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Summary: Graphs having small number of sizes on induced k-subgraphs
Maria Axenovich
Department of Mathematics
Iowa State University
USA
axenovic@math.iastate.edu
and
J´ozsef Balogh
Department of Mathematics
University of Illinois at Urbana-Champaign
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
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