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Sizes of Induced Subgraphs of Ramsey Graphs

Published online by Cambridge University Press:  01 July 2009

Tel Aviv University, Tel Aviv 69978, Israel and IAS, Princeton, NJ, 08540, USA (e-mail:
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA (e-mail:
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA and Sobolev Institute of Mathematics, Novosibirsk, Russia (e-mail:
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA (e-mail:


An n-vertex graph G is c-Ramsey if it contains neither a complete nor an empty induced subgraph of size greater than c log n. Erdős, Faudree and Sós conjectured that every c-Ramsey graph with n vertices contains Ω(n5/2) induced subgraphs, any two of which differ either in the number of vertices or in the number of edges, i.e., the number of distinct pairs (|V(H)|, |E(H)|), as H ranges over all induced subgraphs of G, is Ω(n5/2). We prove an Ω(n2.3693) lower bound.

Copyright © Cambridge University Press 2009

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