CS 4349: Algorithms
Spring 2008
Assignment 6

Due: Monday, March 17 (in class)


1. Ex. 22.1-3 (page 530).  Computing the transpose of a graph.

2. Ex. 22.3-9 (page 548).  Printing the types of edges.
   Write two versions of this procedure, one for directed graphs
   and one for undirected graphs.

3. Ex. 22.4-1 (page 551).  Topological ordering of a DAG.
   Show a table that gives for each node all its DFS properties
   (discovery time, finish time, depth-first number, top number,
    parent).

4. Write a DFS algorithm to find the bridges and cut vertices of a
   given undirected, connected graph G=(V,E).  See problem 22-2 (p. 558)
   for a discussion.  Ideas needed to solve this problem have been
   discussed in class.

5. A graph G=(V,E) is bipartite if the vertex set can be partitioned
   into two sets X and Y such that all edges of G connect a vertex
   in X with a vertex in Y.  It can be shown that a graph is bipartite
   if and only if it has no odd length cycles.  Write a breadth-first
   search (BFS) algorithm to test if a graph is bipartite.  Explain the
   correctness of your algorithm.  (See Ex. 22.2-6, p. 539).