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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