Towards Erd\H{o}s-Hajnal property for dp-minimal graphs
Combinatorics
2023-11-02 v2 Logic
Abstract
We introduce the notion of strongly -free graphs, which contain dp-minimal graphs. We show that under some sparsity assumption, given a rainbow -free blockade we can find a rainbow -free blockade. This might serve as an intermediate step towards Erd\H os-Hajnal property for dp-minimal graphs.
Cite
@article{arxiv.2310.17730,
title = {Towards Erd\H{o}s-Hajnal property for dp-minimal graphs},
author = {Yayi Fu},
journal= {arXiv preprint arXiv:2310.17730},
year = {2023}
}
Comments
Things after the main lemma (lemma 3.4) in version 1 were deleted since the argument after that was a misuse of Rodl's theorem. The author still needs to remove the sparsity assumption in order to get Erd\H os-Hajnal property for dp-minimal graphs. Also reference mistakes were fixed in version 2