Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 34, No 4, (2008), 783p-790p
Abstract:
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.
