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Displaying similar documents to “Computation of the vertex Folkman numbers F ( 2 , 2 , 2 , 4 ; 6 ) and F ( 2 , 3 , 4 ; 6 ) .”

On a Class of Vertex Folkman Numbers

Nenov, Nedyalko (2002)

Serdica Mathematical Journal

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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...