On fractional Ramsey numbers Original Research Article

The classical Ramsey number r(k, l) is the smallest n such that for any red/blue coloring of the edges of Kn 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 rf(x, y) is given and some extensions are considered as well.