to the order defined
by the input order. At each vertex the algorithm marks the colors of
the adjacent vertices, and then chooses the smallest unmarked color
for the color of the current vertex. If all of the colors are already
marked, a new color is created.  A color is considered marked if its
mark number is equal to the current vertex number. This saves the
trouble of having to reset the marks for each vertex. The
effectiveness of this algorithm is highly dependent on the input
vertex order. There are se