Prove that an edge e is contained in every spanning tree for a connected graph G if, and only if, removal of e disconnects G.
There is an edge which is contained in each spanning tree of a connected graph if, and only if, removal of this edge disconnects the connected graph .
An edge is contained in every spanning tree for a connected graph .
Sub graph of obtained by removing e is
Let be a connected graph.
Suppose is an edge contained in every spanning tree for .
If possible, suppose that the graph obtained by removing e from is connected.
Let be the sub graph of G obtained by removing . Then is connected.
Let be the spanning tree of .
Then is also a spanning tree of G because contains all vertices of except the edge
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started