89. The edge-coloring number of a graph is the minimum number of colors needed to color the edges of so that edges sharing a common vertex get different colors. Determine the edge-coloring number for each of the graphs in Exercise 77. Can you make a conjecture about the value of the minimum number of colors needed to color the edges of any graph?
89.
Graph in: (a) 8 (b) 5 (c) 6 (d) 4 (e) 3 (f) 4; the minimum is either the largest valence of any vertex or 1 more than the largest valence.