Let $V$ be a set of all subsets of $\{1,2,3,4,5,6,7\} $ with exactly $4$ elements.
Define graph $G=(V,E)$ as follows:
If $v,w\in V$ then $\{v,w\}\in E$ $\iff$ $|v\cap w|=2$Can one partition the set of edges of $G$ into subsets, such that each is a set of edges of a spanning tree of $G$?
I'm trying to understand how to look at this graphs definition, since it looks like an element of $E$ is of the form $\{\{1,2,3,4\},\{3,4,5,6\}\}$.