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The vertex Folkman number $F_v(a_1, ..., a_s; q)$ is defined as $$F_v(a_1, ..., a_s; q) = \\min\\{\\vert V(G) \\vert : G \\overset{v}{\\rightarrow} (a_1, ..., a_s) \\mbox{ and } K_q \\not\\subseteq G\\}.$$ In this paper we improve the known bounds on the number $F_v(2, 2, 2, 3; 4)$ by proving with the help of a computer that $20 \\leq F_v(2, 2, 2, 3; 4) \\leq 22$."},"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":"1611.06418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-19T19:38:52Z","cross_cats_sorted":[],"title_canon_sha256":"f7504849fd9d834ac07e517c7eea839cd9473a898c58161a1b1c591b4480654c","abstract_canon_sha256":"39d5bf6b1de68aef542cf14c97c45a9808dbb028f8574f3c1c6edac4a63faca7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:07.609607Z","signature_b64":"4uzdYZjqaOZ3nacJt2Ug4iIo+/8liFQWaJXkcH+7wvCTMEoagRHTTZEoKbkXvVdBQoS+AAvx63f0s+XX6xw1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"440e0254fe166acbcec1b2a4cb6f0526d7218c4fc07decf091e70def915a3b54","last_reissued_at":"2026-05-17T23:50:07.609015Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:07.609015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New bounds on the vertex Folkman number $F_v(2, 2, 2, 3; 4)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aleksandar Bikov","submitted_at":"2016-11-19T19:38:52Z","abstract_excerpt":"For a graph $G$ the expression $G \\overset{v}{\\rightarrow} (a_1, ..., a_s)$ means that for every coloring of the vertices of $G$ in $s$ colors there exists $i \\in \\{1, ..., s\\}$ such that there is a monochromatic $a_i$-clique of color $i$. 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