Suppose that in a weighted network there is just one edge (call it XY) with the largest

Chapter 7, Problem 50

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QUESTION:

Suppose that in a weighted network there is just one edge (call it XY) with the largest weight. (a) Give an example of a network with more than one MST and such that XY must be in every MST. (b) Give an example of a network with more than one MST and such that XY is in none of the MSTs.

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QUESTION:

Suppose that in a weighted network there is just one edge (call it XY) with the largest weight. (a) Give an example of a network with more than one MST and such that XY must be in every MST. (b) Give an example of a network with more than one MST and such that XY is in none of the MSTs.

ANSWER:

Step 1 of 4

The example of a network with more than one MST such that  must be in every MST is given in the picture below. The edge  is the edge  in this case.

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