We prove that for any c(1) >0 there exists c(2)>0 such that the following s
tatement is true: If G is a graph with n vertices and with the property tha
t neither G nor its complement contains a complete graph K-1, where l=c(1)
log n then G is c(2) log n-universal, i.e., G contains all subgraphs with c
(2) log n vertices as induced subgraphs. :(C) 1999 Academic Press.