# Decomposing rooted (k,l)-connected graphs into rooted k-connected parts

Let G=(V,E) be an undirected graph, and $r \in V$ a root node. G is called rooted (k,l)-connected if G-X is $(k-\vert X\vert)l$-edge-connected for any $X \subseteq V-r$. Is it true that every rooted (k,l)-connected graph contains l edge-disjoint spanning rooted k-connected subgraphs?