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However, they could not show that the upper bound 5 is sharp. It is known that for a graph $G$ with diameter 2, to determine $rc(G)$ is NP-hard. So, it is interesting to know the best upper bound of $rc(G)$ for such a graph $G$. In this paper, we use different way to obtain the same upper bound, and moreover, examples are given to show"},"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":"1106.1258","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-07T05:06:47Z","cross_cats_sorted":[],"title_canon_sha256":"5f5dc4006701268549ef54ccc45e2fd7c850080bd50a5e67dd9f2c9257f728ef","abstract_canon_sha256":"112ea4225261c9594aa30e34adbd95d10e701aa6d94fec41837ecd082234b755"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:32.121434Z","signature_b64":"9Ret8h+xppfs8lU2dI7In8PHXeo3Vn8qavn7GYIO/NMg9/DOJzMFkqCfXJDWMZB6OW+grNkBceobEnNs4cnUDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e85f03df2d43b87992bbb44f7170a4fa77f8f1ae0a20995dd663fb4ccf38ffff","last_reissued_at":"2026-05-18T04:12:32.120868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:32.120868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp upper bound for the rainbow connection number of a graph with diameter 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jiuying Dong, Xueliang Li","submitted_at":"2011-06-07T05:06:47Z","abstract_excerpt":"Let $G$ be a connected graph. 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