Assignment 5
Chapter 4: 29, 30, Chapter 7: 9, 11, 60
Handout on Red-Black trees: 14.2-5, 14.3-3, 14.3-4
Turn in both of the following:
- Show that if T is a spanning tree for the undirected graph, G, then the
addition of an edge e in E(G) - E(T) creates a unique cycle.
- Show that if any of the edges of this unique cycle is deleted from
E(T) + {e} then the remaining edges form a spanning tree of G.
Hint for 14.2-5: The problem is only concerned with the shape of the tree,
not the contents (i.e., presume it is unlabelled). Use a proof by induction
(on what?) to show that any tree can be transformed into a tree with only
a single branch in which each node is the right child of its parent.