AI 中文总结
本文证明了Hasunuma关于k-连通图中可移除树的猜想的加强版本，并给出高最小度k-边连通图中存在可移除匹配的条件。
AI 中文摘要
T. Hasunuma（发表于《J. Graph Theory》，2023年）提出猜想：若G为k-连通（或k-边连通）图，其最小度δ(G)≥k+m−1，且T为阶数为m的树，则G中存在可移除的T的副本，即与T同构的子树T'，使得G−E(T')为k-连通（或k-边连通）图。本文证明了该猜想的一个加强版本，还研究了高最小度图中的可移除匹配。特别地，本文证明：若G为顶点数至少为2m的k-边连通图，其最小度δ(G)≥k+m，则G中存在大小为m的匹配M，使得G−M为k-边连通图。
英文摘要
T. Hasunuma (J. Graph Theory, 2023) conjectured that if $G$ is a $k$-connected (resp. $k$-edge-connected) graph with minimum degree $δ(G) \ge k + m - 1$, and $T$ is a tree of order $m$, then $G$ contains a removable copy of $T$, that is, a subtree $T'$ isomorphic to $T$ such that $G - E(T')$ is $k$-connected (resp. $k$-edge-connected). We prove (a strengthening of) this conjecture. We also consider removable matchings in graphs with high minimum degree. We show, among others, that if $G$ is a $k$-edge-connected graph on at least $2m$ vertices with minimum degree $δ(G) \ge k + m$, then there exists a matching $M$ of size $m$ in $G$ for which $G-M$ is $k$-edge-connected.
