Abstract
Let G = ( V, E) be a finite undirected connected graph. We show that there is a common perfect elimination ordering of all powers of G which represent chordal graphs. Consequently, if G and all of its powers are chordal then all these graphs admit a common perfect elimination ordering. Such an ordering can be computed in O(| V| · | E|) time using a generalization of the Tarjan and Yannakakis' Maximum Cardinality Search.
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