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Let $\\rt(G)$ denote the number of rainbow triangles in $G$, and define \\[ f(n) = \\min\\{ \\rt(G) : |V(G)| = n,\\ \\deltac(G) \\ge (n+1)/2 \\}. \\] In \\cite{LiNingShiZhang2024}, the following open problem was posed: determine all the values of $f(n)$. In this paper, we determine $f(n)$ completely: $f(n) = (n^2-1)/8$ for odd $n\\geq 3$, $f"},"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":"2606.22106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-20T15:40:42Z","cross_cats_sorted":[],"title_canon_sha256":"1fe61284d573152690d78d609fd80cd9f0227f3284f97713a1ee6ba1c43e0094","abstract_canon_sha256":"39ae401dd8dd8a17077da650065f4ee4aaf49e211760c6cae3da42a175b46107"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:28.373063Z","signature_b64":"+JDGmZSNYmjg8Imf5/hTTJFD/j0juHO774JFcXRTJ64v5J6sGLiA9owdj2ugyYbJTjJENuN/C0rlKyf3icJgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9566581b7b0447ebb63cdfa1cc6f039cbba3f8093ae7198909490ff170800365","last_reissued_at":"2026-06-23T02:13:28.372698Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:28.372698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rainbow triangles in edge-colored graphs with large minimum color degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Ning, Yuting Tian","submitted_at":"2026-06-20T15:40:42Z","abstract_excerpt":"Let $G$ be an edge-colored graph on $n$ vertices, and let $\\deltac(G)$ denote its minimum color degree. 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