Suppose that a maximum flow network contains a node, other than the source node, without incoming arc. Can we delete this node without affecting the maximum flow value? Similarly, can we delete a node, other than the sink node, without outgoing arc?
Let F = (V; A) be a digraph. Show that if u is k-edge-connected to v and v is k-edge-connected to w, then u is k-edge-connected to w.