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Given an integer $k\\ge1$ and graphs $H_1, \\ldots, H_k$, the Gallai-Ramsey number $GR(H_1, \\ldots, H_k)$ is the least integer $n$ such that every Gallai $k$-coloring of the complete graph $K_n$ contains a monochromatic copy of $H_i$ in color $i$ for some $i \\in \\{1, \\ldots, k\\}$. When $H = H_1 = \\cdots = H_k$, we simply write $GR_k(H)$. We continue to study Gallai-Ramsey numbers of even cycles and paths. For all $n\\ge3$ and $k\\ge1$, let"},"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":"1808.10282","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-29T02:17:14Z","cross_cats_sorted":[],"title_canon_sha256":"7a96f9d5de46c663e2acf1f02759ff929d322e5480da8a6fa6931becec6243ac","abstract_canon_sha256":"7fe8b4bd7cbdbc9d1dff70078911afc4a072b8bdf4d376fd58abd04928451a96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:49.261625Z","signature_b64":"Dk7yte0sUefl9ahDSCkrpAuyVG8vyVFfGQq7WPuwGD/6RNNE6OxDXELwqd6G3PphENrgSXnNdl0Iut7Lb5f5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a6239ee60ef6bb841b335be6be99160678403cc156d44876eb52dbccb043e1f","last_reissued_at":"2026-05-18T00:06:49.261157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:49.261157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gallai-Ramsey numbers of $C_{10}$ and $C_{12}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hui Lei, Jingmei Zhang, Yongtang Shi, Zi-Xia Song","submitted_at":"2018-08-29T02:17:14Z","abstract_excerpt":"A Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles, and a Gallai $k$-coloring is a Gallai coloring that uses $k$ colors. Given an integer $k\\ge1$ and graphs $H_1, \\ldots, H_k$, the Gallai-Ramsey number $GR(H_1, \\ldots, H_k)$ is the least integer $n$ such that every Gallai $k$-coloring of the complete graph $K_n$ contains a monochromatic copy of $H_i$ in color $i$ for some $i \\in \\{1, \\ldots, k\\}$. When $H = H_1 = \\cdots = H_k$, we simply write $GR_k(H)$. We continue to study Gallai-Ramsey numbers of even cycles and paths. 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