Homework 4 Solutions

# Homework 4 Solutions - CS180 Spring 2009 Homework 4...

This preview shows page 1. Sign up to view the full content.

CS180 Spring 2009 Homework 4 Solutions 4.9 (a) False. Counter-example: . The set { AB, BC, BD } is a valid minimum-bottleneck spanning tree but it is not a valid minimum spanning tree. (b) True. Suppose T is a minimum spanning tree of G , and T 0 is a spanning tree with a lighter bottleneck edge. Add e max (the edge with maximal weight) in T to T 0 . T 0 now has a cycle, and by the cut property, e max does not belong to any minimum spanning tree, and thus cannot have been in T . 4.11 Label the edges arbitrarily from 1 to m , with the property that the last n - 1 belong to the desired T . Let δ be the minimum difference of two non-equal edge weights. For each edge i , e i e i - n 3 . Now all edge weights are distinct, and the sorted order is the same as the originals. T is now the one with the most total weight reduction, and is now the unique MST of G , so Kruskal’s will return it. 4.29 First, remove from the list any vertices with degree d i = 0; these are isolated vertices in the graph. Otherwise, all d i are positive, and sort so that d 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern