So a coloring of G+e with the smallest possible number of colors is a best coloring of G in which v and w have different colors, that is, χ(G+e) is the smallest number of colors...So a coloring of G+e with the smallest possible number of colors is a best coloring of G in which v and w have different colors, that is, χ(G+e) is the smallest number of colors needed to color G so that v and w have different colors.
