# Why are spanning trees called spanning trees?

• A "spanning subgraph" of a graph $G$ is a subgraph $H$ of $G$ which has the save vertex set, $V(H)=V(G).$ (I don't know why it's called a "spanning" subgraph.) In particular, a "spanning tree" is a spanning subgraph which is a tree, a "spanning path" is a spanning subgraph which is a path. – bof Aug 29 '17 at 8:47