Good morning/afternoon everyone. I need some help with this one. Algorithm Design, Jon Kleinberg, Eva Tardos,...
Good morning/afternoon everyone. I need some help with this one.
Algorithm Design, Jon Kleinberg, Eva Tardos, Chapter 4, Exercise 8
Q: Suppose you are given a connected graph G, with edge costs that are all distinct. Prove that G has a unique minimum spanning tree.
Homework Answers
Solution:-
We will prove this by contradiction.
- Suppose T and T' are two distinct minimum spanning trees.
- Then there exist an edge that is in T' and not in T.
- Then add this edge to T which will give you a cycle.
- Let us consider the maximum weight edge in this cycle.
- The cycle property is violated as this edge appears in either T or T'.
Hence proved.
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Good morning/afternoon everyone. I need some help with this
one.
Algorithm Design, Jon Kleinberg, Eva Tardos,...
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