  This paper presents new results about the optimization based generation of
chemical reaction networks (CRNs) of higher deficiency. Firstly, it is shown
that the graph structure of the realization containing the maximal number of
reactions is unique if the set of possible complexes is fixed. Secondly, a
mixed integer programming based numerical procedure is given for computing a
realization containing the minimal/maximal number of complexes. Moreover, the
linear inequalities corresponding to full reversibility of the CRN realization
are also described. The theoretical results are illustrated on meaningful
examples.
