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# HW4 - CSE 830 Design and Theory of Algorithms Homework#4...

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CSE 830: Design and Theory of Algorithms Homework #4 Due Monday, March 17 th 2008, 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 e whose removal disconnects the graph is called a bridge . Must every bridge e be 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 undiscovered node is marked discovered when it is first encountered, and marked completely-explored when 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 v that has the properties described. a. At some point during a breadth-first search, Θ ( n ) are simultaneously in the discovered state.
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