Geodesic
New Upper Bound for the Edge Folkman Number Fe(3,5;13)
Serdica Mathematical Journal, Tome 34 (2008) no. 4, pp. 783-790.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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.
Keywords: Folkman Graph, Folkman Number 
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     author = {Kolev, Nikolay},
     title = {New {Upper} {Bound} for the {Edge} {Folkman} {Number} {Fe(3,5;13)}},
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Kolev, Nikolay. New Upper Bound for the Edge Folkman Number Fe(3,5;13). Serdica Mathematical Journal, Tome 34 (2008) no. 4, pp. 783-790. http://geodesic.mathdoc.fr/item/SMJ2_2008_34_4_a5/