In summary, therefore, every graph G ∈ S can be produced by a number of cut-and-join crossover steps not exceeding twice the number of edges between heavy vertices starting from building blocks in T 0 . In each step we can produce the graph G by keeping in the population at most one graph G * with which the component under construction will eventually be recombined, the component G 1 currently under construction, a path P that will eventually be recombined with G 1 and the reservoir set T 0 of building block that are required either to be composed into P or directly inserted into G 1 by recombination. Hence a population of size |T 0 | + 3 is sufficient.