Total homework received: 39
Max: 7.8
Min: 2.9
Average: 5.88
Median: 6.1
 
Comments:

B. Quite a number of students forgot that for (undirected) graphs,
cycles are defined to have at least 3 arcs.

D.  Some people wrote that if u_i = u_j for some i<j, then the part of
the path from u_i to u_j forms a cycle.  This is false in general,
as there can be other repeating vertices in between.  What is true 
is that this part of the path forms a closed path.  Also, some people
wrote that "removing" this part of the path would result in a simple path, which   
is false in general.  

E. Few forgot to prove one of the directions. For many,
the presentation on the direction that the graph having a path
through all vertices implies the graph is connected is not written
clearly and explicitly.

F. Some students forgot to specify which path they are considering in
part (a) after drawing a nice digraph.

G. Some students assumed i to be 1 in part (a) and (b). Few assumed
ui=ui+4 for all i.

H. For those who attempted this one, quite a number of them fail to
specify clearly how the arcs are constructed. Many overlook the need
to construct a connected graph to work with.