Abstract Mader (2010) conjectured that for any tree T of order m , every k -connected graph G with minimum degree at least ⌊ 3 k 2 ⌋ + m − 1 contains a subtree T ′ ≅ T such that G − V ( T ′ ) is k -connected. A caterpillar is a tree in which a single path is incident to every edge. The conjecture has been proved when k = 1 and for some special caterpillars when k = 2 . A spider is a tree with at most one vertex with degree more than 2. In this paper, we confirm the conjecture for all caterpillars and spiders when k = 2 .

中文翻译：

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将毛毛虫和蜘蛛保持在 ​​2 个连通图中的连通性

摘要 Mader (2010) 推测对于任何 m 阶树 T，每个 k 连通图 G 的最小度至少为 ⌊ 3 k 2 ⌋ + m − 1 包含一个子树 T ′ ≅ T 使得 G − V ( T ′ ) 是 k 连通的。毛毛虫是一棵树，它的每条边都有一条路径。当 k = 1 时，该猜想已被证明，当 k = 2 时，对于一些特殊的毛毛虫。蜘蛛是最多有一个顶点的度数大于 2 的树。在本文中，我们验证了当 k = 2 时所有毛毛虫和蜘蛛的猜想。