Towards Erdős-Hajnal for graphs with no 5-hole
- The Erdős-Hajnal conjecture says that for every graph H there exists c > 0 such that max(α(G), ω(G)) ≥ n c for every H-free graph G with n vertices, and this is still open when H = C5. Until now the best bound known on max(α(G), ω(G)) for C5-free graphs was the general bound of Erdős and Hajnal, that for all H, max(α(G), ω(G)) ≥ 2 Ω(√ log n) if G is H-free. We improve this when H = C5 to max(α(G), ω(G)) ≥ 2 Ω(√ log n log log n) .
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- Peer reviewed
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- János Bolyai Mathematical Society and Springer-Verlag
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- Copyright © 2019 János Bolyai Mathematical Society and Springer-Verlag.
- This is the accepted manuscript version of the article. The final version is available online from Springer at http://dx.doi.org/10.1007/s00493-019-3957-8
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