{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:50Z","timestamp":1753893830580,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $a_1, \\ldots, a_r$ be positive integers, $m=\\sum_{i=1}^{r} (a_{i}-1)+1$ and $p= \\max \\{a_1, \\ldots, a_r\\}$.  For a graph $G$ the symbol $G\\rightarrow \\{a_1, \\ldots, a_r\\}$ denotes that in every $r$-coloring of the vertices of $G$ there exists a monochromatic $a_i$-clique of color $i$ for some $i=1, \\ldots, r$.  The vertex Folkman numbers $F(a_1,\\dots,a_r;m-1)=\\min \\{| V(G) | : G\\rightarrow (a_1 \\ldots a_r)$ and $K_{m-1} \\not \\subseteq G \\}$ are considered. We prove that $F(a_1, \\ldots, a_r; m-1) \\leq m+3p$, $p \\geq 3$. This inequality improves the bound for these numbers obtained by \u0141uczak, Ruci\u0144ski and Urba\u0144ski (2001).<\/jats:p>","DOI":"10.37236\/1040","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:03:46Z","timestamp":1578719026000},"source":"Crossref","is-referenced-by-count":5,"title":["New Upper Bound for a Class of Vertex Folkman Numbers"],"prefix":"10.37236","volume":"13","author":[{"given":"N.","family":"Kolev","sequence":"first","affiliation":[]},{"given":"N.","family":"Nenov","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,2,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:26:09Z","timestamp":1579321569000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,2,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1040","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,2,15]]},"article-number":"R14"}}