1997•Calhoun: The Naval Postgraduate School Institutional Archive (Naval Postgraduate School)Requires access
A Partial Ordering of the Chordal Graphs.
Craig W. Rasmussen, Thomas. Carroll
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Abstract
The chordal graphs have been well-studied because of their desirable algorithmic characteristics. Many problems that are intractable in the general case are solvable by fast algorithms in the chordal case. We show that the chordal graphs are partially ordered under edge set inclusion, and describe algorithms for bidirectional traversal of maximal chains in the corresponding cover graph. We also describe the embedding of several subclasses of the chordal graphs as subposets of the chordal poset, and suggest application of these order relations to the design of improved heuristics for obtaining approximate solutions to problems on arbitrary graphs.