ON A CLASS OF VERTEX FOLKMAN GRAPHS

TitleON A CLASS OF VERTEX FOLKMAN GRAPHS
Publication TypeJournal Article
Year of Publication2002
AuthorsNenov N
JournalAnnuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique
Volume94
Pagination15-25
ISSN0205-0808
Keywordsvertex Folkman graphs, vertex Folkman numbers
Abstract

Let $a_1,...,a_r$ be positive integers and $m=\sum\limits_{i=1}^{r}(a_i-1)+1$. For a graph $G$ the symbol $G\rightarrow(a_1,...,a_r)$ means that in every $r$-colouring of the vertices of $G$ there exists a monochromatic $a_i$-clique of colour $i$, for some $i, 1 \leq i \leq r$. In this paper we consider the graphs $G\rightarrow(a_1,...,a_r)$ (vertex Folkman graphs) with $\textrm{cl}(G) < m - 1$.

2000 MSC

05C55

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