Arno Rupp and Victoria Zamarra -- Edge Coloring: A Journey Through Understanding 
                                    and Application
  
  Including the general material on graph theory was a good choice because you
  need a lot of the basic definitions to talk about edge-coloring problems.
  However, I think that maybe in your minds, all problems about graphs got 
  associated with edge-coloring, and that is not true.  For instance, the
  "Seven Bridges" problem is historically where the idea of graphs got introduced.
  But it's not about coloring the edges.  It's about finding an "Euler circuit"
  or an "Euler path" in a graph -- a sequence of edges that are incident in 
  pairs and that include all the edges in the graph.  
 
  Along the same lines, there was a (rather serious) confusion regarding the 
  distinction between edge-colorings and vertex-colorings in graphs in your presentation 
  that I tried to point out to you in my questions.  However, I see that the 
  misunderstanding has partly persisted in the paper:  See comment 1 below.  This 
  is not really a big part of what you are saying, but it is not correct either. 
  
  Technical point -- when you are making a reference to a bibliography entry
  that is a book or an article (where you can identify a page containing
  the information you are using), then you should really provide that as well.
  That is, in addition to just citing something like [4] in the text, you 
  should say something like ([4], p. 230).  

  Specific Comments:

  1)  Pages 4 - 5:  It is fine that you include a discussion of the 4-Color Map
      Theorem here because it is definitely one of the important and interesting
      results about graphs.  HOWEVER, I don't think you have (quite) undertood that
      that theorem is NOT a theorem about EDGE-coloring of graphs.  It's a theorem
      about VERTEX-coloring.  The idea is that a map is turned into a planar graph
      by replacing each country or region shown in the map by a VERTEX, and 
      edges between pairs of those vertices when the two countries or regions
      share a boundary.  The degree of a vertex in one of those graphs can be 
      any positive integer (or even zero if the country or region is an island 
      not sharing a boundary with any other country or region).  The question 
      is whether you can color the countries with four colors in such a way that 
      no pair of countries or regions sharing a boundary are colored the same.  
      This means that the colors apply to the VERTICES (NOT the edges) and the 
      condition is that no two vertices connected by an edge share the same color.  
      The theorems about degrees of vertices that you are stating later for 
      EDGE-colorings don't apply, and cannot apply because, as mentioned above, 
      the degrees of vertices in these graphs can be much larger than 4.  Vizing's 
      Theorem would say, for instance, that you need at least the maximum vertex 
      degree number of colors for an EDGE-coloring, and that certainly doesn't fit 
      with the idea that you can color the map using 4 colors at most!

  2)  Page 7 -- It would be better to say that a complete graph K_n is a graph
      on n vertices such that every pair of distinct vertices is connected by 
      an edge.  That is if V = {1,2,3,4}, for instance, then E = {{1,2},{1,3},{1,4},
      {2,3},{2,4},{3,4}}.  Note that K_n has (n choose 2) edges.  

  3)  Page 12 -- In the solution for problem 5 from Bryant's book, note that 
      the edges of each color give one way to pair off the boys and the girls
      in "friendly pairs."  Since there are d colors of edges, then, you get
      d different pairings.  (You didn't say that, but I think you were thinking
      it!)

   Final Project Grade Computation 
 
   Bibliography:  10/10  

   Paper:         54/60

   Presentation:  29/30

   Total:         93/100