Since the search space must remain independent of the representation of the graph, it can only depend on some properties that are common to all its representations. Such a property is called a topological invariant. The only invariant used so far is whether there exists a vertex whose outgoing edges are not all coplanar, but many other invariants exist, such as the three used by ToposPro . These properties can be used to considerably reduce the search space by separating vertices according to them.