A vertex incremental approach for maintaining chordality

For a chordal graph G = (V, E), we study the problem of whether a new vertex u V and a given set of edges between u and vertices in V can be added to G so that the resulting graph remains chordal. We show how to resolve this efficiently, and at the same time, if the answer is no, specify a maximal subset of the proposed edges that can be added along with u, or conversely, a minimal set of extra edges that can be added in addition to the given set, so that the resulting graph is chordal. In order to do this, we give a new characterization of chordal graphs and, for each potential new edge uv, a characterization of the set of edges incident to u that also must be added to G along with uv. We propose a data structure that can compute and add each such set in O(n) time. Based on these results, we present an algorithm that computes both a minimal triangulation and a maximal chordal subgraph of an arbitrary input graph in O(nm) time, using a totally new vertex incremental approach. In cont...

• Type: Journal
• Year: 2006
• Where: DM
• Authors: Anne Berry, Pinar Heggernes, Yngve Villanger
• Keywords: Chordal, Chordal Graphs, DM 2006, Maximal Subset