10/22   http://www.csua.berkeley.edu/~ilyas/problems/coloring
        If you know the answer, please e-mail me, but don't give it
        away here. -- ilyas
        \_ Don't ask us to do your homework for you, mr. cheaty-pants!
           \_ I solved this already.  I also received one solution from
              someone on soda. -- ilyas
        \_ "Small" as in fewest vertices or "small" as in some notion
           the graph even need to be planar?
              sufficient for planar graphs.  -- ilyas
           of Euclidean diameter or something like that? Also, an edge
           can exist if and only if the distance is exactly 1? And can
           edges intersect (provided the graph is still planar)? Hell, does
           the graph even need to be planar? Can 2 vertices be assigned
           to the same position in the plane?
           \_ Small in a sense of fewest vertices.  An edge can exist
              if and only if the distance is exactly 1.  Edges can intersect,
              the graph does not need to be planar.  Two distinct vertices
              cannot occupy the same position on the plane. -- ilyas
        \_ what's a 4-coloring? Does this question need more explaination?
           \_ A 4-coloring is an assignment of colors to vertices, such
              that no more than 4 colors are used, and no two adjacent
              vertices share a color.  The terminology I am using comes
              from a related problem asking whether 4 colors are always
              sufficient for planar graphs (which was solved by Appel
              and Haken with the aid of a computer in 1976). -- ilyas