Connectivity in evolving graph with geometric properties

Mader conjectured in 2010 that for any tree T of order m, every k-connected graph G with minimum degree at least $\lfloor \frac{3k}{2}\rfloor +m-1$ contains a subtree $T^{\prime }\cong T$ such that $G-V(T^{\prime })$ is k-connected. This conjecture has been proved for $k=1$; however, it remains open ...$\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}$$$$\mathrm{}$$\mathrm{}$$$$\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}$$\mathrm{}$$⌈\frac{}{\mathrm{}}⌉\mathrm{}$${}^{}\mathrm{}$${}^{}$${}^{\mathrm{}}$

Mader conjectured in 2010 that for any tree T of order m, every k-connected graph G with minimum degree at least contains a subtree such that is k-connected. This conjecture has been proved for ; however, it remains open for general ; for , ...

Let G =(V,E) be a simple graph. A subset S of V is a dominating set of G if for any vertex v ∈ V - S, there exists some vertex u ∈ S such that uv ∈ E(G). The domination number, denoted by γ(G), is the cardinality of a minimum dominating set of G. The ...