Angewandte Mathematik Und Informatik Universit at Zu K Oln Minimal Elimination of Planar Graphs

We prove that the problem to get an inclusion minimal elimination ordering can be solved in linear time for planar graphs. The basic structure of the linear time algorithm is as follows. We select a vertex r as maximum and get a rst approximation of a minimal elimination ordering considering a vertex x as smaller than y if x has a larger distance than y from r. Using planarity, one can determine the ll-in edges joining two vertices of the same distance from r almost immediately. The algorithm determines an O(n)-representation of these ll-in edges. To determine the nal ll-in ordering, we use similar techniques as in the general parallel minimal elimination algorithm of 5].