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arXiv · 0706.4099

On graphs with subgraphs of large independence numbers

Noga Alon·Benny Sudakov
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Abstract

Let G be a graph on n vertices in which every induced subgraph on s=\log^3 n vertices has an independent set of size at least t=\log n. What is the largest q=q(n) so that every such G must contain an independent set of size at least q ? This is one of several related questions raised by Erdos and Hajnal. We show that q(n)=Θ(\log^2 n/\log \log n), investigate the more general problem obtained by changing the parameters s and t, and discuss the connection to a related Ramsey-type problem.

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Noga Alon, Benny Sudakov. 2007-06-27. On graphs with subgraphs of large independence numbers. https://arxiv.org/abs/0706.4099

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