{"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 $i$. 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 $20 \\leq F_v(2, 2, 2, 3; 4) \\leq 22$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06418","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}