A separator-based method for generating weakly chordal graphs

We propose a scheme for generating a weakly chordal graph on [Formula: see text] vertices with [Formula: see text] edges. In this method, we first construct a tree and then generate an orthogonal layout (which is a weakly chordal graph on the [Formula: see text] vertices) based on this tree. We then insert additional edges, if needed, for a total of [Formula: see text] edges. Our algorithm ensures that the graph remains weakly chordal after each edge is inserted. The time complexity of an insertion query is [Formula: see text], where [Formula: see text] and [Formula: see text] are the degrees of the vertices [Formula: see text] and [Formula: see text] we want to join with an edge and an insertion takes constant time. The advantages of this method are that it uses very simple data structures and exploits the basic structural properties of a weakly chordal graph.