:46Z","abstract_excerpt":"The anti-Ramsey number, $AR(n,G)$, for a graph $G$ and an integer $n\\geq|V(G)|$, is defined to be the minimal integer $r$ such that in any edge-colouring of $K_n$ by at least $r$ colours there is a multicoloured copy of $G$, namely, a copy of $G$ that each of its edges has a distinct colour. 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