 The Ramsey number R ( k , l ) is the smallest number r such that every graph with at least r vertices contains either a k @-@ vertex clique or an l @-@ vertex independent set . Ramsey numbers require enormous effort to compute ; when max ( k , l ) ≥ 3 only finitely many of them are known precisely , and an exact computation of R ( 6 @,@ 6 ) is believed to be out of reach . In 1953 , the calculation of R ( 3 @,@ 3 ) was given as a question in the Putnam Competition ; in 1955 , motivated by this problem , Gleason and his co @-@ author Robert M. Greenwood made significant progress in the computation of Ramsey numbers with their proof that R ( 3 @,@ 4 ) 
