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Baskoro, Broersma and Surahmat (2005) conjectured that \\[ R(F_\\ell,K_n)=2\\ell(n-1)+1 \\] for $\\ell\\ge n\\ge3$, where $F_\\ell$ is the join of $K_1$ and $\\ell K_2$. In this paper, we prove that this conjecture is true for the case $n=6$."},"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":"1701.06050","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-21T17:01:20Z","cross_cats_sorted":[],"title_canon_sha256":"797bb0d94c5d1318954d5a26872f9e5444cef1770185eb8d6ce99fc5d6286338","abstract_canon_sha256":"23ee39b84780998fa837c30d277ea52422f5bf79e1d03325b5ea1e87ed3898e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:19.494162Z","signature_b64":"DjQsvUuJ1Wi+IePPTvl0OO8yt2tLK6W/axGOrP6o3lRXVuXZdIkzM4H4SXBpLMuRBSGddZP5aLgM3sfVacC8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"476f99ecda1e68625256741cb5a7376213178862b13df5321c0a44a8b2638d5a","last_reissued_at":"2026-05-18T00:52:19.493597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:19.493597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Graph Ramsey Number $R(F_\\ell,K_6)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shin-ya Kadota, Tomokazu Onozuka, Yuta Suzuki","submitted_at":"2017-01-21T17:01:20Z","abstract_excerpt":"For a given pair of two graphs $(F,H)$, let $R(F,H)$ be the smallest positive integer $r$ such that for any graph $G$ of order $r$, either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. Baskoro, Broersma and Surahmat (2005) conjectured that \\[ R(F_\\ell,K_n)=2\\ell(n-1)+1 \\] for $\\ell\\ge n\\ge3$, where $F_\\ell$ is the join of $K_1$ and $\\ell K_2$. 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