Affiliation:
1. Princeton University Princeton New Jersey USA
2. Mathematical Institute University of Oxford Oxford UK
3. University of Waterloo Waterloo Ontario Canada
Abstract
AbstractThe Erdős–Hajnal conjecture says that for every graph there exists such that every graph not containing as an induced subgraph has a clique or stable set of cardinality at least . We prove that this is true when is a cycle of length five. We also prove several further results: for instance, that if is a cycle and is the complement of a forest, there exists such that every graph containing neither of as an induced subgraph has a clique or stable set of cardinality at least .
Funder
Engineering and Physical Sciences Research Council
Air Force Office of Scientific Research
Natural Sciences and Engineering Research Council of Canada
National Science Foundation
Cited by
6 articles.
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