Towards Erdős-Hajnal for Graphs with No 5-Hole
Abstract
The 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).
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Cite this version of the work
Maria Chudnovsky, Jacob Fox, Alex Scott, Paul Seymour, Sophie Spirkl
(2019).
Towards Erdős-Hajnal for Graphs with No 5-Hole. UWSpace.
http://hdl.handle.net/10012/18518
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