Large chromatic number and Ramsey graphs
  Let Q(n,c) denote the minimum clique size an n-vertex graph can have if its chromatic number is c. Using Ramsey graphs we give an exact, albeit implicit, formula for the case c is at least (n+3)/2. 
Csaba Bir\'o, Zolt\'an F\"uredi, Sogol Jahanbekam
math.CO