This construction started from the graph with a single vertex say  and inductively constructed  from  as follows: let  have  vertices, then take a set  of  vertices and for each subset  of  of size  add a disjoint copy of  and join it to  with a matching.
Starting with a single vertex, this construction builds up by adding copies of a vertex to existing sets, connecting them with matches. The process is done inductively, starting with one vertex and then expanding based on the size of subsets.