We note that an analogous result can also be obtained for variants of graph construction in Thm. 3. To see this, it suffices to construct graphs containing the base elements and add them to the reservoir. As an alternative, it also suffices to consider 2-cuts and allow the opening or closing of a bond in exchange for a K 2 , i.e., edge-swaps, as a mutation operator. The strong connectedness of the search space graph has important consequences for the performance of a GA built upon the cut-and-join cross-over operations: it ensures that any desired molecule can be reached with a non-zero probability from any starting point. This is true as long as there is a finite probability that the required base set or the repertoire set remains in the population for any finite number of steps. The reason is simply that the construction pathways described above are finite, and each step is realized with a finite probability.