Geodesic
On a Class of Vertex Folkman Numbers
Serdica Mathematical Journal, Tome 28 (2002) no. 3, pp. 219-232.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

Let a1 , . . . , ar, be positive integers, i=1 ... r, m = ∑(ai − 1) + 1 and p = max{a1 , . . . , ar }. For a graph G the symbol G → (a1 , . . . , ar ) means that in every r-coloring of the vertices of G there exists a monochromatic ai -clique of color i for some i ∈ {1, . . . , r}. In this paper we consider the vertex Folkman numbers F (a1 , . . . , ar ; m − 1) = min |V (G)| : G → (a1 , . . . , ar ) and Km−1 ⊂ G} We prove that F (a1 , . . . , ar ; m − 1) = m + 6, if p = 3 and m ≧ 6 (Theorem 3) and F (a1 , . . . , ar ; m − 1) = m + 7, if p = 4 and m ≧ 6 (Theorem 4).
Keywords: Vertex Folkman Graph, Vertex Folkman Number 
@article{SMJ2_2002_28_3_a3,
     author = {Nenov, Nedyalko},
     title = {On a {Class} of {Vertex} {Folkman} {Numbers}},
     journal = {Serdica Mathematical Journal},
     pages = {219--232},
     publisher = {mathdoc},
     volume = {28},
     number = {3},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2002_28_3_a3/}
}
TY  - JOUR
AU  - Nenov, Nedyalko
TI  - On a Class of Vertex Folkman Numbers
JO  - Serdica Mathematical Journal
PY  - 2002
SP  - 219
EP  - 232
VL  - 28
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2002_28_3_a3/
LA  - en
ID  - SMJ2_2002_28_3_a3
ER  - 
%0 Journal Article
%A Nenov, Nedyalko
%T On a Class of Vertex Folkman Numbers
%J Serdica Mathematical Journal
%D 2002
%P 219-232
%V 28
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SMJ2_2002_28_3_a3/
%G en
%F SMJ2_2002_28_3_a3
Nenov, Nedyalko. On a Class of Vertex Folkman Numbers. Serdica Mathematical Journal, Tome 28 (2002) no. 3, pp. 219-232. http://geodesic.mathdoc.fr/item/SMJ2_2002_28_3_a3/