Before revision:  A path-addition adds a long path between any two vertices to a graph . An s-subdivision replaces an edge by a path of length s, and a node-to-circle expansion substitutes a vertex by a 3-regular circle, so that each vertex of the circle inherits an edge incident to the original vertex. We introduce universality for an operation and a graph class, so the every graph has an image in the graph class. In particular, we show the fan22 crossing free graphs are universal for 2-subdivision and for node-to-circle 3 expansion  .
After revision:  A path-addition adds a long path between any two vertices to a graph . An s-subdivision replaces an edge by a path of length s, and path-addition operations to distinguish all these graph classes. In particular, we show that the 2-subdivision and for node-to-circle 3 expansion .