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Hasunuma [J. Graph Theory 102 (2023) 423-435] conjectured that for any tree$T$ of order $m$, every $k$-connected (or $k$-edge-connected) graph $G$ withminimum degree at least $k+m-1$ contains a tree $T'\cong T$ such that $G-E(T')$is still $k$-connected (or $k$-edge connected). Hasunuma verified thisconjecture for $k\leq 2$. In this paper, we confirm this conjecture for $k=3$.

Connectivity keeping edges of trees in 3-connected or 3-edge-connected graphs