 
Summary: Graphs having small number of sizes on induced ksubgraphs
Maria Axenovich
Department of Mathematics
Iowa State University
USA
axenovic@math.iastate.edu
and
J´ozsef Balogh
Department of Mathematics
University of Illinois at UrbanaChampaign
USA
jobal@math.uiuc.edu
October 26, 2005
Abstract
Let G be a graph on n vertices, k, are integers such that 2 k n  2 , n is large
enough. Let
k(G) = {E(H) : H is an induced subgraph of G on k vertices}.
We show that if k(G) then G has a complete or an empty subgraph on at least n +1
vertices, and a homogeneous set of order at least n  2 + 2. These results are sharp.
1 Introduction
