A relative Nielsen number
N(f;X,A) for a selfmap f : (X,A) → (X,A) of a pair of spaces is introduced which
shares such properties with the Nielsen number N(f) as homotopy invariance and
homotopy type invariance. As N(f;X,A) ≥ N(f) = N(f;X,∅) , the relative Nielsen
number is in the case A≠∅ a better lower bound than N(f) for the minimum
number MF[f;X,A] of fixed points of all maps in the homotopy class of f.
Conditions for a compact polyhedral pair (X,A) are given which ensure that the
relative Nielsen number is in fact the best possible lower bound, i.e. that
N(f;X,A) = MF[f;X,A].
