Answer
Proving that the reverse-delete algorithm always produces a minimum spanning tree when given as input a weighted
graph with distinct edge weights.
Work Step by Step
The reverse-delete algorithm must terminate and produce a spanning
tree,
- because the algorithm never disconnects the graph
and upon termination there can be no more simple circuits.
-The edge deleted at each stage of the algorithm must have
been the edge of maximum weight in whatever circuits it was
a part of.
-Therefore by Exercise 33 it cannot be in any minimum
spanning tree.
-- Since only edges that could not have been
in any minimum spanning tree have been deleted, the result
must be a minimum spanning tree.
