A Folkman Linear Family

For graphs $F$ and $G$, let $F\to (G,G)$ signify that any red/blue edge coloring of $F$ contains a monochromatic $G$. Define Folkman number $f(G;p)$ to be the smallest order of a graph $F$ such that $F\to (G,G)$ and $\omega(F) \le p$\mathrm{.}Itisshownthat$f(G;p)\le cn$forgraphs$G$oforder$n$with$\Delta(G)\le \Delta$,where$\Delta\ge 3$,$c=c(\Delta)$and$p=p(\Delta)$ are positive constants.