Chudnovsky, MariaFox, JacobScott, AlexSeymour, PaulSpirkl, Sophie2022-08-122022-08-122019-11-01https://doi.org/10.1007/s00493-019-3957-8http://hdl.handle.net/10012/18518This is a post-peer-review, pre-copyedit version of an article published in Combinatorica. The final authenticated version is available online at: https://doi.org/10.1007/s00493-019-3957-8The Erdős-Hajnal conjecture says that for every graph H there exists c > 0 such that max(α(G), w(G)) ≥ nc 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), w(G)) for C5-free graphs was the general bound of Erdős and Hajnal, that for all H, max(α(G), w(G)) ≥ 2 Ω(p log n) if G is H-free. We improve this when H = C5 to max(α(G), w(G)) ≥ 2 Ω(p log n log log n).enErdős-Hajnal conjectureArticle