Title | On the 2-coloring diagonal vertex Folkman numbers with minimal possible clique number |
Publication Type | Journal Article |
Year of Publication | 2008 |
Authors | Kolev N, Nenov N |
Journal | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Volume | 98 |
Keywords | Folkman graphs, Folkman numbers |
Abstract | For a graph $G$ the symbol $G\xrightarrow{v}(p,p)$ means that in every 2-coloring of the vertices of $G$, there exists a monochromatic $p$-qlique. The vertex diagonal Folkman numbers $$ F_v(p,p;p+1)=\min\{|V(G)| : G\xrightarrow{v}(p,p) \;\mbox{and}\; K_{p+1}\not\subset G \} $$ are considered. We prove that $F_v(p,p;p+1)\leq\frac{13}{12}p!,\,\;p\geq 4$. |
2000 MSC | 05C55 |
Attachment | Size |
---|---|
98-101-126.pdf | 1.79 MB |