Mader's conjecture for graphs with small connectivity

Mader conjectured that for any tree T $T$ of order m $m$ , every k $k$ -connected graph G $G$ with minimum degree at least ⌊ 3 2 ⌋ + − 1 $\lfloor \frac{3k}{2}\rfloor +m-1$ contains a subtree ′ ≅ $T^{\prime} \cong T$ such V ( ) $G-V(T^{\prime} )$ is -connected. In this article, we give characterization subgraph to contain an embedding specified avoiding some vertex. As corollary, confirm Mader's conjecture ≤ $k\le 3$ .