Let T be any tree of order d ≥ 1. We prove that every connected graph G with minimum degree d contains a subtree T ′ isomorphic to T such that G − V (T ) is connected.

We prove that in every simple graph G with minimum degree d ≥ 2, there are edges {uv, vw} such that G contains b3d/2c edge-disjoint {u, v, w}-paths. If d is even, the paths can be chosen such that… (More)