Give careful proofs of each statement, referring to the Graph Notes I and II.1-II.4 below. In your proofs, make sure to:
Start with the hypothesis of the proposition and end with the conclusion.
State and use the definitions of the terms used.
Make a chain of logical deductions from the hypothesis and definitions (possibly using previous results), all the way to the conclusion.
Do not rely on vague sketches: use words and formulas to make sure you have covered every possible case.
Proposition: If T is a tree, then T−e is disconnected for any edge e ∈ T.

Question

Give careful proofs of each statement, referring to the Graph Notes I and II.1-II.4 below. In your proofs, make sure to:
Start with the hypothesis of the proposition and end with the conclusion.
State and use the definitions of the terms used.
Make a chain of logical deductions from the hypothesis and definitions (possibly using previous results), all the way to the conclusion.
Do not rely on vague sketches: use words and formulas to make sure you have covered every possible case.
Proposition: If T is a tree, then T−e is disconnected for any edge e ∈ T.

anonymous · Answer

So...