This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: is a light edge crossing the cut .S; V N S/ (by Exercise 23.13). Now consider the edge .x; y/ 2 T that crosses .S; V N S/ . It, too, is a light edge crossing this cut. Since the light edge crossing .S; V N S/ is unique, the edges .u; ±/ and .x; y/ are the same edge. Thus, .u;±/ 2 T . Since we chose .u; ±/ arbitrarily, every edge in T is also in T . Here’s a counterexample for the converse: x y z 1 1 232 Selected Solutions for Chapter 23: Minimum Spanning Trees Here, the graph is its own minimum spanning tree, and so the minimum spanning tree is unique. Consider the cut . f x g ; f y; ´ g / . Both of the edges .x; y/ and .x; ´/ are light edges crossing the cut, and they are both light edges....
View Full
Document
 Spring '10
 .

Click to edit the document details