a graph with independence number alpha is called (alpha,k)-balanced if every induced subgraph on k vertices has independence number alpha as well. we will discuss the maximum number of vertices in an (alpha,k)-balanced graph for fixed k and alpha, a problem with obvious connections to ramsey theory. we focus specifically on the case k=2alpha which is motivated from polyhedral combinatorics. (joint work with a. brieden, z. furedi and r. ramamurthi)