CSE 830: Design and Theory of Algorithms Homework #4 Due Monday, March 17th2008, 3pm 1.Is the path between a pair of vertices in a minimum spanning tree necessarily the shortest path between the two vertices in the full graph? Give a proof or a counter-example.2.Suppose G is a connected undirected graph. An edge ewhose removal disconnects the graph is called a bridge. Must every bridge ebe an edge in a depth-first search tree of G, or can e be a back edge? Give a proof or a counter-example. 3.In breadth-first and depth-first search, an undiscoverednode is marked discoveredwhen it is first encountered, and marked completely-exploredwhen it has been fully searched. At any given moment, various numbers of nodes can be in any of these states. In all cases below, describe a graph on n vertices with a particular starting vertex vthat has the properties described. a.At some point during a breadth-first search, Θ(n) are simultaneously in the discovered state.
This is the end of the preview.
access the rest of the document.