Explanation Given: T 1 andT 2 are spanning trees of the simple graphGande 1 is an edge inT 1 that is not inT 2 . Proof: Lete 1 = {u, v}. The graph T 2 ∪ { e 1 } contains a (unique) simple circuitCcontaining edgee 1 . NowT 1 − {e 1 } has two components, one of which containsuand the other of which containsv. We travel along the circuitC,starting atuand not using edgee 1 first, until we first reach a vertex in the component ofT 1 − {e 1 } that containsv;obviously we must reach such a vertex eventually, since we eventually reachvitself. The edge we last traversed ise 2

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Author: ROSEN

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Question

Chapter 11.4, Problem 55E

To determine

To prove:

There is an edgee₂ inT₂ that is not inT₁ such thatT₁ remains a spanning tree ife₁ is removed from it ande₂ is added to it, andT₂ remains a spanning tree ife₂ is removed from it ande₁ is added to it.

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Chapter 11.4, Problem 54E

Chapter 11.4, Problem 56E

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Chapter 11 Solutions

DISCRETE MATH

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

Knowledge Booster

To prove: There is an edgee 2 inT 2 that is not inT 1 such thatT 1 remains a spanning tree ife 1 is removed from it ande 2 is added to it, andT 2 remains a spanning tree ife 2 is removed from it ande 1 is added to it.

Solution Summary: The author explains that T 1 and T 2 are spanning trees of the simple graphGande 1 that is not inT 1.

To prove:

There is an edgee₂ inT₂ that is not inT₁ such thatT₁ remains a spanning tree ife₁ is removed from it ande₂ is added to it, andT₂ remains a spanning tree ife₂ is removed from it ande₁ is added to it.

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Chapter 11 Solutions

To prove: There is an edgee 2 inT 2 that is not inT 1 such thatT 1 remains a spanning tree ife 1 is removed from it ande 2 is added to it, andT 2 remains a spanning tree ife 2 is removed from it ande 1 is added to it.

Solution Summary: The author explains that T 1 and T 2 are spanning trees of the simple graphGande 1 that is not inT 1.

To prove: There is an edgee2 inT2 that is not inT1 such thatT1 remains a spanning tree ife1 is removed from it ande2 is added to it, andT2 remains a spanning tree ife2 is removed from it ande1 is added to it.

Want to see the full answer?

Chapter 11 Solutions

To prove:

There is an edgee₂ inT₂ that is not inT₁ such thatT₁ remains a spanning tree ife₁ is removed from it ande₂ is added to it, andT₂ remains a spanning tree ife₂ is removed from it ande₁ is added to it.