A typical decomposition question asks whether the edges of some graph G can be partitioned into disjoint copies of another graph H. One of the oldest and best known conjectures in this area, posed by Ringel in 1963, concerns the decomposition of complete graphs into edge-disjoint copies of a tree. It says that any tree with n edges packs \(2n+1\) times into the complete graph \(K_{2n+1}\). In this paper, we prove this conjecture for large n.

中文翻译：

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林格尔猜想的证明

一个典型的分解问题询问某个图G的边是否可以划分为另一个图H 的不相交副本。该领域最古老和最著名的猜想之一是由 Ringel 在 1963 年提出的，它涉及将完整图分解为树的边不相交副本。它表示任何具有n 条边的树将\(2n+1\)次打包到完整的图\(K_{2n+1}\) 中。在本文中，我们证明了大n 的这个猜想。