Explanation Given: A weighted graph is with distinct edge weights. Proof: The reverse-delete algorithm proceeds by successively deleting edges of maximum weight from a connected graph as long as doing so does not disconnect the graph. The reverse-delete algorithm should terminate and create a spanning tree. The algorithm never separates the graph and upon end there can be no more simple circuits. The edge removed at each stage of the algorithm must have been the edge of maximum weight in circuits it fit. Let C be any cycle in G and the edge e = ( v , w ) be the most important edge in C

DISCRETE MATHEMATICS LOOSELEAF W/CONNECT

8th Edition

ISBN: 9781264309405

Author: ROSEN

Publisher: MCG

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Chapter 11.5, Problem 35E

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The reverse-delete algorithm always produces a minimum spanning tree when given as input a weighted graph with distinct edge weights.

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Chapter 11.5, Problem 34E

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Chapter 11 Solutions

DISCRETE MATHEMATICS LOOSELEAF W/CONNECT

Ch. 11.1 - Prob. 1E Ch. 11.1 - Vhich of these graphs are trees?Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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The reverse-delete algorithm always produces a minimum spanning tree when given as input a weighted graph with distinct edge weights.

Solution Summary: The author explains that the reverse-delete algorithm always produces a minimum spanning tree when given an input graph with distinct edge weights.

To show: The reverse-delete algorithm always produces a minimum spanning tree when given as input a weighted graph with distinct edge weights.

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Chapter 11 Solutions

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The reverse-delete algorithm always produces a minimum spanning tree when given as input a weighted graph with distinct edge weights.