On fractional Ramsey numbers

Abstract The classical Ramsey number r ( k , l ) is the smallest n such that for any red/blue coloring of the edges of K n either the red subgraph has clique number at least k , or the blue subgraph has clique number at least l . In this paper, we consider a similar parameter — the fractional Ramsey number — in which ‘clique number’ is replaced by ‘fractional clique number’. An exact formula for r f ( x , y ) is given and some extensions are considered as well.