The definitions I have are:
A cut set of a graph $G$ induced by a partition of $G$'s vertices
into sets $X$ and $Y$ is the set of all edges with one endpoint in $X$
and another endpoint in $Y$.An edge cut of a connected graph $G$ is a set $S$ of $G$'s edges
such that $G$-$S$ is disconected and $G$-$S$' is connected for any
proper subset $S$' of $S$.
They do not appear to mean the same thing, yet my course materials refer to both as "cuts" of G. So please help me understand: do the "edge cut" and "cut set" of a graph refer to the same set?
Best Answer
A cut set is not necessarily an edge cut. Think about it: If $X$ in the definition of cut set is not itself connected, then you need to restore more than one edge to reconnect $G$.
Also, cut sets appear to be defined even for a graph that is not connected to begin with.