An (s, t)-matching in a bipartite graph G = (U, V,E) is a subset of the edges F such that each component of G[F ] is a tree with at most t edges and each vertex in U has s neighbours in G[H]. We give sharp conditions for a bipartite graph to contain an (s, t)-matching. As a special case, we prove a conjecture of Bonacina, Galesi, Huynh and Wollan [1].

中文翻译：

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树匹配

二部图 G = (U, V,E) 中的 (s, t) 匹配是边 F 的子集，使得 G[F ] 的每个组件是一棵树，最多具有 t 条边和 U 中的每个顶点在 G[H] 中有 s 个邻居。我们给出了包含 (s, t) 匹配的二部图的尖锐条件。作为一个特例，我们证明了 Bonacina、Galesi、Huynh 和 Wollan [1] 的猜想。