New upper bounds for vertex Folkman numbers Fu(3, k; k + 1) - Shao, Zehui,; Pan, Linqiang,; Xu, Xiaodong, (Utilitas Mathematica, 2009)
For a graph G, the symbol G → (a1,a2,⋯, ar)u means that in every r-coloring of V(G), there exists a monochromatic ai-clique of color i for some i ∈ {1,2, ⋯,r}. The vertex Folkman number is defined as Fu(a 1,a2,⋯,ar;k) = min{|V(G)| : G → (a1,a2,⋯ ,ar)u &K k⊈ G}. In this note, with the help of computer search, 4 vertex Folkman graphs are found and new upper bounds for vertex Folkman numbers F u(3, k; k + 1) are given.