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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),...
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