The index of coincidence Nielsen classes of maps between surfaces

For a given pair of closed orientable surfaces Sh, Sg and given integers d1, d2, one would like to find bounds for the index of the Nielsen coincidence classes among all possible pairs of maps (f1,f2) :Sh→Sg where |deg(f1)|=d1 and |deg(f2)|=d2. We show that these bounds are infinite when h>g=1, or when h⩾g>1 and both di<(h−1)/(g−1). We calculate these bounds when h=g and d2=1. We also consider the similar question for the root case, which is simpler, and we solve it completely. Few results are given when di=(h−1)/(g−1) for either i=1 or i=2.