# maximal acyclic subgraph

Prove that a maximal acylic subgraph of a graph $G$ consists of a spanning tree from each component of $G$.

My approach: to obtain a maximal acyclic subgraph of $G$ we can delete edges from cycles in the graph, while keeping components connected. In this way we obtain a tree in each component of $G$ and they are spanning because we kept the components connected.

Does this prove the statement? Thanks for any tips.