Geodesic
New upper bound for a class of vertex Folkman numbers
The electronic journal of combinatorics, Tome 13 (2006)
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

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 Łuczak, Ruciński and Urbański (2001).
DOI : 10.37236/1040
Classification : 05C55 
@article{10_37236_1040,
     author = {N. Kolev and N. Nenov},
     title = {New upper bound for a class of vertex {Folkman} numbers},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1040},
     zbl = {1081.05072},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1040/}
}
TY  - JOUR
AU  - N. Kolev
AU  - N. Nenov
TI  - New upper bound for a class of vertex Folkman numbers
JO  - The electronic journal of combinatorics
PY  - 2006
VL  - 13
UR  - http://geodesic.mathdoc.fr/articles/10.37236/1040/
DO  - 10.37236/1040
ID  - 10_37236_1040
ER  - 
%0 Journal Article
%A N. Kolev
%A N. Nenov
%T New upper bound for a class of vertex Folkman numbers
%J The electronic journal of combinatorics
%D 2006
%V 13
%U http://geodesic.mathdoc.fr/articles/10.37236/1040/
%R 10.37236/1040
%F 10_37236_1040
N. Kolev; N. Nenov. New upper bound for a class of vertex Folkman numbers. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1040

Cité par Sources :