2004 F

Answer any six of the following eight questions. Each question is 17 points. (Note that the 7th & 8th answers, if any, in your answering order will NOT count.)

1. Find a Minimum Spanning Tree of the following graph using either Kruskal's or Prim's algorithm and detail your steps.

2. Give an algorithm that determines whether or not a given undirected graph G(V,E) contains a cycle. Your algorithm should run in O(V) time, independent of |E|. Assume that the input graph is represented using adjacency lists.