Chapter 35, Problem 6P

a.

Program Plan Intro

To give an example of a graph with at least4 vertices for which set of maximum weight edges $S_G$ is equal to the maximum weight spanning tree $T_G$ of graph G.

b.

Program Plan Intro

To give an example of a graph with at least4 vertices for which set of maximum weight edges $S_G$ is not equal to the maximum weight spanning tree $T_G$ of graph G.

c.

Program Plan Intro

To prove that $S_G\subseteq T_G$ for any graph G.

d.

Program Plan Intro

To prove that $w\left(S_G\right)\subseteq w\left(T_G\right)/2$ for any graph G.

e.

Program Plan Intro

To give an $O\left(V+E\right)$ -time algorithm to compute a 2-approximation to the maximum spanning tree.