# New Upper Bound for the Edge Folkman Number Fe(3,5;13)

Serdica Mathematical Journal (2008)

- Volume: 34, Issue: 4, page 783-790
- ISSN: 1310-6600

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topKolev, Nikolay. "New Upper Bound for the Edge Folkman Number Fe(3,5;13)." Serdica Mathematical Journal 34.4 (2008): 783-790. <http://eudml.org/doc/281359>.

@article{Kolev2008,

abstract = {2000 Mathematics Subject Classification: 05C55.For a given graph G let V(G) and E(G) denote the vertex and the edge set of G respevtively.
The symbol G e → (a1, …, ar)
means that in every r-coloring of E(G) there exists a monochromatic ai-clique of color i
for some i ∈ \{1,…,r\}. The edge Folkman numbers are defined by the equality
Fe(a1, …, ar; q) = min\{|V(G)| : G e → (a1, …, ar; q) and cl(G) < q\}.
In this paper we prove a new upper bound on the edge Folkman number Fe(3,5;13), namely
Fe(3,5;13) ≤ 21. This improves the bound Fe(3,5;13) ≤ 24, proved by Kolev and Nenov.Supported by the Scientific Research Fund of the St. Kl. Ohridski Sofia University under contract 90-2008.},

author = {Kolev, Nikolay},

journal = {Serdica Mathematical Journal},

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

language = {eng},

number = {4},

pages = {783-790},

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

title = {New Upper Bound for the Edge Folkman Number Fe(3,5;13)},

url = {http://eudml.org/doc/281359},

volume = {34},

year = {2008},

}

TY - JOUR

AU - Kolev, Nikolay

TI - New Upper Bound for the Edge Folkman Number Fe(3,5;13)

JO - Serdica Mathematical Journal

PY - 2008

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 34

IS - 4

SP - 783

EP - 790

AB - 2000 Mathematics Subject Classification: 05C55.For a given graph G let V(G) and E(G) denote the vertex and the edge set of G respevtively.
The symbol G e → (a1, …, ar)
means that in every r-coloring of E(G) there exists a monochromatic ai-clique of color i
for some i ∈ {1,…,r}. The edge Folkman numbers are defined by the equality
Fe(a1, …, ar; q) = min{|V(G)| : G e → (a1, …, ar; q) and cl(G) < q}.
In this paper we prove a new upper bound on the edge Folkman number Fe(3,5;13), namely
Fe(3,5;13) ≤ 21. This improves the bound Fe(3,5;13) ≤ 24, proved by Kolev and Nenov.Supported by the Scientific Research Fund of the St. Kl. Ohridski Sofia University under contract 90-2008.

LA - eng

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

UR - http://eudml.org/doc/281359

ER -

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