发表机构
Mathematical Institute, Academia Sinica（数学研究所，中央研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了稠密图中的Erdős–Sós猜想，即当n足够大且k不小于γn时，边数超标的n顶点图包含所有k顶点树，还解决了Erdős与Graham关于树的多色拉姆齐数的51年难题。
AI 中文摘要
Erdős–Sós猜想指出，每个有n个顶点、边数超过(k-2)n/2的图都包含每一棵有k个顶点的树。我们证明，对于任意γ，存在n₀，使得当n≥n₀且k≥γn时，该猜想成立。作为结果的推论，我们解决了Erdős与Graham提出的、历时51年的关于树的多色拉姆齐数的问题。
英文摘要
The Erd\H os--Sós conjecture states that every $n$-vertex graph with more than $(k-2)n/2$ edges contains every $k$-vertex tree. We prove that for every $γ$ there is an $n_0$ such that for all $n\ge n_0$ and $k \ge γn$ the conjecture holds. As a corollary of our result, we obtain a solution of a 51-year-old problem of Erd\H os and Graham on the multicolor Ramsey numbers of trees.
CommentsMinimal changes to the first version, mainly just added a paragraph acknowledging the recent AI proof
