Towards Erdős-Hajnal for Graphs with No 5-Hole
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Date
2019-11-01
Authors
Chudnovsky, Maria
Fox, Jacob
Scott, Alex
Seymour, Paul
Spirkl, Sophie
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Nature
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).
Description
This 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/s00493-019-3957-8
Keywords
Erdős-Hajnal conjecture