Let $T$ and $T'$ be two spanning trees of a connected graph $G$. Suppose that an edge $e$ is in $T$ but not in $T'$. Show that there is an edge $e'$ in $T'$, but not in $T$, such that $T-\{e\}\cup\{e'\}$ and $T'-\{e'\}\cup\{e\}$ are spanning trees of $G$.
existence of a spanning tree
1
$\begingroup$
graph-theory
trees
-
1Welcome to math.SE, Rik! Since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", "Show" etc.) to be rude when asking for help; please consider editing your post. – 2012-11-10