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Non-Ramsey Graphs Are c log n-Universal☆

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Abstract

We prove that for any c1>0 there exists c2>0 such that the following state- ment is true: If G is a graph with n vertices and with the property that neither G nor its complement contains a complete graph Kl, where l=c1 log n then G is c2 log n-universal, i.e., G contains all subgraphs with c2 log n vertices as induced subgraphs.

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Communicated by the Managing Editors

f1

E-mail: [email protected]

f2

E-mail: [email protected]

1

The first author was partially supported by DFG Grant PR 296/4-2.

2

The second author was partially supported by NSF Grant DMS-9704114. Part of this work was done while the second author was an Alexander von Humboldt Senior Scientist visiting Humbolt-Universität zu Berlin.

Copyright © 1999 Published by Elsevier Inc. All rights reserved.