# On a Class of Vertex Folkman Numbers

Serdica Mathematical Journal (2002)

- Volume: 28, Issue: 3, page 219-232
- ISSN: 1310-6600

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topNenov, Nedyalko. "On a Class of Vertex Folkman Numbers." Serdica Mathematical Journal 28.3 (2002): 219-232. <http://eudml.org/doc/11558>.

@article{Nenov2002,

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).},

author = {Nenov, Nedyalko},

journal = {Serdica Mathematical Journal},

keywords = {Vertex Folkman Graph; Vertex Folkman Number; vertex Folkman graph; vertex Folkman number},

language = {eng},

number = {3},

pages = {219-232},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {On a Class of Vertex Folkman Numbers},

url = {http://eudml.org/doc/11558},

volume = {28},

year = {2002},

}

TY - JOUR

AU - Nenov, Nedyalko

TI - On a Class of Vertex Folkman Numbers

JO - Serdica Mathematical Journal

PY - 2002

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 28

IS - 3

SP - 219

EP - 232

AB - 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).

LA - eng

KW - Vertex Folkman Graph; Vertex Folkman Number; vertex Folkman graph; vertex Folkman number

UR - http://eudml.org/doc/11558

ER -

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