迈向 dp-极小图的 Erdős-Hajnal 性质

Yayi Fu

迈向 dp-极小图的 Erdős-Hajnal 性质

组合数学 2023-11-02 v2 逻辑

作者: Yayi Fu

摘要

我们引入强 $\binom{k}{2}$ -自由图的概念,其包含 dp-极小图。我们证明在某些稀疏性假设下,给定彩虹 $\binom{k}{2}$ -自由 blockade,可找到彩虹 $\binom{k-1}{2}$ -自由 blockade。这可作为迈向 dp-极小图的 Erdős-Hajnal 性质的中间步骤。

关键词

dp-极小图 Erdős-Hajnal 性质强自由图彩虹 blockade 稀疏性

引用

@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}
}

备注

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

迈向 dp-极小图的 Erdős-Hajnal 性质

摘要

关键词

引用

备注

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