A separator-based method for generating weakly chordal graphs

We propose a scheme for generating a weakly chordal graph on n vertices with m edges. In this method, we first construct a tree and then generate an orthogonal layout (which is a weakly chordal graph on the n vertices) based on this tree. In the next and final step, we insert additional edges to give us a weakly chordal graph on m edges. Our algorithm ensures that the graph remains weakly chordal after each edge is inserted. The time complexity of an insertion query is O(n^3) time and an insertion takes constant time. On the other hand, a generation algorithm based on finding a 2-pair takes O(nm) time using the algorithm of Arikati and Rangan [1].