Ramsey numbers involving graphs with large degrees

Let FF be a graph of order v(F)≥3v(F)≥3 and size e(F)e(F), and let ρ(F)=(e(F)−1)/(v(F)−2)ρ(F)=(e(F)−1)/(v(F)−2). It is shown that if GnGn is a graph of order nn with average degree dn≥2dn≥2, then r(F,Gn)≥c(dnlogdn)ρ(F) for all nn, where c=c(F)>0c=c(F)>0 is a constant.