IMI-BAS BAS
 

BulDML at Institute of Mathematics and Informatics >
IMI >
IMI Periodicals >
Serdica Mathematical Journal >
2002 >
Volume 28 Number 3 >

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 Graph
Vertex 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

Files in This Item:

File Description SizeFormat
sjm-vol28-num3-2002-p219-p232.pdf499.9 kBAdobe PDFView/Open

 



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

 

Valid XHTML 1.0!   Creative Commons License DSpace Software Copyright © 2002-2009  The DSpace Foundation - Feedback