On the lower bound for Fv(k, k;k + 1) and Fe(3,4;5) - Xu, Xiaodong,; Shao, Zehui, (Utilitas Mathematica, 2010)
For a graph G, the symbol G → (a1,a2) v (resp. G → (a1,a2)e) means that in every 2-coloring of V(G) (resp. E(G)), there exists a monochromatic ai-clique of color i for some i ε {1,2}. The 2-color vertex (resp. edge) Folkman number is defined as Fv(a1,a 2;k) = min{|V(G)| : G → (a1,a2) v Λ Kk G}, (resp. Fe(a 1,a2;k) = min{|V(G)| : G → (a1,a 2)e A Kk G}. ) In this note, we show that Fe(3,k;k + 1) > Fv(k,k;k + 1) > 4k - 1. In addition, we obtain that Fe(3,4;5) ≥ 22.