4.a
We want Prim's algorithm, or something like that, to find the minimum
spanning tree (mst) of a graph.

We start with a vertex, any vertex, so 1 is fine. 
During the algorithm we maintain two set: U the set of vertices on
the mst, and V-U, the set of vertices not on the mst.
Initially U is {1}

In each iteration of the algorithm we find a vertex v, such that 
v is in V-U, and for some u in U, the cost of edge (u v) is a
minimum. That is, edge (u v) is the lowest cost edge that joins some 
vertex in U with some vertex in V-U.

We add this edge to the set MST (minimum spanning tree), remove v
from V-U, and add v to U.

We terminate when V-U is empty, or there is no edge between U and V-U.

A scheme solution is fine if they do that.


4.b
The algorithm uses 3 sets, U, U-V and MST, so here goes


             U              U-V          MST
0           {1}           {2,3,4,5,6}    {}
1           {1,3}         {2,4,5,6}      {(1 3)}
2           {1,3,4}       {2,5,6}        {(1 3),(3 4)}
3           {1,3,4,6}     {2,5}          {(1 3),(3 4),(4 6)}
4           {1,3,4,6,2}   {5}            {(1 3),(3 4),(4 6)(3 2)}
5           {1,3,4,6,2,5} {}             {(1 3),(3 4),(4 6),(3 2),(2 5)}