Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/500

 Title: On a Class of Vertex Folkman Numbers Authors: Nenov, Nedyalko Keywords: Vertex Folkman GraphVertex Folkman Number Issue Date: 2002 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 28, No 3, (2002), 219p-232p Abstract: 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). URI: http://hdl.handle.net/10525/500 ISSN: 1310-6600 Appears in Collections: Volume 28 Number 3

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