  Formal models for gene assembly in ciliates have been developed, in
particular the string pointer reduction system (SPRS) and the graph pointer
reduction system (GPRS). The reduction graph is a valuable tool within the
SPRS, revealing much information about how gene assembly is performed for a
given gene. The GPRS is more abstract than the SPRS and not all information
present in the SPRS is retained in the GPRS. As a consequence the reduction
graph cannot be defined for the GPRS in general, but we show that it can be
defined (in an equivalent manner as defined for the SPRS) if we restrict
ourselves to so-called realistic overlap graphs. Fortunately, only these graphs
correspond to genes occurring in nature. Defining the reduction graph within
the GPRS allows one to carry over several results within the SPRS that rely on
the reduction graph.
